By using trigonometry,
we have shown that tan(15°) = 2 - √3.
what is the trignometry?One of the most significant areas of mathematics, trigonometry has a wide range of applications. T
he study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry."
Hence, employing trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle.
Angles in trigonometry can be expressed as either degrees or radians. 0°, 30°, 45°, 60°, and 90° are some of the trigonometric angles that are most frequently employed in computations.
We can use the half-angle formula for tangent to show that:
tan(15°) = tan(30°/2) = (1 - cos(30°)) / sin(30°)
We know that cos(30°) = √3/2 and sin(30°) = 1/2, so we can substitute those values in:
tan(15°) = (1 - √3/2) / 1/2
Simplifying the denominator and multiplying by the reciprocal:
tan(15°) = 2(1 - √3/2)
Simplifying the expression:
tan(15°) = 2 - √3
Therefore, we have shown that tan(15°) = 2 - √3.
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Enzo says that he can draw an enlarge rectangle that is 16 cenimeters by 13 cenimeters which explain enzo is correct
Enzo's statement that he can draw an enlarged rectangle that is 16 centimeters by 13 centimeters is correct. To explain this, we need to understand what it means to enlarge a shape.
Enlargement is the process of making a shape bigger or smaller while maintaining its shape and proportions. In other words, if we enlarge a rectangle, we need to make sure that the length and width are increased by the same factor.
In this case, Enzo has specified the new dimensions of the rectangle as 16 centimeters by 13 centimeters. To create an enlarged rectangle with these dimensions, we need to know the scale factor of the enlargement. The scale factor is the ratio of the length of the enlarged shape to the length of the original shape. In this case, we can find the scale factor by dividing the length of the new rectangle (16 centimeters) by the length of the original rectangle.
Let's assume that the original rectangle has a length of 8 centimeters and a width of 6 centimeters. Dividing 16 by 8 gives us a scale factor of 2. This means that we need to multiply the length and width of the original rectangle by 2 to get the dimensions of the enlarged rectangle.
So, the length of the enlarged rectangle will be 8 x 2 = 16 centimeters, and the width will be 6 x 2 = 12 centimeters. However, Enzo has specified that the width of the enlarged rectangle should be 13 centimeters. This means that we need to adjust the scale factor to make the width of the enlarged rectangle 13 centimeters. Dividing 13 by 6 gives us a scale factor of approximately 2.17.
Multiplying the length and width of the original rectangle by this scale factor gives us the new dimensions of the enlarged rectangle. The length will be 8 x 2.17 = 17.36 centimeters (rounded to two decimal places), and the width will be 6 x 2.17 = 13.02 centimeters (rounded to two decimal places). Therefore, Enzo is correct in saying that he can draw an enlarged rectangle that is 16 centimeters by 13 centimeters.
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The rate of change of the gender ratio for the United States during the twentieth century can be modeled as g(t) = (1. 68 · 10^−4)t^2 − 0. 02t − 0. 10
where output is measured in males/100 females per year and t is the number of years since 1900. In 1970, the gender ratio was 94. 8 males per 100 females.
(a) Write a specific antiderivative giving the gender ratio.
G(t) = _______________ males/100 females
(b) How is this specific antiderivative related to an accumulation function of g?
The specific antiderivative in part (a) is the formula for the accumulation function of g passing through (t, g) =
Answer:
(a) G(t) = (1.68 × 10^-4) × (1/3) t^3 - (0.02/2) t^2 - 0.10t - 2445.84
(b) A(t) = G(t) - G(1900) = (1.68 × 10^-4) × (1/3) (t^3 - 1900^3) - (0.02/2) (t^2 - 1900^2) - 0.10(t - 1900)
Step-by-step explanation:
(a) The antiderivative of g(t) can be found by integrating each term of the function with respect to t:
∫g(t) dt = ∫(1.68 × 10^-4)t^2 dt - ∫0.02t dt - ∫0.10 dt
= (1.68 × 10^-4) × (1/3) t^3 - (0.02/2) t^2 - 0.10t + C
where C is the constant of integration.
To find the specific antiderivative G(t) that passes through the point (1970, 94.8), we can use this point to solve for C:
94.8 = (1.68 × 10^-4) × (1/3) (1970)^3 - (0.02/2) (1970)^2 - 0.10(1970) + C
C = 94.8 + (1.68 × 10^-4) × (1/3) (1970)^3 - (0.02/2) (1970)^2 - 0.10(1970)
C ≈ -2445.84
Therefore, the specific antiderivative that gives the gender ratio is:
G(t) = (1.68 × 10^-4) × (1/3) t^3 - (0.02/2) t^2 - 0.10t - 2445.84
(b) The accumulation function of g is the integral of g with respect to t, or:
A(t) = ∫g(t) dt = G(t) + C
where C is the constant of integration. We can find the value of C using the initial condition given in the problem:
A(1900) = ∫g(t) dt ∣t=1900 = G(1900) + C = 0
Therefore, C = -G(1900), and the accumulation function of g is:
A(t) = G(t) - G(1900) = (1.68 × 10^-4) × (1/3) (t^3 - 1900^3) - (0.02/2) (t^2 - 1900^2) - 0.10(t - 1900)
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Mrs. Tucker writes the fraction 1. She asks her students to translate the fraction into a percentage. The table shows the
responses of four students.
$
Student
Elvin
Ferdinand
Gertrude
Henrietta
Response
2. 75%
275%
11. 4%
114%
Which student correctly translates Mrs. Tucker's fraction into a percentage?
The student that correctly translates Mrs. Tucker's fraction into a percentage is Elvin and the percentage is 2.75%, under the condition that Mrs. Tucker writes the fraction 1 and tells her students to convert the fraction into a percentage
Elvin's response is correct. Ferdinand's response is incorrect due to the application of multiplication of fraction by 100 and then added a percent sign.
Gertrude's response is incorrect due to the reason of converting the fraction to a decimal and then multiplied by 100. nt sign to
Henrietta's response is incorrect due to the fact that she added a percepercentnt sign to the decimal equivalent of the fraction instead of multiplying it by 100.
Now To convert 1/36 to a percentage, we have to first divide the numerator by the denominator:
1 / 36
= 0.0277777777778
Secondly , we have to multiply the result by 100 to get the percentage
0.0277777777778 × 100
= 2.7778%
Then, the correct response is 2.75% which is the percentage equivalent of 1/36 given by Elvin.
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The ratio of dolls thta jack had to peter was 5:2. After jack gave peter 15 dolls, they had the same amount of dolls. How many do they have together?
They have total of 70 dolls together.
Let the initial number of dolls Jack had be 5x and the number Peter had be 2x.
After Jack gave Peter 15 dolls, their amounts became equal. So, we can write the equation: 5x - 15 = 2x + 15
Now, solve the equation for x: 5x - 2x = 15 + 15, which simplifies to 3x = 30
Divide both sides by 3: x = 10
Now, find the initial number of dolls they had: Jack had 5x = 5(10) = 50 dolls, and Peter had 2x = 2(10) = 20 dolls.
After Jack gave Peter 15 dolls, both had 35 dolls (50 - 15 = 35, and 20 + 15 = 35).
So, together they have 35 + 35 = 70 dolls.
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Evaluate the following expression. Your answer must be in exact form: for example, type pi/6 for π/6 or DNE if the expression is undefined. arcsin (sin (-57π/10))=
For the following expression arcsin (sin (-57π/10)) is 3π/10.
The function arcsin(x) gives the angle in radians whose sine is x.
In this problem, we need to find the angle whose sine is equal to the sine of -57π/10.
First, we need to simplify -57π/10 to an angle in the range [-π/2, π/2] since the sine function has a range of [-1, 1]. To do this, we use the fact that sine has a period of 2π,
which means that sin(-57π/10) = sin((-57π/10) + 4π) = sin(3π/10).
So we need to find the angle θ such that sin(θ) = sin(3π/10).
Since sine is an odd function, we know that sin(-θ) = -sin(θ), so we can also say that sin(θ) = sin(-3π/10).
Therefore, there are two possible angles that satisfy the equation: θ = 3π/10 or θ = -3π/10.
However, since the range of the arcsine function is [-π/2, π/2], only the angle in that range that satisfies the equation is θ = 3π/10.
Therefore, we can write:
arcsin(sin(-57π/10)) = arcsin(sin(3π/10)) = 3π/10
The answer is 3π/10.
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stretch your thinking write a word problem for the following
equation. 4/5 x 1/4+ 3/5=
"A recipe for chocolate chip cookies calls for 4/5 cup of sugar per batch. If a baker wants to make 3 batches of cookies, and only has 1/4 cup of sugar left in the pantry, how much additional sugar will the baker need to buy?" is an example of a word problem for the given equation.
To solve this word problem, we can use the equation 4/5 x 1/4 + 3/5 = to find out how much sugar is needed for one batch of cookies, and then multiply that amount by 3 to get the total amount of sugar needed for 3 batches.
The first part of the equation, 4/5 x 1/4, represents the amount of sugar needed for one batch of cookies, which is 1/5 cup. Adding the remaining 3/5 cup of sugar needed for the recipe gives a total of 4/5 cup of sugar per batch.
To find out how much additional sugar the baker needs to buy, we can multiply 4/5 by 3 (the number of batches), and then subtract the amount of sugar already in the pantry (1/4 cup). This gives us:
4/5 x 3 - 1/4 = 12/5 - 1/4 = 43/20
Therefore, the baker will need to buy 43/20 cups of additional sugar to make 3 batches of chocolate chip cookies.
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A basketball coach wants to purchase shooting shirts for each member of a basketball team.
The cost of shooting shirts can be represented by the equation C = 0. 2x^2 + 1. 6x + 15, where
C is the amount it cost to purchase x shooting shirts. How many shooting shirts can the
basketball coach order for $300?
C = 2x? + 1. 6x + 15
The basketball coach can order approximately 34 shooting shirts for $300.
To determine the number of shooting shirts the basketball coach can order for $300, we need to solve the equation C = 0.2x^2 + 1.6x + 15, where C represents the cost and x represents the number of shooting shirts.
The equation is given as C = 0.2x^2 + 1.6x + 15.
To find the number of shooting shirts for $300, we set the cost C equal to 300 and solve for x:
0.2x^2 + 1.6x + 15 = 300
0.2x^2 + 1.6x + 15 - 300 = 0
0.2x^2 + 1.6x - 285 = 0
Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
For this equation, a = 0.2, b = 1.6, and c = -285. Plugging in these values into the quadratic formula:
x = (-1.6 ± sqrt(1.6^2 - 4 * 0.2 * -285)) / (2 * 0.2)
Simplifying the equation further:
x = (-1.6 ± sqrt(2.56 + 228)) / 0.4
x = (-1.6 ± sqrt(230.56)) / 0.4
x = (-1.6 ± 15.18) / 0.4
Now we have two solutions:
x1 = (-1.6 + 15.18) / 0.4 = 33.95
x2 = (-1.6 - 15.18) / 0.4 = -44.95
Since the number of shooting shirts cannot be negative, we discard the negative solution.
Therefore, the basketball coach can order approximately 34 shooting shirts for $300.
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Prepare the operating activities section of the statement of cash flows for peach computer using the indirect method. (list cash outflows and any decrease in cash as negative amounts.)
Cash outflows and decreases in cash are reported as negative amounts in the operating activities section of the statement of cash flows for Peach Computer using the indirect method.
How to prepare the operating activities section of the statement of cash flows for Peach Computer using the indirect method?The operating activities section of the statement of cash flows for Peach Computer using the indirect method would include the following cash inflows and outflows:
Cash inflows:
Sales revenue from the sale of computersCash received from customers for computer repairs and servicesInterest received on loans or investmentsCash outflows:
Payments to suppliers for inventory purchasesPayments to employees for salaries and wagesPayments for operating expenses such as rent, utilities, and advertisingPayments of income taxesPayments of interest on loansPayments to creditors for accounts payableAny decrease in cash would be represented as negative amounts in this section.
It's important to note that the specific amounts and details would vary based on Peach Computer's individual financial transactions and operations. The operating activities section provides a summary of the cash inflows and outflows directly related to the company's core business operations during the specified period.
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The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are given in the table.
A 2-column table with 9 rows. Column 1 is labeled Weight (x) with entries 8, 12, 18, 24, 30, 32, 35, 37, 40. Column 2 is labeled Height (y) with entries 22, 23, 26, 30, 32, 33, 35, 36, 38.
Using technology, what is the correlation coefficient?
–0. 997
–0. 503
0. 503
0. 997
The correlation coefficient using technology is 0.997.
Using the given data in the table, the correlation coefficient can be calculated using technology, such as a statistical calculator or spreadsheet software.
Using python
import numpy as np
# Input the data
weight = np.array([8, 12, 18, 24, 30, 32, 35, 37, 40])
height = np.array([22, 23, 26, 30, 32, 33, 35, 36, 38])
# Calculate the correlation coefficient
correlation_coefficient = np.corrcoef(weight, height)[0, 1]
# Print the correlation coefficient
print("Correlation Coefficient:", correlation_coefficient)
The out put will be
Correlation Coefficient: 0.997088376189
The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, in this case, weight (x) and height (y) of a child.
Upon calculating, the correlation coefficient (r) is approximately 0.997. This indicates a strong positive linear relationship between the child's weight and height over the two-year period.
Corelation shows dependency of x on y variable and vice versa.
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If 4:15=a:2 1/2(two and a half), what is the value of a
The value of 'a' is 2/3.
What is the value of 'a' if the ratio of 4 to 15 is equivalent to the ratio of 'a' to 2 1/2?The problem presents a ratio, 4:15, that is equal to a ratio involving 'a' and 2 1/2. To solve for 'a', we need to isolate it on one side of the equation by cross-multiplying.
In the first step, we convert 2 1/2 to an improper fraction, 5/2, so that we can use it in the equation. We then cross-multiply by multiplying both sides of the equation by 5/2.
This eliminates the denominator on the right-hand side and simplifies the left-hand side.
Solve for 'a'
To solve for 'a', we can use cross-multiplication.
First, we need to convert 2 1/2 to an improper fraction:
2 1/2 = 5/2
Now we can write the equation as:
4/15 = a/(5/2)
To solve for 'a', we cross-multiply:
4/15 * 5/2 = a
a = 2/3
Finally, we solve for 'a' by multiplying 4/15 by 5/2 and simplifying the result. The answer is 2/3, which represents the value of 'a'.
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Find the measure of arc AD
90 + 63 = 153
this is because the pink square means that degree is 90°
3. Jumal and Jabari are helping Jumal's father with a construction project. He needs to build a triangular frame as a piece to be used in the whole project, but he has not been given all the information he needs to cut and assemble the sides of the frame. He is even having a hard time envisioning the shape of the triangle from the information he has been given. Here is the information about the triangle that Jumal's father has been given.
Side a 10.00 meters
Side b= 15.00 meters
Angle A = 40.0°
Jumal's father has asked Jumal and Jabari to help him find the measure of the other two angles and the missing side of this triangle. Carry out each student's strategy as described below. Then draw a diagram showing the shape and dimensions of the triangle that Jumal's father should construct.
The triangles created using the law of sines and the law of cosines for Jumal's approach and Jabari's approach are attached
What is the Law of Sines?The Law of Sines states that the ratio of a sine of an angle to the length of the side facing the angle is the same for the three sides of the triangle.
Jumal's approach
a. The measure of the angle B can be found as follows;
sin(40)/10 = sin(B)/15
B = 15 × arcsine(sin(40)/10) ≈ 74.6°
b. The measure of angle C can be found using the angle sum property of a triangle as follows;
∠C = 180 - (40 + 74.6) = 65.4°
c. The length of the side c is therefore;
sin(40)/10 = sin(65.4)/c
c = sin(65.4) × 10/sin(40) ≈ 14.1
The length of the side c is about 14.1 meters
The triangle can be obtained by using the specified and obtained dimensions as shown in the attached drawing
Jabari's Approach
a. The Law of Cosines indicates; a² = b² + c² - 2·b·c·cos(A)
Therefore;
100 = 225 + c² - 2 × 15 × c × cos(40)
10² = 15² + c² - 23·c
c² - 23·c + 125 = 0
c = (23 ± √(29))/2
c = 14.2 and 8.8
c. Please find attached then possible drawings based on the calculated dimensions, created with MS Word
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6
The expression √532 + 46√3 is equivalent to the expression r + p, where r and p are positive
integers. What is the value of r + p?
The value of r+p in the expression is 2(√133 + 23√3)
To simplify the given expression, we need to first simplify the square root of 532.
We can factor 532 as 2 × 2 × 7 × 19, and then group the factors in pairs of two to simplify the square root:
√532 = √(2 × 2 × 7 × 19) = √(2 × 2) × √(7 × 19)
= 2√(7 × 19)
= 2√133
Now we can substitute this expression into the original expression and combine like terms:
√532 + 46√3
= 2√133 + 46√3
= 2√133 + 2(23√3)
= 2(√133 + 23√3)
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Look at picture please
Based on the inequality, 24.5x > 162 + 4.25x, Trina must sell more than 8 units of the handmade vases to make a profit.
What is inequality?Inequality refers to a mathematical statement that two or more algebraic expressions are unequal or inequivalent.
Mathematically, inequalities are depicted as:
Greater than (>)Greater than or equal to (≥)Less than (<)Less than or equal to (≤)Not equal to (≠).Selling price per handmade vase = $24.50
Variable cost per unit = $4.25
Fixed selling cost = $162
Let the number of vases to sell to make a profit = x
The total sales revenue = 24.5x
The total cost = 162 + 4.25x
To make a profit, 24.5x must be greater than 162 + 4.25x.
Inequality:24.5x > 162 + 4.25x
20.25x > 162
x > 8
Check:
Total sales revenue = $196 ($24.5(8)
Total cost = $196 ($162 + $4.25(8)
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In ARST, r = 58 cm, m/S=48° and m/T=29°. Find the length of s, to the nearest
centimeter.
The value of length 's' is 44.3 cm
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
The measure of angle R = 180-( 48+29)
R = 180- 77
R = 103°
sinR/ r = sinS/s
sin103 / 58 = sin48/s
s × sin103 = 58 × sin48
s × 0.974 = 43.1
s = 43.1/0.974
s = 44.3 cm
therefore the value of length is is 44.3 cm
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Two water balloons were launched into the air at different moments and collided. The water balloons were modeled by the quadratic functions: y = −7x2 + 26x + 3 and y = −6x2 + 23x + 5, where y represents the height in meters and x represents the time in seconds after the launch. What is the time, in seconds, that the balloons collided at the highest point?
The height at x = 2 seconds is greater (25 meters), the balloons collided at the highest point at 2 seconds. We can use quadratic functions to solve this.
To find the time in seconds that the balloons collided at the highest point, we will first find the points where the balloons have the same height (y) by setting the two quadratic functions equal to each other:
-7x² + 26x + 3 = -6x² + 23x + 5
Next, we will solve for x:
x² - 3x - 2 = 0
Now, factor the quadratic equation:
(x - 2)(x - 1) = 0
The solutions for x are 1 and 2 seconds. To find the highest point of collision, we need to determine which of these times results in a greater height. Plug each value of x into one of the original equations and compare the y values:
For x = 1:
y = -7(1)² + 26(1) + 3 = 22
For x = 2:
y = -7(2)² + 26(2) + 3 = 25
The balloons collided at the highest point at 2 seconds.
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Question 4 of 15
Cryshel is mailing pillows with a total volume of 9. 5 ft3. She needs a mailing
box that has a volume greater than 9. 5 ft.
• Box A: length = 3 ft, width = 2 ft, height = 1. 5 ft
• Box B: length = 2. 5 ft, width = 2 ft, height = 2 ft
Which box is large enough to hold all of her pillows?
O
A. Neither box
B. Both box A and box B
ОО
C. Box B
D. Box A
Answer:
C. Box B
Step-by-step explanation:
You want to know which of these two boxes has a volume greater than 9.5 ft³:
Box A: 3 ft by 2 ft by 1.5 ftBox B: 2.5 ft by 2 ft by 2 ftVolumeThe volume of each box is found by multiplying its dimensions:
Box A: (3 ft)(2 ft)(1.5 ft) = 9 ft³
Box B: (2.5 ft)(2 ft)(2 ft) = 10 ft³
Only box B is large enough, choice C.
<95141404393>
A quantitative data set has mean 25 and standard deviation 2. At least what percentage of the observations lie between 19 and 31 ?
At least 95% of the observations lie between 19 and 31.
To see why, we can use Chebyshev's theorem, which states that for any data set, regardless of the shape of the distribution, at least 1 - (1/k²) of the observations lie within k standard deviations of the mean. In this case,
we want to know the percentage of observations that lie within two standard deviations of the mean, since 19 and 31 are both two standard deviations away from the mean of 25.
So, we can use k = 2 in Chebyshev's theorem, which gives us:
1 - (1/2²) = 1 - (1/4) = 0.75
Therefore, at least 75% of the observations lie within two standard deviations of the mean. However, since we know the data set is normally distributed (since we know the mean and standard deviation), we can use the empirical rule,
which states that for normally distributed data, approximately 68% of the observations lie within one standard deviation of the mean, and approximately 95% of the observations lie within two standard deviations of the mean.
Therefore, we can conclude that at least 95% of the observations lie between 19 and 31.
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HELP ASAP!!!!!!!!!!!
Answer:
25%
Step-by-step explanation:
The total number of 7th grade students = 9 + 11 + 11 + 13 = 44
Out of the 44 students 11 play bass
Probability that a seventh grader chosen at random will play the base is:
11/44 = 1/4 = 0.25
As a percentage, this would be 0.25 x 100 = 25%
can someone help me solve -2√180u²v
Answer:-12 with the weird checkmark symbol then a five inside the checkmark symbol times u squared v
Step-by-step explanation:
Find the area of the surface extending upward from the circle x^2 + y^2 = 1 in the cy-plane to the plane z = 2 - x - y.
The area of the surface is π square units.
We can use a surface integral to find the area of the surface. The surface integral of a scalar function f over a surface S is given by:
∬S f dS
In this case, we want to find the area of the surface, so f = 1, and the integral reduces to:
∬S dS
We can parameterize the surface S using cylindrical coordinates:
x = r cosθ
y = r sinθ
z = 2 - r cosθ - r sinθ
The surface S is defined by the equation x^2 + y^2 = 1, which in cylindrical coordinates is r^2 = 1. Therefore, the surface integral becomes:
∬S dS = ∫∫R ||rθ|| dr dθ
where R is the region in the rθ-plane that corresponds to the surface S.
To find the limits of integration for r and θ, we need to determine the bounds of the region R. Since r^2 = 1, we have r = 1 for all θ. The region R is therefore a circle of radius 1 centered at the origin, and we can integrate over the full range of θ:
∫0^2π ∫0^1 r dr dθ = π
Therefore, the area of the surface is π square units.
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How do you solve the cube root function of x²/³ = 16?
The cube root of the given function is [tex]x=2\sqrt[3]{2}[/tex].
The given function is x³=16.
Here, the given function can be written as
[tex]x=\sqrt[3]{16}[/tex]
[tex]x=\sqrt[3]{2\times2\times2\times2}[/tex]
[tex]x=\sqrt[3]{2^3\times2}[/tex]
[tex]x=2\sqrt[3]{2}[/tex]
Therefore, the cube root of the given function is [tex]x=2\sqrt[3]{2}[/tex].
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"Your question is incomplete, probably the complete question/missing part is:"
How do you solve the cube root function of x³=16.
A national grocery chain is considering expanding their selection of prepared meals available for purchase. They believe that nationwide, 67 percent of households purchase at least one prepared meal per week from the grocery store. The results of a survey given to a random sample of Maryland households found that 641 out of 1,035 households purchase at least one meal per week at the store
61.93% of the surveyed Maryland households purchase at least one prepared meal per week from the grocery store.
A national grocery chain is considering expanding their selection of prepared meals, and they believe that 67 percent of households purchase at least one meal per week from the grocery store. In a survey conducted in Maryland, 641 out of 1,035 households purchase at least one meal per week at the store.
To determine the percentage of Maryland households purchasing at least one prepared meal per week, follow these steps:
Divide the number of households purchasing at least one meal per week (641) by the total number of households surveyed (1,035).
Multiply the result by 100 to get the percentage.
Here's the calculation: (641 / 1,035) x 100 = 61.93%
So, 61.93% of the surveyed Maryland households purchase at least one prepared meal per week from the grocery store.
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Using a compass a ruler and a protractor draw a circle having
By using the compass a ruler and a protractor a circle having a Radius MO of 3 cm, Diameter OP of 6cm, Chord QR of 4cm, and Central angle <OMS of 60° has been Drawn.
Given data:
Radius MO = 3 cm
Diameter OP = 6cm
Chord QR = 4cm
Central angle <OMS = 60°
Steps to follow to draw the circle,
Step 1: Mark the M point as the center.
Step 2: Now take the compass and take a 3 cm reading on it by using the ruler.
Step 3: Draw the circle by using M as the center
Step 4: Mark a point O on the circle
Step 5: Draw a straight line segment OP passing through M
Step 6: Mark a point Q on the circle
Step 7: Using compass width and take a 3 cm reading on it and by taking Q as center cut the circle at R.
Step 8: Now join Q and R points.
Step 9: Using compass width and take a 3 cm reading on it and by taking O as the center cut the circle at S.
Step 10: Now join S and M points
Therefore, The circle, central angle on the circle, and chord on the circle are drawn.
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The complete question is,
1. Directions: Using a compass, ruler, and protractor, draw a circle having:
1.) M as the center
2.) radius MO of 3 cm
3.) diameter OP of 6cm
4.) chord QR of 4cm
5.) central angle:<OMS of 60°
In what time will Rs. 6350 amounts to Rs. 8255 if the simple Interest is calculated at 10% per annum ?Also, find the rate of interst if He returns in 1 1/2 years .
Therefore, it will take 3 years for Rs. 6350 to amount to Rs. 8255 at 10% per annum. Therefore, the rate of interest is 32.6% per annum if the loan is returned in 1 1/2 years.
What is interest?Interest is the amount of money that a lender charges a borrower for the use of money or assets. It is typically expressed as a percentage of the amount borrowed or invested, and is paid by the borrower to the lender as compensation for the use of the money. There are two main types of interest: simple interest and compound interest. Simple interest is calculated based on the initial amount borrowed or invested, and is paid out at regular intervals over a fixed period of time. Compound interest, on the other hand, is calculated based on the initial amount plus any accumulated interest, and is paid out at the end of the investment period.
Here,
Using the formula for simple interest:
Simple Interest = (Principal x Rate x Time) / 100
where Principal is the initial amount, Rate is the interest rate per annum, and Time is the duration of the loan in years. To find the time it takes for Rs. 6350 to amount to Rs. 8255 at 10% per annum, we can set up the equation:
8255 - 6350 = (6350 x 10 x Time) / 100
Simplifying the equation, we get:
1905 = 635 x Time
Time = 1905 / 635
Time = 3 years
To find the interest rate if the loan is returned in 1 1/2 years, we can rearrange the formula for simple interest as:
Rate = (100 x Simple Interest) / (Principal x Time)
Plugging in the values, we get:
Rate = (100 x (8255 - 6350)) / (6350 x 1.5)
Rate = 3105 / 9525
Rate = 0.326 or 32.6%
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(1 point) Evaluate the double integral I = s do xy dA where D is the triangular region with vertices (0,0),(1,0), (0,6).
To evaluate the double integral I = ∬D xy dA, where D is the triangular region with vertices (0,0),(1,0), (0,6), we need to set up the limits of integration for x and y.
Since D is a triangular region, we can integrate over the two sides that meet at the origin and then integrate over the third side. Let's integrate over the sides that form the right angle at (0,0).
For the side along the x-axis, y = 0 to y = 6x.
For the side along the y-axis, x = 0 to x = 1.
Thus, the double integral becomes:
I = ∫0^1 ∫0⁶x xy dy dx
Evaluating the inner integral with respect to y, we get:
I = ∫0^1 [x(y²/2)]0⁶x dx
Simplifying and evaluating the outer integral with respect to x, we get:
I = ∫0^1 18x⁴ dx
I = 18/5
Therefore, the value of the double integral I = ∬D xy dA over the triangular region with vertices (0,0),(1,0), (0,6) is 18/5.
To evaluate the double integral I = ∬_D xy dA for the triangular region D with vertices (0,0), (1,0), and (0,6), we first need to set up the limits of integration.
The base of the triangle lies on the x-axis, from x = 0 to x = 1. The height of the triangle lies on the y-axis, from y = 0 to the line y = 6(1-x), since the slope of the hypotenuse is -6 and passes through (1,0).
Now we can set up the integral:
I = ∬_D xy dA = ∫_(0 to 1) ∫_(0 to 6(1-x)) xy dy dx
Let's first integrate with respect to y:
∫_(0 to 6(1-x)) xy dy = [x(y²)/2]_(0 to 6(1-x)) = 18x(1-x)²
Next, integrate with respect to x:
I = ∫_(0 to 1) 18x(1-x)² dx
Using integration by substitution or expanding and integrating term by term, we get:
I = 2
So, the value of the double integral is 2.
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ķojo and kofta were given 38000 to share. kojo had 7500 more than kofta find each of their shares Show working
Answer:
Kofta receives $15,250 and Kojo receives $22,750.
Step-by-step explanation:
Let x represent the amount of money that Kofta has.
x + (x +7,500) = 38,000
- 7,500 - 7,500
___________________
x + x = 30,500
2x = 30,500
÷ 2 = ÷2
-------------------
x = 15,250
Therefore, Kofta has $15,250.
Let k represent the amount of money that Kojo has.
k + 15,250 = 38,00
k = 38,000 - 15,250
k = $22,750
Therefore, Kojo has $22,750
Line x is parallel to line y. Line z intersect lines x and y. Determine whether each statement is Sometimes True.
Answer:
Step-by-step explanation:
a and b are sometimes true.
This is when line z intersects x and y at right angles.
The base and all three faces of a triangle pyramid are equilateral triangles with side lengths of 3ft. the height of each triangle is 2.6ft. what are the lateral area and the total surface area of the triangular pyramid?
The lateral area of the triangular pyramid is 11.7 sq ft and the total surface area is 15.6 sq ft.
To find the lateral area and total surface area of the triangular pyramid with base and faces as equilateral triangles, we can follow these steps:
1: Find the area of one equilateral triangle.
To find the area of an equilateral triangle with side length 3 ft and height 2.6 ft, we can use the formula:
Area = (1/2) × base × height
Area = (1/2) × 3 × 2.6 = 3.9 sq ft
2: Calculate the lateral area.
Since the pyramid has three equilateral triangles as faces, we can multiply the area of one triangle by 3 to find the lateral area:
Lateral Area = 3 × 3.9 = 11.7 sq ft
3: Calculate the total surface area.
The total surface area includes both the lateral area and the base area. Since the base is also an equilateral triangle with the same dimensions, we can simply add the area of the base to the lateral area to find the total surface area:
Total Surface Area = Lateral Area + Base Area = 11.7 + 3.9 = 15.6 sq ft
In conclusion, the lateral area is 11.7 sq ft and the total surface area is 15.6 sq ft.
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32
{(-0. 25, 2. 5), (1. 75, -5. 5), (3. 25, -11. 5)}
Write an equation in the form of y = mx + b that represents this linear function?
Therefore, the equation in the form of y = mx + b that represents this linear function is: y = -3.2x + 0.1
To write an equation in the form of y = mx + b for a linear function, we need to find the slope (m) and the y-intercept (b).
We can use any two points from the given set of points to find the slope:
m = (y2 - y1) / (x2 - x1)
Let's use the first and second points:
m = (-5.5 - 2.5) / (1.75 - (-0.25))
m = -8 / 2.5
m = -3.2
Now, we can use the slope and one of the points to find the y-intercept:
y = mx + b
-5.5 = (-3.2)(1.75) + b
b = -5.5 + 5.6
b = 0.1
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