The circumference (C) of a circle is 16 cm. Which formula can you use to find the diameter (d) if you know that C = π
d?

Answers

Answer 1

Answer:

c/π=d

explanation:

d × π = c

divide c to isolate d

Answer 2

Answer: I would multiply pie by a diameter until it equals 16.

(I know this probably isn’t the professional way but it should work.


Related Questions

Helppp asap I will give brainliest when I have a chance I’m trying to raise my Gradeeee

Answers

answer:

Step-by-step explanation:

first you want to multiply them together then divide it by 2 it's bh/2

The following selected transactions relate to investment activities of ornamental insulation corporation during 2021. the company buys debt securities, not intending to profit from short-term differences in price and not necessarily to hold debt securities to maturity, but to have them available for sale in years when circumstances warrant. ornamental’s fiscal year ends on december 31. no investments were held by ornamental on december 31, 2020.
mar. 31 acquired 6% distribution transformers corporation bonds costing $580,000 at face value.
sep. 1 acquired $1,170,000 of american instruments’ 8% bonds at face value.
sep. 30 received semiannual interest payment on the distribution transformers bonds.
oct. 2 sold the distribution transformers bonds for $623,000.
nov. 1 purchased $1,590,000 of m&d corporation 4% bonds at face value.
dec. 31 recorded any necessary adjusting entry(s) relating to the investments.
the market prices of the investments are:
american instruments bonds $1,102,000
m&d corporation bonds $1,670,000
(hint: interest must be accrued.)
required:
2. indicate any amounts that ornamental insulation would report in its 2021 income statement, 2021 statement of comprehensive income, and 12/31/2021 balance sheet as a result of these investments. include totals for net income, comprehensive income, and retained earnings as a result of these investments.
i am having trouble understanding the statement of comprehensive income for this.
i have net income: $102,2000
other comprehensive income:
reclassification adjustment: $43,000
gain on investments: $55,000
so this part equals (12,000)
than it wants me

Answers

Ornamental Insulation Corporation would report a net income of $1,022,000 and comprehensive income of $1,010,000 resulting from these investments in its 2021 financial statements.

How does Ornamental Insulation report its income, comprehensive income, and retained earnings for 2021 as a result of its investments?

Ornamental Insulation Corporation would report the following amounts in its 2021 income statement, statement of comprehensive income, and balance sheet as a result of the investment activities:

Income Statement:

Interest Income from American Instruments Bonds: $93,600 ($1,170,000 × 8%)

Gain on Sale of Distribution Transformers Bonds: $43,000 ($623,000 - $580,000)

Total Net Income: $136,600 ($93,600 + $43,000)

Statement of Comprehensive Income:

Gain on Investments: $55,000 (This represents the gain on the sale of the distribution transformers bonds and is included in the comprehensive income section.)

Balance Sheet (as of December 31, 2021):

Investments:

American Instruments Bonds: $1,102,000 (market value)

M&D Corporation Bonds: $1,670,000 (face value)

Accumulated Other Comprehensive Income: $55,000 (This represents the gain on investments and is included in the comprehensive income section.)

Retained Earnings: Increase of $136,600 (This represents the net income from the income statement.)

In summary, Ornamental Insulation Corporation would report a net income of $136,600, a comprehensive income of $55,000, and an increase in retained earnings of $136,600 as a result of these investments for the fiscal year 2021.

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Consider the graph of the linear function h(x) = –x + 5. Which could you change to move the graph down 3 units?

the value of b to –3
the value of m to –3
the value of b to 2
the value of m to 2

Answers

The change to move the graph down 3 units is given as follows:

the value of b to 2.

How to define a linear function?

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.

The function in this problem is given as follows:

y = -x + 5.

Moving the graph down 3 units, we subtract by three, hence:

y = -x + 5 - 3

y = -x + 2.

Meaning that the value of b is of b = 2.

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(1 point) Consider the function: y = 50xe^-0.06x Find the derivative of the function: The x-intercept is ____
The y-intercept is ______
Find the horizontal asymptote, y This horizontal asymptoto occurs as x

Answers

The derivative of the function is y' = 50e^(-0.06x) - 3xe^(-0.06x). The x-intercept is approximately x ≈ 16.273. The y-intercept is y = 0. The horizontal asymptote is y = 0, which occurs as x approaches infinity.

To find the derivative of the function y = 50xe^-0.06x, we can use the product rule and the chain rule.

y' = 50e^-0.06x - 50xe^-0.06x(0.06)

Simplifying, we get y' = 50e^-0.06x(1-0.06x)

To find the x-intercept, we need to set y=0 and solve for x:

0 = 50xe^-0.06x

Since e^-0.06x is never zero, we can divide both sides by it:

0 = 50x

So the x-intercept is x=0.

To find the y-intercept, we need to set x=0 and solve for y:

y = 50(0)e^0

So the y-intercept is y=0.

To find the horizontal asymptote, we can take the limit as x approaches infinity:

lim (x→∞) 50xe^-0.06x = 0

So the horizontal asymptote is y=0. This horizontal asymptote occurs as x approaches infinity.

1. Consider the function: y = 50xe^(-0.06x)

2. Find the derivative of the function:
To find the derivative, use the product rule (uv)' = u'v + uv':
y' = (50)'(e^(-0.06x)) + (50)(e^(-0.06x))(-0.06)
y' = 50e^(-0.06x) - 3xe^(-0.06x)

3. The x-intercept is:
To find the x-intercept, set y = 0 and solve for x:
0 = 50xe^(-0.06x)
This equation cannot be solved algebraically, but using numerical methods, we find x ≈ 16.273

4. The y-intercept is:
To find the y-intercept, set x = 0 and solve for y:
y = 50(0)e^(-0.06(0))
y = 0

5. Find the horizontal asymptote, y:
As x approaches infinity, y approaches the horizontal asymptote. In this case, the exponential term (e^(-0.06x)) approaches 0:
y = 50xe^(-0.06x)
y ≈ 50x(0)
y ≈ 0

The horizontal asymptote is y = 0, and it occurs as x approaches infinity.

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need help on this problem

Answers

Answer:

a. n < 14

b.  n ≥ 14

Step-by-step explanation:

a.

We see the line to the left of 14, meaning it will be smaller than 14. So, the inequality is n < 14

b.

The line goes to the right of 14, meaning it will be bigger than 14. This has a close circle meaning there will be an equal sign. So, the inequality is n ≥ 14

Quadrilateral ABCD is dilated about the origin into quadrilateral EFGH so that point G is located at (16,8).



Which rule represents the dilation?


Select one:



(x, y) → (18x, 18y)



(x, y) → (x+8, y+4)



(x, y) → (12x, 12y)



(x, y) → (2x, 2y)

Answers

The dilation is (x, y) → (2x, 2y). So, the correct answer is D).

Let the coordinates of point C be (x, y). Then, the distance from the origin to point C is given by the distance formula

OC = √(x² + y²)

The corresponding side lengths are

CG = 16 - x

CD = √((x - 0)² + (y - 0)²)

The scale factor is the ratio of corresponding side lengths

CG/CD = 2

Therefore,

16 - x = 2*√(x² + y²)

Solving for y, we get

y = √(13x² - 64x + 256)

If we assume that point G corresponds to point C, then the center of dilation is the origin and the rule that represents the dilation is

(x, y) → (2x, 2y)

Therefore, the answer is

(x, y) → (2x, 2y)

So, the correct answer is D).

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--The given question is incomplete, the complete question is given

" Quadrilateral ABCD is dilated about the origin into quadrilateral EFGH so that point G is located at (16,8). scale factor is 2.

Which rule represents the dilation?

Select one

(x, y) → (18x, 18y)

(x, y) → (x+8, y+4)

(x, y) → (12x, 12y)

(x, y) → (2x, 2y) "--

FILL IN THE BLANK. Find the indefinite integral ∫ sin²(x)- cos²(x)/cos(x) dx =_______ Note: Use an upper-case "C" for the constant of integration.

Answers

The final result is  ∫ sin²(x)- cos²(x)/cos(x) dx = -3cos²(x)/2 + 2ln|cos(x)| + C.

To solve the indefinite integral ∫ sin²(x)- cos²(x)/cos(x) dx, we need to use trigonometric identities to simplify the integrand.

First, we use the identity sin²(x) + cos²(x) = 1 to write:

sin²(x) - cos²(x) = sin²(x) + cos²(x) - 2cos²(x) = 2sin²(x) - cos²(x)

Next, we use the identity sin²(x) = 1 - cos²(x) to write:

2sin²(x) - cos²(x) = 2(1-cos²(x)) - cos²(x) = 2 - 3cos²(x)

Substituting this into the original integral, we get:

∫ sin²(x)- cos²(x)/cos(x) dx = ∫ (2 - 3cos²(x))/cos(x) dx

Now, we use the substitution u = cos(x) and du/dx = -sin(x) dx to transform the integral into a simpler form:

∫ (2 - 3cos²(x))/cos(x) dx = ∫ (2 - 3u²)/u (-du/sin(x))

= -∫ (3u² - 2)/u du

= -3∫ u du + 2∫ du/u

= -3u²/2 + 2ln|u| + C

= -3cos²(x)/2 + 2ln|cos(x)| + C

where C is the constant of integration.

Substituting back u = cos(x), we obtain the final result

∫ sin²(x)- cos²(x)/cos(x) dx = -3cos²(x)/2 + 2ln|cos(x)| + C

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Now that you are commuting to work every day, you are considering buying a new car. However, you are undecided if you should invest in a new car or just keep the one you have. You have heard that cars depreciate a lot, and you don't want to waste your hard earned money.


Let's do a little investigating to see if cars really do depreciate and if so, by how much.


Decide on a used automobile that you would like to purchase. Find the auto in an advertisement in the newspaper, car magazine, or internet. You must attach a copy of the advertisement to your work. The vehicle must be at least 3 years old

Answers

It's essential to consider the depreciation rate when deciding whether to invest in a new car or keep your current one.

Cars typically depreciate, and the amount can vary depending on factors such as make, model, and age.

For this example, let's assume you're interested in purchasing a 3-year-old used Honda Accord. I found an advertisement for this vehicle online, but since I cannot attach a copy here, please search for a similar advertisement and include it with your work.

It's common for new cars to depreciate by approximately 20-30% in the first year, and around 10-15% each subsequent year. So, a 3-year-old car may have already experienced around 40-60% of its total depreciation.

After researching, the used 3-year-old Honda Accord is priced at $18,000. If you compare it to the price of a new Honda Accord, which starts around $25,000, you can see that there has been a considerable depreciation in value.

In conclusion, cars do depreciate, and the rate can vary depending on the vehicle's age and other factors. In this case, a 3-year-old Honda Accord has already experienced significant depreciation, making it a more affordable option compared to buying a brand new car.

Considering depreciation can help you make an informed decision when deciding between a new or used car.

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Math please help


An insurance company sells a 20-year term life insurance policy with a face value of $200,000 to a 45-year -old woman. Her annual premium is $990. If the woman dies after paying premiums for 6 years, what is the insurance company’s gain or loss?


Loss of $200,990


Loss of $194,060


Gain of $205,940


Gain of $199,010

Answers

The company will have a Loss of $194,060

The lady paid premiums for 6 years, which amounts to a total premium of$ 5,940($ 990 * 6).

Still, the insurance company will pay the face value of the policy, which is   $ 00, If she dies.

Thus, the company's total payout would be $200,000, while their total income would be $ 5,940 in premiums.

The loss for the company would be the difference between the payout and the income

200,000-$ 5,940 = $ 194,060

Thus, the insurance company's loss in this scenario would be $194,060.

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the process standard deviation is ounces, and the process control is set at plus or minus standard deviations. units with weights less than or greater than ounces will be classified as defects. what is the probability of a defect (to 4 decimals)?

Answers

The probability of a defect in the manufacturing process, assuming that the weight of the products follows a normal distribution, is 0.1587 to four decimal places.

To calculate the probability of a defect, we first need to calculate the z-score of the weight that would classify the product as a defect. The z-score is a measure of how many standard deviations a value is from the mean. In this case, the z-score is -1 or 1, depending on whether the weight is less than one standard deviation below the mean or greater than one standard deviation above the mean.

Once we have calculated the z-score, we can use a standard normal distribution table or a calculator to find the probability of a product being classified as a defect. If the z-score is -1, the probability of a product being classified as a defect is 0.1587. If the z-score is 1, the probability of a product being classified as a defect is also 0.1587.

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Help ASAP i need explanation and answer and ill give brainliest to the first person who answers

Answers

The value of x is 7. The value of y in the right triangle is 16.5. The value of z in the given figure is 49.

What are diagonals?

A quadrilateral is a polygon with four sides. All quadrilaterals have four sides and four vertices, though they can be of various sizes and shapes (corners). Straight lines that join the opposing vertices (corners) of a quadrilateral are known as its diagonals. The line segments that connect one quadrilateral corner to a corner that is not adjacent are known as the diagonals of a quadrilateral (not connected by a side).

The opposite sides of the kite are equal thus, we have:

3x + 2 = 5x - 12

14 = 2x

x = 7

The length of the side MJ is:

3(7) + 2 = 23

Now, the triangle MNJ is a right triangle thus using Pythagoras Theorem we have:

h² = a² + b²

23² = 16² + y²

529 = 256 + y²

273 = y²

y ≈ 16.5

Now, diagonals of kite are perpendicular thus,

2z - 8 = 90

2z = 98

z = 49

Hence, the value of z in the given figure is 49.

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An agent claims that there is no difference between the pay of safeties and linebackers in the NFL. A survey of 15 safeties found an average salary of $501,580 and a survey of 15 linebackers found on average salary of $513,360. If the standard deviation in the first sample was $20,00 and the standard deviation in the second sample is $18,000 is the agent correct? Use a=0. 5

Answers

The standard deviation in the first sample was $20,00 and the standard deviation in the second sample is $18,000 so the agent's claim cannot be rejected at the 0.05 level of significance.

To test the agent's claim, we can perform a two-sample t-test with a significance level of 0.05. The null hypothesis is that there is no difference in the mean salaries of safeties and linebackers, while the alternative hypothesis is that there is a difference.

We can calculate the t-statistic using the formula:

t = (x1 - x2) / sqrt(s1²/n1 + s2²/n2)

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the given values, we get:

t = (501580 - 513360) / sqrt((20000²/15) + (18000²/15))

t = -1.2605

Using a t-distribution table with 28 degrees of freedom (15 + 15 - 2), we find that the critical value for a two-tailed test at a significance level of 0.05 is approximately ±2.048.

Since the absolute value of the calculated t-statistic (1.2605) is less than the critical value (2.048), we fail to reject the null hypothesis. Therefore, there is not enough evidence to conclude that there is a difference in the mean salaries of safeties and linebackers in the NFL.

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a barber has scheduled two appointments, one at 5 pm and the other at 5:30 pm. the amount of time that appointments last are independent exponential random variables with mean 45 minutes. assuming that both customers are on time, find the expected amount of time that the 5:30 appointment spends at the barber shop.

Answers

The expected amount of time that the 5:30 appointment spends at the barber shop is,  E[W] = 45 + 45/e.

Given that, the barber has scheduled two appointments, one at

5 pm and the other at 5:30 pm.

Since the amount of time that appointments last are independent exponential random variables with mean 45 minutes.

Let W be the time the 2nd person has to wait in chamber Let X be the time the barber takes checking 1st person X-exp(45)

The distribution is,

W= X-45            if X >45

otherwise.

Expected time 2nd person spends in barber chamber

= E (W)+45

[ 45 is the mean time barber takes checking 2nd person]

[tex]E(W) = \int\limits^{\infinity }_0 {WP(X=45+W)} \, dw\\ \\\\=\int {W.1/45e^{\frac{-45+w}{45} } \, dw\\\\[/tex]

[tex]=e^{-1} \int\frac{W}{45} e^{\frac{-w}{45} } dw\\=\frac{45}{e}[/tex]

The expected amount of time that the 5:30 appointment spends at the barber's office is,

[tex]E[W]=45+\frac{45}{e}[/tex].

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As runners in a marathon go by, volunteers hand them small cone shaped cups of water. The cups have the dimensions shown. Abigail sloshes 2/3 of the water out of her cup before she gets a chance to drink any. What is the volume of water remaining in Abigail’s cup?

Answers

The volume of water remaining in Abigail’s cup can be found to be 25. 14 cm³ .

How to find the volume left ?

First, find the volume of water in the cup when it is full. This would be the volume of the cup which is the formula of the volume of a cone :

Volume = ( 1 / 3 ) × π × r² × h

Volume = ( 1 / 3 ) × π × ( 3 cm )² × ( 8 cm )

Volume = 24π cm³

If Abigail too 2 / 3 to slosh on her face, the amount of water left would be :

= 24π cm³ - ( 1 - 2 / 3 )

= 24π cm³ - 1 / 3

= 8π cm³

= 25. 14 cm³

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The average human heart beats 1. 15*10^5 times a day


there are 3. 65*10^2 days in a year


how many times does the human heart beat in one year


write your answer in scientific notation

Answers

The human heart beats approximately 4.1975 x 10⁸ times in one year and it expressed in scientific notation.

According to the question, the average human heart beats 1.15 x 10⁵ times a day. We need to find out how many times the heart beats in one year, which is 3.65 x 10² days.

To calculate the total number of heartbeats in one year, we can multiply the number of heartbeats in a day by the number of days in a year. Therefore, we have:

Total number of heartbeats in one year = 1.15 x 10⁵ beats/day x 3.65 x 10² days/year

= (1.15 x 3.65) x (10⁵ x 10²) beats/year

= 4.1975 x 10⁸ beats/year

This number may seem large, but it is necessary for the heart to pump blood throughout the body to keep us alive and healthy.

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multiply 5/12 by the reciprocal of 17/-6

Answers

Answer:

[tex]\frac{-5}{34}[/tex]

Step-by-step explanation:

[tex]\frac{5}{12} * \frac{-6}{17}[/tex]  = [tex]\frac{-30}{204}[/tex]

We can simplify.

[tex]\frac{-15}{102}[/tex]  ⇒ Divided both by 2

[tex]\frac{-5}{34}[/tex]  ⇒  Divided both by 3

[tex]\frac{-5}{34}[/tex] is the final answer

a cylinder and a cone have the same diameter: 8 inches. the height of the cylinder is 6 inch what is the volume of each

Answers

The volume of the cylinder with a height of 6 inches and a diameter of 8 inches is 904.78 cubic inches.

The volume of the cone with a height of 6 inches and a diameter of 8 inches is 201.06 cubic inches.

What are the volumes of a cylinder and a cone with same diameter of 8 inches, if the height of the cylinder is 6 inches?

The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. Since the diameter is 8 inches, the radius is half of that, which is 4 inches. So, the volume of the cylinder is:

V = π(4)²(6)

V = π(16)(6)

V = 96π

V ≈ 301.59 cubic inches (rounded to two decimal places)

The formula for the volume of a cone is V = (1/3)πr²h. Again, since the diameter is 8 inches, the radius is 4 inches. So, the volume of the cone is:

V = (1/3)π(4)²(6)

V = (1/3)π(16)(6)

V = (1/3)(96π)

V ≈ 100.53 cubic inches (rounded to two decimal places)

However, since the problem only asked for the diameter and not the radius, we can simplify the calculations by using the formula for the volume of a cylinder with diameter D directly, which is:

V = π(D/2)²h

V = π(8/2)²(6)

V = π(4)²(6)

V = 16π(6)

V ≈ 301.59 cubic inches (rounded to two decimal places)

Similarly, we can use the formula for the volume of a cone with diameter D directly, which is:

V = (1/3)π(D/2)²h

V = (1/3)π(8/2)²(6)

V = (1/3)π(4)²(6)

V = (1/3)(16π)(6)

V ≈ 100.53 cubic inches (rounded to two decimal places)

Thus, the main answer is the volume of the cylinder is 904.78 cubic inches and the volume of the cone is 201.06 cubic inches, both rounded to two decimal places.

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The cost of product is birr 92 & the company is having a policy of 15% mark-up on cost,then what tha sale price will be?

Answers

The sale price of the product would be Birr 105.80.

If the cost of the product is Birr 92 and the company has a policy of 15% mark-up on the cost, then the sale price can be found by adding 15% of the cost to the cost itself.

To calculate this, we can use the formula:

Sale price = Cost + Mark-up

where the mark-up is 15% of the cost.

Mark-up = 15% of Cost = 0.15 * 92 = Birr 13.80

So, the sale price = Cost + Mark-up = 92 + 13.80 = Birr 105.80.

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which number is equal to 7 hundred thousands 4 thousands 3 tens and 6 ones?

Answers

The number that is equal to the place values, 7 hundred thousands 4 thousands 3 tens and 6 ones, is 704,036

Place value: Determining the number that is equal to the place values

From the question, we are to determine the number that is equal to the given place values

From the given information, the given place value is

7 hundred thousands 4 thousands 3 tens and 6 ones

Now, we will write each of the values in figures

7 hundred thousands = 700,000

4 thousands = 4,000

3 tens = 30

6 ones = 6

To determine the number that is equal to the place values, we will sum all the digits

700,000 + 4,000 + 30 + 6

704,036

Hence,

The number that is equal to the place value is 704,036

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All of these rectangles have an area of 12 square inches. Each square represents 1 square inch. Which rectangles do not have a perimeter of 14 inches?​

Answers

The rectangles with dimensions 1 x 12 and 2 x 6 do not have a perimeter of 14 inches. These rectangles have perimeters of 26 inches and 16 inches, respectively.

To determine which rectangles with an area of 12 square inches do not have a perimeter of 14 inches, we will first find the possible dimensions of the rectangles and then calculate their perimeters.

1. Since the area of a rectangle is given by length x width, let's find the factors of 12:
  - 1 x 12
  - 2 x 6
  - 3 x 4
2. Now, let's calculate the perimeters for each of these rectangles using the formula 2(length + width):
  - For the 1 x 12 rectangle, the perimeter is 2(1+12) = 2(13) = 26 inches
  - For the 2 x 6 rectangle, the perimeter is 2(2+6) = 2(8) = 16 inches
  - For the 3 x 4 rectangle, the perimeter is 2(3+4) = 2(7) = 14 inches
The rectangles with dimensions 1 x 12 and 2 x 6 do not have a perimeter of 14 inches. These rectangles have perimeters of 26 inches and 16 inches, respectively.

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The curve y = ax2 + bx + c passes through the point (2, 12) and is tangent to the line yat at the origin. Find a, b, and c. a = 4,6 - 0,C-1 Oa - 2. b = 0,C=0 O a = 1,"

Answers

The equation of the curve is y = x2 + 4.

To solve this problem, we need to use the fact that the curve y = ax2 + bx + c passes through the point (2, 12) and is tangent to the line yat at the origin.

First, we know that the tangent to the curve at the origin is the line y = 0x + c = c. Since the curve is tangent to this line at the origin, we know that the derivative of the curve at x = 0 is equal to 0.

Taking the derivative of y = ax2 + bx + c, we get y' = 2ax + b. Setting x = 0, we get y' = b. Since y' = 0 at x = 0, we know that b = 0.

So now we have y = ax2 + c. We can use the fact that the curve passes through the point (2, 12) to solve for a and c.

Substituting x = 2 and y = 12 into the equation y = ax2 + c, we get 12 = 4a + c.

Since we know that a = 4, 6, or 1, we can substitute each of these values into the equation and solve for c.

When a = 4, we get 12 = 4(4)(2) + c, which simplifies to 12 = 32 + c. Solving for c, we get c = -20.

When a = 6, we get 12 = 4(6)(2) + c, which simplifies to 12 = 48 + c. Solving for c, we get c = -36.

When a = 1, we get 12 = 4(1)(2) + c, which simplifies to 12 = 8 + c. Solving for c, we get c = 4.

So the values of a, b, and c are:
a = 1
b = 0
c = 4

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67. 8 x 9. 7 pls someone answer within the next 20 Minutes with work I'm in school lol

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the answer for this question for
657.66

help meee 5774 + 252 - 2586 ×35​

Answers

Answer:

The answer is -84,484

Step-by-step explanation:

using Bodmas

multiplication first

5774+252-(2586×35)

5774+252-90510

6026-90510

-84,484

Given that : f(x) = 2 sec x + tan x 0 ≤ x ≤ 2π
a) Find the derivative.
b) Find the critical numbers.

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The derivative of the given function is f'(x) = 2(sec x * tan x) + sec^2 x. b) The critical numbers for the function are x = 0 and x = π.of the given function is f'(x) = 2(sec x * tan x) + sec^2 x.

The critical numbers for the function are x = 0 and x = π.

Derivative and critical numbers,

a) Find the derivative: We're given the function f(x) = 2 sec x + tan x.

To find its derivative, we need to find the derivatives of the individual terms (sec x and tan x) and then add them together.

The derivative of sec x is sec x * tan x. So, for the term 2 sec x, the derivative is 2 * (sec x * tan x).

The derivative of tan x is sec^2 x.

Now, we add both derivatives to find the derivative of f(x): f'(x) = 2(sec x * tan x) + sec^2 x

b) Find the critical numbers: Critical numbers are the points where the derivative of the function is either 0 or undefined.

To find the critical numbers, we'll set f'(x) equal to 0 and solve for x, as well as identify where the derivative is undefined.

First, let's set f'(x) to 0: 0 = 2(sec x * tan x) + sec^2 x

We need to solve this equation for x. It's a bit tricky, so let's rewrite the equation in terms of sin and cos: 0 = 2((1/cos x) * (sin x/cos x)) + (1/cos x)^2

Now let's simplify the equation: 0 = 2(sin x/cos^2 x) + 1/cos^2 x

To eliminate the denominators, we'll multiply through by cos^2 x: 0 = 2(sin x) + cos x

Now, we can use the unit circle to find the values of x in the interval 0 ≤ x ≤ 2π that satisfy this equation: For sin x = 0, x = 0, π For cos x = -2, there's no solution in the given interval because the range of cosine is -1 ≤ cos x ≤ 1.

Therefore, the critical numbers are x = 0 and x = π. Your answer:

a) The derivative of the given function is f'(x) = 2(sec x * tan x) + sec^2 x.

b) The critical numbers for the function are x = 0 and x = π.

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A certain product is marked down to $82. 81 after a 15. 5% decrease. Determine the original price. (4 points)


$69. 90


$92. 50


$98. 00


$128. 35

Answers

The original price of the product was approximately $98.00.

How to determine the original price of a product after a given markdown?

To determine the original price before the 15.5% decrease, we can use the following equation:

Original price - (15.5% of original price) = $82.81

Let's solve for the original price:

Original price - (0.155 * Original price) = $82.81

Simplifying the equation:

0.845 * Original price = $82.81

Dividing both sides by 0.845:

Original price = $82.81 / 0.845

Calculating the original price:

Original price ≈ $98.00

Therefore, the original price of the product was approximately $98.00.

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PLEASE HELP WILL MARK BRANLIEST!!!

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The number of bracelets that can be made using all the colors one time only is 720.

Given that Diana is making bracelet with 6 different colors we need to find the number of bracelets that can be made using all the colors one time only,

Since there are 6 beads so, the number of bracelets can be made = 6!

= 720

Hence the number of bracelets that can be made using all the colors one time only is 720.

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A manager notices that the employees in his division seem under heightened stress. he reviews their results on the osi and notices that the distribution of 25


employees in his division has a mean of 53. he notices that the mean of entire department is 49 (n=150). sd for both = 10.


what are the 95% confidence limits for the division?

Answers

The 95% confidence interval for the population mean of the division is (49.08, 56.92).

We can use the formula for the confidence interval for a population mean:

CI = [tex]\bar{X}[/tex] ± z*(σ/√n)

where [tex]\bar{X}[/tex] is the sample mean, z is the z-score for the desired confidence level (95% in this case), σ is the population standard deviation (which we assume to be equal to the sample standard deviation), and n is the sample size.

In this problem, [tex]\bar{X}[/tex] = 53, σ = 10, n = 25, and the z-score for a 95% confidence level is 1.96 (from a standard normal distribution table).

Plugging in these values, we get:

CI = 53 ± 1.96*(10/√25) = 53 ± 3.92

Therefore, the 95% confidence interval for the population mean of the division is (49.08, 56.92).

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The radius of a circle is 11 kilometers.what is the circle area

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Answer:

380.1 square kilometers

Step-by-step explanation:

Solve each system by substitution
-5x-6y=2
Y=3

Answers

This equation would turn into: -5x-6(3)=2. We then would multiply to make: -5x - 18 = 2. Next we would add 18 to both sides to create: -5x = 20. Last in this step would be dividing which would give us: x = 4.

Answer:

x = -4, y = 3.

Step-by-step explanation:

Substitute y = 3 into the first equation:

-5x - 6(3) = 2

-5x = 2 + 18

-5x = 20

x = -4

1. Existence of limit (a) Determine whether the following limit exists. If yes, find the limit. If no, give a reasonable explanation * + 2y + 3xy lim (.)+(0,0) * + 3y (b) Determine whether the following limit exists. If yes, find the limit. If no, give a reasonable explanation zy2 lim (x,)+(0,0) 2.4 +y Page 2 (c) Determine whether the following function is continuous at (x,y) = (0,0). Give a reasonable explanation. Hint: Try applying the absolute value to f(x,y) and finding another function g(x,y) such that 0 <\/(x,y) = g(x,y). Use this bounding function g to say what happens to the absolute value (x,y). Here you should apply what's called the sandwich (or squeeze) theorem. o if (x,y) = (0,0) Note: If the function is continuous at (0,0), then 2 lim = 0. (x,y)+(0042 + y2 Observe that ?? <** + y for all 1,9,80 s i. This implies |/(x,y) S (xy|for all 2, y. Page 3

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a) To determine if the limit exists, we need to check if the limit from all directions approaching (0,0) are equal. Let's approach (0,0) along the x-axis first, so y = 0:

lim (x,y)->(0,0) [(x) + 2(y) + 3(x)(y)]
= lim x -> 0 [(x) + 2(0) + 3(x)(0)] = lim x -> 0 x = 0

Next, let's approach (0,0) along the y-axis, so x = 0:

lim (x,y)->(0,0) [(x) + 2(y) + 3(x)(y)]
= lim y -> 0 [(0) + 2(y) + 3(0)(y)] = lim y -> 0 2y = 0

Now, let's approach (0,0) along the line y = mx, where m is some constant:

lim (x,y)->(0,0) [(x) + 2(y) + 3(x)(y)]
= lim x -> 0 [(x) + 2(mx) + 3(x)(mx)]
= lim x -> 0 [(1+3m)x + 2mx^2]
= 0 if m=0, and DNE (does not exist) for all other values of m.

Since the limit is not equal from all directions, the limit DNE at (0,0).

b) To determine if the limit exists, we need to check if the limit from all directions approaching (0,0) are equal. Let's approach (0,0) along the x-axis first, so y = 0:

lim (x,y)->(0,0) [(2.4) + (y)]
= lim x -> 0 [(2.4) + (0)] = 2.4

Next, let's approach (0,0) along the y-axis, so x = 0:

lim (x,y)->(0,0) [(2.4) + (y)]
= lim y -> 0 [(2.4) + (y)] = 2.4

Now, let's approach (0,0) along the line y = mx, where m is some constant:

lim (x,y)->(0,0) [(2.4) + (y)]
= lim x -> 0 [(2.4) + (mx)]
= 2.4 if m=0, and DNE (does not exist) for all other values of m.

Since the limit is equal from all directions, the limit exists and is equal to 2.4 at (0,0).

c) To determine if the function is continuous at (0,0), we need to check if the limit as (x,y) approaches (0,0) of f(x,y) exists and is equal to f(0,0).

Let g(x,y) = sqrt(x^2 + y^2), which satisfies 0 <= |(x,y)| <= g(x,y) for all (x,y). We have:

|f(x,y)| = |(x+y)/(4+x^2+y^2)| <= |(x+y)/4| <= (1/4)g(x,y)

So, we can bound f(x,y) by (1/4)g(x,y). By the sandwich (or squeeze) theorem, we have:

lim (x,y)->(0,0) (1/4)g(x,y) = 0

Thus, by the sandwich theorem, we have:

lim (x,y)->(0,0) f(x,y) = 0

Since the limit exists and is equal to f(0,0) = 0, the function is continuous at (0,0).

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