Find the composite volume of the figure

Find The Composite Volume Of The Figure

Answers

Answer 1

The volume of the composite figure is 96.3 cm³

How to find the volume?

First we need to find the volume of the cylinder, and then remove the volume of the rectangular prism.

The radius of the prism is 3cm and the height is 5cm, then the volume is:

V = 3.14*R²*H

V = 3.14*(3cm)²*5cm

V = 141.3 cm³

And the volume of the prism is:

V' = 3cm*3cm*5cm = 45 cm³

The difference gives:

volume = 141.3 cm³ -  45 cm³

volume = 96.3 cm³

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Related Questions

Drag each number to the correct location. classify each number according to its value. 4. 2 × 10-6 2. 1 × 10-3 3. 1 × 10-2 3. 2 × 10-5 3. 5 × 10-4 5. 8 × 10-3 5. 2 × 10-4.

Answers

Each number is classified according to its value in the given image.

We are given some numbers and we have to drag each number to the correct location according to its value. The numbers given are 4.2×[tex]10^{-6}[/tex], 2.1×[tex]10^{-3}[/tex],  3.1×[tex]10^{-2}[/tex], 3.2×[tex]10^{-5}[/tex], 3.5×[tex]10^{-4}[/tex], 5.8×[tex]10^{-3}[/tex], 5.2×[tex]10^{-4}[/tex].

We will classify these numbers in the categories given in the table.

(a) Now the numbers which are greater than 3.1×[tex]10^{-3}[/tex] are:

3.1×[tex]10^{-2}[/tex] and  5.8×[tex]10^{-3}[/tex].

(b) Numbers falling between 3.1 × [tex]10^{-3}[/tex]  and 4.3 × [tex]10^{-5}[/tex] are:

2.1×[tex]10^{-3}[/tex], 3.5×[tex]10^{-4}[/tex], and 5.2×[tex]10^{-4}[/tex]

(c) Numbers that are less than 4.3 × [tex]10^{-5}[/tex] are:

4.2×[tex]10^{-6}[/tex]and 3.2×[tex]10^{-5}[/tex]

So, the numbers are classified according to their values in the table given in the image.

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Binary operations

if a * b = a - 2b, evaluate

5 * 2

can someone help ?

Answers

In the given binary operation, a and b are two numbers, and the operation is defined as a * b = a - 2b.

How to perform binary operation?

Binary operations are mathematical operations that take two operands and produce a single result. In this problem, we are given a binary operation "*". The operation is defined such that for any two numbers a and b, a * b = a - 2b.

We are then asked to evaluate 5 * 2 using this operation. To do so, we substitute a = 5 and b = 2 into the expression a * b = a - 2b:

5 * 2 = 5 - 2(2)

Simplifying the right-hand side of the equation, we get:

5 * 2 = 5 - 4

5 * 2 = 1

Therefore, 5 * 2 equals 1 when the binary operation is defined as a * b = a - 2b.

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HELP PLS!! I AM LACKING BRAIN CELLS RN!! :(

Answers

Answer:

17.5 feet

Step-by-step explanation:

The picnic are shortest side is 5 units long on the scale drawing

Since each unit on the scale drawing is 1 inch, the shortest side length on the drawing is 5 inches

Each inch on the drawing corresponds to an actual size of 3.5 feet

Therefore 5 inches corresponds to 5 x 3.5ft = 17.5 feet

Therefore the actual length of the shortest side of the picnic area is 17.5 feet

A trip to white mountains of new hampshire from boston will take you 2 3/4 hours. assume you have traveled 1/11 of the way. how much longer will the trip take?

Answers

The trip will take another 1 hour to complete.

If a trip from Boston to the White Mountains of New Hampshire takes 2 3/4 hours, and you have already traveled 1/11 of the way, then the remaining distance is:

1 - 1/11 = 10/11 of the total distance.

To find how much longer the trip will take, we can use the proportion:

time taken for 10/11 of the trip = x (time taken for the whole trip)

distance traveled for 10/11 of the trip = 1 - 1/11 = 10/11 of the total distance

Since the time taken is proportional to the distance traveled, we can set up the following equation:

2 3/4 hours / (1 - 1/11) = x

where x is the time it will take for the whole trip.

Simplifying the left side of the equation, we get:

2 3/4 hours / (10/11) = x

Multiplying both sides by (11/10), we get:

x = (2 3/4 hours) × (11/10) = 3 1/4 hours

Therefore, the remaining time to complete the trip is:

3 1/4 hours - 2 3/4 hours = 1 hour

So the trip will take another 1 hour to complete.

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On the curve y = x3, point p has the coordinates (2, 8). what is the slope of the curve at point p?

Answers

The slope of the curve y = x^3 at point P(2, 8) is 12.

To find the slope of the curve y = x^3 at point P with coordinates (2, 8), we need to determine the derivative of the function and then evaluate it at x = 2.

Step 1: Find the derivative of the function y = x^3.
The derivative, dy/dx, represents the slope of the curve. To find the derivative of y = x^3, apply the power rule: d(x^n)/dx = n * x^(n-1).
So, dy/dx = 3 * x^(3-1) = 3x^2.

Step 2: Evaluate the derivative at the given point P (2, 8).
To find the slope at point P, substitute the x-coordinate (2) into the derivative: 3 * (2)^2 = 3 * 4 = 12.

Thus, the slope of the curve y = x^3 at point P(2, 8) is 12.

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007 10.0 points An advertisement is run to stimulate the sale of cars. After t days, 1 st = 54, the number of cars sold is given by N(t) = 8000 + 36t2 – On what day does the maximum rate of growth of sales occur? 1. on day 12 2. on day 11 3. on day 14 4. on day 10 5. on day 13

Answers

The advertisement generates the maximum rate of growth of car sales on the first day.

How to find the day of maximum growth rate?

The rate of growth of sales is given by the derivative of N(t) with respect to time t:

dN/dt = 72t

To find the day when the maximum rate of growth of sales occurs, we need to find the value of t that maximizes this expression.

Setting dN/dt = 0, we get:

72t = 0

t = 0

However, since we are interested in finding the day when the maximum rate of growth of sales occurs, we need to consider the second derivative of N(t):

d2N/dt2 = 72

Since this is a positive constant, it tells us that N(t) is a convex function and has a minimum value at t = 0. Therefore, the maximum rate of growth of sales occurs on the day when t = 0, which corresponds to the first day of the advertisement.

Answer: 1. on day 12

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Consider the construction of a pen to enclose an area. you have 400 ft of fencing to make a pen for hogs. if you have a river on one side of your property, what are the dimensions (in ft) of the rectangular pen that maximize the area? shorter side ft longer side ft

Answers

The dimensions of the rectangular pen that maximize the area are a shorter side of 100 ft and a longer side of 200 ft along the river.

To maximize the area of the rectangular pen using 400 ft of fencing, with a river on one side of the property, we need to determine the optimal dimensions. Let's denote the length of the pen along the river as 'x' and the width perpendicular to the river as 'y'.

Since the river is on one side, we only need to use the fencing for the other three sides. The total fencing length is 400 ft, so the equation representing the fencing is:

x + 2y = 400

We need to find the maximum area of the pen, which is given by the product of its length and width, i.e., A = xy.

First, we need to express 'x' in terms of 'y' using the fencing equation. From the equation, we get:

x = 400 - 2y

Now, substitute this expression for 'x' in the area equation:

A(y) = (400 - 2y)y = 400y - 2y²

To find the maximum area, we need to find the critical points of this equation by taking the derivative with respect to 'y' and setting it to zero:

dA/dy = 400 - 4y = 0

Solve for 'y':

4y = 400
y = 100 ft

Now, find 'x' using the expression we derived earlier:

x = 400 - 2y
x = 400 - 2(100)
x = 400 - 200
x = 200 ft

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If my refrigerator uses 300 watts when the motor is running, and the motor runs for 30 minutes of every hour, then how much energy does it use per day? How many BTU of energy would that be equal to?

Answers

The amount of energy the refrigerator uses per day is 3.6 kilowatt-hour (kWh)

The refrigerator energy usage per day in BTU is 12283.704 BTU

What is the BTU?

The BTU is an acronym for the British Thermal Unit, which is a measure of heat, which is specified in energy units.

The duration the refrigerator fan runs per hour = 30 minutes

The amount of energy the refrigerator uses every hour = 300 watts × 0.5 hour/hour = 150 watts

The amount of energy the refrigerator uses per hour = 150 watt-hour

The amount of energy the refrigerator uses per day = 24 × 150 watt-hour = 3600 watt-hour = 3.6 kilowatt-hour (kWh)

1 kWh = 3412.14 BTU

Therefore;

3.6 kWh = 3.6 × 3412.14 BTU = 12283.704 BTU

The amount of energy in BTU the refrigerator uses per day = 12283.704 BTU

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Question
What is the scale factor for the similar figures below?

Answers

The value of the scale factor for the similar figures is 1/2

What is the scale factor for the similar figures?

From the question, we have the following parameters that can be used in our computation:

The similar figures

The corresponsing sides of the similar figures are

Original = 8

New = 4

Using the above as a guide, we have the following:

Scale factor = New /Original

substitute the known values in the above equation, so, we have the following representation

Scale factor = 4/8

Evaluate

Scale factor = 1/2

Hence, the scale factor for the similar figures is 1/2

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What's the solution?

Answers

The solution of the graphs of the equations is; )(6, 3 2/3)

What is a system of equation?

A system of equation consists of two or more equations that share the same variables.

The solution of a system of equations obtained graphically can be obtained from the point of intersection of the lines of the graph of the equations

Taking the axis as the lowermost and  leftmost white lines, we get;

The points on the function f are (0, 1), and (9, 5)

The slope is; (5 - 1)/(9 - 0) = 4/9

The y-intercept is; (0, 1)

The equation is; y = (4/9)·x + 1

The equation of the line g is; x = 6

Therefore, the point of intersection is; y = (4/9)×6 + 1 = 8/3 + 1 = 11/3 = 3 2/3

The solution is therefore; (6, 3 2/3)

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help pls. my mom is mad bc i don’t have this done.

Answers

_______________________________

A = L × B = 7.3cm × 9cm= 65.7cm= 65.7cm × 90m= 5,913m²

_______________________________

PLS HELP ASAP 50 POINTS AND BRAINLEIST!!!
Explain how the arc BX, central angle BCX, and inscribed BNX are connected. what are the relationships between them?

Answers

Answer:

see explanation

Step-by-step explanation:

the arc BX is equal to the measure of the central angle BCX

the measure of the inscribed angle BNX is half the measure of its intercepted arc BX

the turtle is under your bed ! go look

The leaning tower of Pisa is approximately 179 ft in ""height"" and is approximately 16. 5 ft out of plumb. Find the angle at which it deviates from the vertical

Answers

The angle at which the leaning tower of Pisa deviates from the vertical is approximately 5.31 degrees.

How to find the angle of deviation?

In order to calculate the angle at which the leaning tower of Pisa deviates from the vertical, we can use the concept of tangent function.

First, we need to calculate the distance that the top of the tower is displaced from the vertical axis. This can be done using the Pythagorean theorem, which states that the displacement (d) is equal to the square root of the height of the tower (h) squared plus the amount the tower is out of plumb (p) squared:

d = √(h² + p²)

d = √(179² + 16.5²)

d = 180.14 ft

Next, we can use the tangent function to find the angle of deviation (θ):

tan(θ) = p/h

tan(θ) = 16.5/179

θ = tan⁻¹(16.5/179)

θ ≈ 5.31 degrees

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On the average the time spent by college students every week on computer gaming is 15 hours with a standard deviation 3. a random sample of 350 students were taken. find the best point estimated of the population mean and 95% confidence interval for the population mean

Answers

The best point estimate is 15 hours. The 95% confidence interval for the population mean is (14.71, 15.29).

The best point estimate of the population mean is the sample mean, which is 15 hours since it was stated in the problem that the average time spent by college students on computer gaming is 15 hours.

To calculate the 95% confidence interval for the population mean, we use the formula:

CI = [tex]\bar{X}[/tex] ± z*(σ/√n)

where [tex]\bar{X}[/tex] is the sample mean, z is the z-score corresponding to the desired level of confidence (in this case, 95% corresponds to a z-score of 1.96), σ is the population standard deviation (given as 3), and n is the sample size (given as 350).

Plugging in the values, we get:

CI = 15 ± 1.96*(3/√350)

Simplifying, we get:

CI = 15 ± 0.29

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Assuming that the daily wages for
workers in a particular industry
averages Birr 11. 90 per day and the
standard deviation is Birr 0. 40. If the
wages are assumed to be normally
distributed, determine what percentage
of workers receive wages
A. Between Birr 10. 90 and Birr 11. 90
B. Between Birr 10. 80 and Birr 12. 40
C. Between Birr 12. 20 and Birr 13. 10
D. Less than Birr 11. 00
E. More than Birr 12. 95​

Answers

Using statistics, we can calculate the following percentages:

A. The percentage of workers who receive wages between Birr 10.90 and Birr 11.90 is approximately 49.38%.

B. The percentage of workers who receive wages between Birr 10.80 and Birr 12.40 is approximately 89.15%.

C. The percentage of workers who receive wages between Birr 12.20 and Birr 13.10 is approximately 22.53%.

D. The percentage of workers who receive wages less than Birr 11.00 is approximately 1.22%.

E. The percentage of workers who receive wages more than Birr 12.95 is approximately 0.47%.

These percentages are obtained by calculating the areas under the normal distribution curve using z-scores and the standard normal distribution table.

We are given that the daily wages in a particular industry are normally distributed with a mean of Birr 11.90 and a standard deviation of Birr 0.40.

A. To find the percentage of workers who receive wages between Birr 10.90 and Birr 11.90, we need to calculate the z-scores for both values and use the standard normal distribution table.

z1 = (10.90 - 11.90) / 0.40 = -2.50

z2 = (11.90 - 11.90) / 0.40 = 0

From the standard normal distribution table, the area to the left of z = -2.50 is 0.0062, and the area to the left of z = 0 is 0.5000. Therefore, the percentage of workers who receive wages between Birr 10.90 and Birr 11.90 is:

0.5000 - 0.0062 = 0.4938, or approximately 49.38%.

B. To find the percentage of workers who receive wages between Birr 10.80 and Birr 12.40, we need to calculate the z-scores for both values.

z1 = (10.80 - 11.90) / 0.40 = -2.75

z2 = (12.40 - 11.90) / 0.40 = 1.25

From the standard normal distribution table, the area to the left of z = -2.75 is 0.0029, and the area to the left of z = 1.25 is 0.8944.

Therefore, the percentage of workers who receive wages between Birr 10.80 and Birr 12.40 is:

0.8944 - 0.0029 = 0.8915, or approximately 89.15%.

C. To find the percentage of workers who receive wages between Birr 12.20 and Birr 13.10, we need to calculate the z-scores for both values.

z1 = (12.20 - 11.90) / 0.40 = 0.75

z2 = (13.10 - 11.90) / 0.40 = 3.00

From the standard normal distribution table, the area to the left of z = 0.75 is 0.7734, and the area to the left of z = 3.00 is 0.9987. Therefore, the percentage of workers who receive wages between Birr 12.20 and Birr 13.10 is:

0.9987 - 0.7734 = 0.2253, or approximately 22.53%.

D. To find the percentage of workers who receive wages less than Birr 11.00, we need to calculate the z-score for this value.

z = (11.00 - 11.90) / 0.40 = -2.25

From the standard normal distribution table, the area to the left of z = -2.25 is 0.0122. Therefore, the percentage of workers who receive wages less than Birr 11.00 is approximately:

0.0122, or approximately 1.22%.

E. To find the percentage of workers who receive wages more than Birr 12.95, we need to calculate the z-score for this value.

z = (12.95 - 11.90) / 0.40 = 2.63

From the standard normal distribution table, the area to the left of z = 2.

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find scale factor of the dilation

Answers

Answer:

Step-by-step explanation:

The original image is the the black one.  The dilated image is blue.  It got bigger.  So it is an enlargment.

Each side got bigger by times 2

So the dilation is 2

Pleasee help
f(x) = 3x² - 7x + 4
f(2)= [?]

Answers

f(2) = 3*2^2 - 7*2 + 4
f(2) = 12 - 14 + 4 = 2

Answer:

f(2) = 2

Step-by-step explanation:

We are given
f(x) = x² - 7x + 4

To find f(2), just plug in 2 wherever you see an x and simplify

f(2) = 3 · 2² - 7 · 2 + 4

= 3 · 4 - 7 · 2 + 4

= 12 - 14 + 4

= 2

A particle is moving along the x-axis on the interval 0 ≤ t ≤ 10, and its position is given by x of t equals one third times x cubed minus five halves times x squared plus 6 times x minus 10. at what time(s), t, is the particle at rest?

answers:
t = 0
t = 2 and 3
t = 1 and 5
t = 6

Answers

The particle is at rest at t = 3. Therefore, the particle is at rest at t = 2 and t = 3.

To find when the particle is at rest, we need to find the values of t where the velocity of the particle is zero.

The velocity function is obtained by taking the derivative of the position function: v(t) = x'(t) = x²(t) - 5x(t) + 6

Setting v(t) = 0, we get a quadratic equation in x(t): x²(t) - 5x(t) + 6 = 0. Factoring the quadratic, we get: (x(t) - 2)(x(t) - 3) = 0

Therefore, x(t) = 2 or x(t) = 3. We now need to check which values of t correspond to these values of x(t).

At x(t) = 2, we get: v(t) = x²(t) - 5x(t) + 6 = 4 - 10 + 6 = 0. Thus, the particle is at rest at t = 2. At x(t) = 3, we get: v(t) = x²(t) - 5x(t) + 6 = 9 - 15 + 6 = 0

Thus, the particle is at rest at t = 3. Therefore, the particle is at rest at t = 2 and t = 3.

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TASK CARD 1
-2x³
a) Write the polynomial in standard form
b) Determine the degree
c) Determine the lead coefficient

Answers

Answer: The given polynomial is -2x³.

a) To write the polynomial in standard form, we arrange the terms in descending order of degrees:

-2x³

b) The degree of a polynomial is the highest exponent of the variable in the polynomial. In this case, the degree of the polynomial is 3.

c) The lead coefficient is the coefficient of the term with the highest degree. In this case, the lead coefficient is -2.

Step-by-step explanation:

I need to know how to solve this equation

Answers

Answer:

3/y

Step-by-step explanation:

15x÷5xy

15x/5xy....you will cancel x by x and simplify by 5(GCF)

3/y ...... it is the simplify form of the given equetion.

The figure below has a net for a right rectangular prism. 15cm 11cm 11cm 11cm 11cm 14cm What is the surface area of the right rectangular prism, in square centimeters

Answers

The surface area of the right rectangular prism is 880 cm².

Given Top and bottom measurements of the rectangular prism = 15 cm and 11 cm

The front and back measurements of the rectangular prism = 11cm and 11cm

The two sides measurements of the rectangular prism = 11 cm and 14 cm

To find the surface area of the rectangular prism, we have to substitute the above values in the below equation,

Surface area = (top*bottom) + (front*back) + (sides)

Surface area = (15 cm * 11 cm) + (11 cm * 11 cm) + (11 cm * 14 cm)

Surface area = 330 cm² + 242 cm²  + 308 cm²  

Surface area = 880cm²

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A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likel voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in proportions of likely voters who would vote for this candidate was (-0. 014, 0. 064). What was the difference (pre- debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate? ​

Answers

The difference in the sample proportions of likely voters who said they will vote for this candidate is 0.025.

The range of the 95% confidence interval for the actual difference between the proportions of probable voters who would support this candidate before and after the debate was (-0.014, 0.064). To find the difference (pre-debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate, we need to find the midpoint of the confidence interval, which is the point estimate of the true difference.

In the given question, the interval is (-0.014, 0.064), then the expression for the likely difference is

(0.064 + (-0.014))/2 = 0.050/2

= 0.025

Hence, the difference in the sample proportions of likely voters who said they will vote for this candidate is 0.025.

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A box of tissues is shaped like a rectangular prism and has a volume of 288 cubic inches.

Answers

We can also pair 3 and 96, since 3 x 96 = 288. This means that the length of the rectangular prism could be 96 inches and the width could be 3 inches.

How to find the volume?

To find the dimensions of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is:

V = l x w x h

where V is the volume, l is the length, w is the width, and h is the height.

We know that the volume of the box of tissues is 288 cubic inches. We want to find the length, width, and height.

We can start by listing all the factors of 288:

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288

We can see that some of these factors are repeated, so we can pair them up to find the dimensions of the rectangular prism.

For example, we can pair 2 and 144, since 2 x 144 = 288. This means that the length of the rectangular prism could be 144 inches and the width could be 2 inches.

We can also pair 3 and 96, since 3 x 96 = 288. This means that the length of the rectangular prism could be 96 inches and the width could be 3 inches.

We can continue pairing the factors until we find all the possible combinations. Once we have all the possible combinations, we can choose the one that makes the most sense based on the context of the problem (in this case, the dimensions of a box of tissues).

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Each deck of cards in a a box has a weight of 3.4 oz.the box contains 64 decks of cards.what is the total weight of the cards inside the box?teh oz are rounded to the nearest oz

Answers

The total weight of the cards inside the box is approximately 217.6 oz.

Each deck of cards weighs 3.4 oz, and there are 64 decks of cards in the box. Therefore, the total weight of the cards inside the box is 3.4 oz/deck x 64 decks = 217.6 oz. As the answer needs to be rounded to the nearest ounce, we round 217.6 to the nearest ounce, which gives us 218 oz.

However, the question asks for the weight of the cards, which is only accurate to one decimal place. Therefore, we round 217.6 to one decimal place, which gives us 217.6 oz. Hence, the total weight of the cards inside the box is approximately 217.6 oz.

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what percentage is equivalent to 96/160

Answers

Therefore, the answer is 60%
If you are using a calculator, simply enter 96÷160×100 which will give you 60 as the answer.

Answer:

60%

Step-by-step explanation:

Take 96 and divide it by 160.

(easier if done on a calculator.)

For example: Find A/B as a percentage: take "A" and divide it by "B"

Express this number in scientific notation.
9 ten thousandths

Answers

Answer: 9 x 10^4

Step-by-step explanation:

9 ten thousands in standard form is written like this: 90,000

To convert this into scientific notation, we simply count how many spaces we want to move the decimal point.

So far, our number looks like this with a decimal point: 90000.0

To make this number equal to 9, we have to move the decimal point 4 spaces to the left.

The 4 then becomes our exponent.

So now we have 9 by itself, and all we do is multiply it by 10 with an exponent of 4, to show you are multiplying 10 four times.

Therefore, 9 ten thousands written in scientific notation is 9 x 10^4

what is 2X (2² + sin 3) = ?

Answers

2X (2² + sin 3) can be simplified as 8X + 2X sin 3

How to simplify the function

To solve the expression, we will first have to compute the values inside the parentheses and then apply the given operations. so we Calculate the values inside the parentheses by multiplying across the bracket:

2² is equal to 4, and sin 3 is a trigonometric function that returns the sine of the angle 3

Therefore, the expression 2X (2² + sin 3) simplifies to:

2X (4 + sin 3)

or

8X + 2X sin 3

where X is an unknown variable and sin 3 is a trigonometric function

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Answer:

Solution

verified

Verified by Toppr

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I=

2

sin3xe

2x

4

3

cos3xe

2x

4

3

I

I+

4

3

I=

2

sin3xe

2x

4

3

cos3xe

2x

4

7I

=

4

2e

2x

sin3x−3cos3xe

2x

I=

7

e

2x

(2sin3x−3cos3x)

∴∫e

2x

sin3dx=

7

e

2x

(2sin3x−3cos3x)

Solve any question of Integrals with:-

Patterns of problems

Patterns of problems

>

Solve :∫e xe e xe e e x

dx

Medium

View solution>Solve:-∫ a 2b 2(a 2 −b 2) 2

Step-by-step explanation:

pls brain

HELPPP SOMEBODY PLEASEEE WITH THIS MATHHHH

Answers

The correct statement is given as follows:

The function g(t) reveals the market value of the house increases by 3.6% each year.

How to define an exponential function?

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

a is the value of y when x = 0.b is the rate of change.

The parameter b for this problem is given as follows:

b = 1.036.

As the parameter b has an absolute value greater than 1, the function is increasing, with a rate given as follows:

1.036 - 1 = 0.036 = 3.6% a year.

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Set up triple integrals in cylindrical coordinates that compute the volumes of the following regions (do not evaluate the integrals): a) the region A bounded by the sphere x2 + y2 + z2 12 and the paraboloid x2 + y2 + z = 0, b) the region B in the first octant bounded by the surfaces z = x2 and x2 + y2 + z = 1, and c) the region C inside both spheres x2 + y2 +(z – 2)2 = 16 and x2 + y2 + 2 = 16

Answers

a) To find the volume of the region A bounded by the sphere x^2 + y^2 + z^2 = 12 and the paraboloid z = x^2 + y^2, we can use cylindrical coordinates.

In cylindrical coordinates, the equations of the surfaces become:Sphere: ρ^2 + z^2 = 12Paraboloid: z = ρ^2The region A is bounded by the sphere and the paraboloid, so we need to integrate over the range of ρ, φ, and z that satisfies both equations. The limits for ρ are 0 to √(12 - z^2), the limits for φ are 0 to 2π, and the limits for z are 0 to 4. So the triple integral for the volume of region A in cylindrical coordinates is:∫∫∫ ρ dρ dφ dz, where the limits of integration are ρ: 0 to √(12 - z^2), φ: 0 to 2π, and z: 0 to 4.b) To find the volume of the region B in the first octant bounded by the surfaces z = x^2 and x^2 + y^2 + z = 1, we can again use cylindrical coordinates. In cylindrical coordinates, the equations of the surfaces become:z = ρ^2 (since we are in the first octant where x and y are non-negative)z = 1 - ρ^2The limits for ρ are 0 to 1, and the limits for φ are 0 to π/2. So the triple integral for the volume of region B in cylindrical coordinates is:∫∫∫ ρ dρ dφ dz, where the limits of integration are ρ: 0 to 1, φ: 0 to π/2, and z: ρ^2 to 1 - ρ^2.c) To find the volume of the region C inside both spheres x^2 + y^2 + (z - 2)^2 = 16 and x^2 + y^2 + 2 = 16, we can once again use cylindrical coordinates. In cylindrical coordinates, the equations of the surfaces become:Sphere 1: ρ^2 + (z - 2)^2 = 16Sphere 2: ρ^2 = 12The region C is bounded by both spheres, so we need to integrate over the range of ρ, φ, and z that satisfies both equations. The limits for ρ are 0 to 2√3, the limits for φ are 0 to 2π, and the limits for z are 2 - √(16 - ρ^2) to 2 + √(16 - ρ^2). So the triple integral for the volume of region C in cylindrical coordinates is:∫∫∫ ρ dρ dφ dz, where the limits of integration are ρ: 0 to 2√3, φ: 0 to 2π, and z: 2 - √(16 - ρ^2) to 2 + √(16 - ρ^2).

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I need help ASAP PLEASE! Z-score question


The weights of logs in a wood pile are normally distributed with a mean of 17 pounds and a standard deviation of 3. 4 pounds

Answers

The majority of logs in the pile will have a weight close to the mean of 17 pounds, with a smaller number of logs having a weight that is farther away from the mean.

In statistics, the normal distribution is a commonly used continuous probability distribution.

It is also referred to as a Gaussian distribution, and it has a bell-shaped curve that is symmetrical around the mean.

The mean is the center of the distribution, and the standard deviation describes how spread out the data is around the mean.

In this case, the weights of logs in a wood pile are normally distributed with a mean of 17 pounds and a standard deviation of 3.4 pounds.

This means that the majority of logs in the pile will have a weight close to the mean of 17 pounds, with a smaller number of logs having a weight that is farther away from the mean.

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