Find dx/dy, if x=sin^3t,y=cos^3t.

The solution to the equations obtained using inverse trigonometric function values are;

1. x ≈ 0.65

4. x ≈ 0.95

Trigonometric functions indicates the relationships between the angles in a right triangle and two of the sides of the triangle. Trigonometric functions are periodic functions.

The value of x is obtained from the inverse trigonometric function of the output value of the trigonometric function, as follows;

The inverse function for sine is arcsine

The inverse function for cosine is arccosine

The inverse function for the tangent of an angle is arctangent

1. sin(x) = 0.6051

Therefore; x = arcsine(0.6051) ≈ 0.65 radians

The value of x in the interval [0·π, 2·π] is x ≈ 0.65

4. tan(x) = 1.3972

Therefore, x = arctan(1.3972) ≈ 0.95

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Option B is correct. In this context, the meaning is: Among hot dogs with the same number of calories, the sodium content varies, with a standard deviation of about 75 milligrams

The calculated test statistic is 3.75

The test statistics can be gotten from the data that we already have available in this question

The coefficient is given as 2.235

The Standard error of the coefficient is given as 0.596

The formula used is given as

Such that t = coefficient /  Standard error

where the coefficient = 2.235

The standard error = 0.596

We have to apply the values to formula:

= 2.235 / 0.596

= 3.75

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The jar can hold 28.26 cubic inches of peanut butter

The first step is to write out the parameters

A cylindrical jar of peanut has a height of 4 inches

The diameter is 3 inches

The next step is to calculate the radius, this is done by dividing the diameter by 2

radius= 3/2

= 1.5

The formula used to calculate the cubic inches of peanut butter is

V= πr²h

= 3.14 × 1.5² × 4

= 3.14 × 2.25 × 4

= 28.26

Hence the jar can hold 28.26 cubic inches of peanut butter

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The area of the whole figure is 31.5 sq. units.

The area of a given figure connotes its expanse in a 2 dimensional plane. The shape and size of a given figure determines how to calculate its area.

From the given question, the figure given can be likened to a rhombus. So that;

area of a rhombus = (diagonal 1 * diagonal 2)/ 2

Then,

area of the figure = (diagonal 1 * diagonal 2)/ 2

where: diagonal 1 = 7.5, and diagonal 2 = 8.4

So that;

area of the figure = (7.5*8.4)/ 2

                             = 63/ 2

                             = 31.5

The area of the whole figure is 31.5 sq. units.

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To compute the direct labor rate and efficiency variances, we will use the given terms: Actual Hours (AH), Standard Hours (SH), Actual Rate (AR), and Standard Rate (SR). Here's a step-by-step explanation:

Step 1: Calculate the Actual Labor Cost
Actual Labor Cost = AH * AR

Step 2: Calculate the Standard Labor Cost
Standard Labor Cost = SH * SR

Step 3: Calculate the Labor Rate Variance
Labor Rate Variance = (AR - SR) * AH

Step 4: Classify the Labor Rate Variance
If the Labor Rate Variance is positive, it is unfavorable. If it is negative, it is favorable. If it is zero, there is no variance.

Step 5: Calculate the Standard Labor Cost for Actual Hours
Standard Labor Cost for Actual Hours = AH * SR

Step 6: Calculate the Labor Efficiency Variance
Labor Efficiency Variance = (AH - SH) * SR

Step 7: Classify the Labor Efficiency Variance
If the Labor Efficiency Variance is positive, it is unfavorable. If it is negative, it is favorable. If it is zero, there is no variance.

By following these steps, you can compute the direct labor rate and efficiency variances for the period and classify each as favorable, unfavorable, or no variance.

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The total area of the composite figure is 576 square meters

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

The composite figure

The total area of the composite figure is the sum of the individual shapes

So, we have

Surface area = Rectangle + Trapezoid

Using the area formulas, we have

Surface area = 29 * 16 + 1/2 *(14 + 18) * (36 - 29)

Evaluate

Surface area = 576

Hence. the total area of the figure is 576 square meters

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Complete question

Find the area of the polygon.

See attachment

The area of the polygon is ____ square meters.

Answer:

Step-by-step explanation:

The volume of a pyramid can be calculated using the formula:

V = (1/3) * Base Area * Height

To calculate the volume of this pyramid, we need to first find the area of its regular hexagonal base. The formula for the area of a regular hexagon is:

A = (3√3/2) * s^2

where s is the length of one side of the hexagon. Substituting s = 10, we get:

A = (3√3/2) * 10^2 = 259.80 square units (approx)

Now we can use the formula for the volume of a pyramid to find the volume of this pyramid:

V = (1/3) * 259.80 * 12 = 1039.20 cubic units (approx)

Therefore, the approximate volume of the pyramid is 1039.20 cubic units.

Answer:

m = -2

Step-by-step explanation:

We Know

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (-3,2) (-2,0)

We see the y decrease by 2, and the x increase by 1, so the slope is

m = -2

Answer:

Step-by-step explanation:

The Pythagorean theorem has the formula a squared(leg) + b squared(leg) = c squared(longest leg). This means [tex]12^{2} +16^{2} =20^{2} -- > 144+256=400[/tex] which is true meaning number 1 is a right triangle. [tex]10^{2} +49.5^{2} = 50.5^{2} -- > 100+2450.25=2550.25[/tex] is true meaning number 2 is also a right triangle because the sum of the shortest legs squared are equal to the longest leg (hypotenuse) squared.

The radius of the base of the cone is approximately 12.65 feet if The cone is formed from 3,200 ft of gravel.

Height of cone =  24 feet

The volume of the cone = [tex]3,200 ft^3[/tex]

To find the volume of the cone, the formula used here is:

V =π* [tex]r^2h[/tex]

Here, the values of V and H are known terms. we need to calculate the radius r of the cone.

π = 3.14 constant value

Substituting the values in the above equation, we get:

[tex]3,200 = (1/3)^2*(24)*[/tex] π

[tex]r^2[/tex]= 3,200 / (8π)

[tex]r^2[/tex] = 400 / π

r = 12.65

Therefore, we can conclude that the radius of the base of the cone is  12.65 feet.

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The credit card's effective interest rate for the year is [tex]40.51%.[/tex]%

We can use the following formula:

Effective annual interest rate is calculated as[tex](1 + APR/365)365 - 1.[/tex]

The interest is compounded everyday in this case and the APR is 33.01 percent. When we enter these values into the formula, we obtain:

Effective annual interest rate =[tex](1 + 0.3301/365)^365 - 1[/tex]

Effective annual interest rate =[tex]1.4051 - 1[/tex]

Effective annual interest rate =[tex]1.4051 - 1[/tex]

So the credit card's effective interest rate for the year is[tex]40.51%.[/tex]%

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The area enclosed by the circle is given as 7494.12 m² and the mistake Frank have made is he subtracted the area of the square and the area of 4 semi-circles.

We are given that the figure is made by attaching semicircles to each side of a 54 dash m​-by-54 dash m square. Frank says the area is 1 comma 662.12 m squared.

We have to find the error made by Frank,

Area of the square = Side of the square x Side of the square

In the question; the side of the square given is 54 m and this would also be the diameter of the semicircle attached to each side of a square.

So, the radius of the semicircle = diameter /2  = 54/2 = 27 m

Now, the area of the square = 54 x 54 = 2916 m².

Also, the area of the semi-circle = [tex]\frac{\pi r^2}{2}[/tex] = [tex]\frac{3.14*27^2}{2}[/tex] = 1144.53 m² .

As there are a total of 4 semi-circles attached to the square, so the area of all the 4 semi-circles = 4 x 1144.53  = 4578.12

Now, the total area of the figure = Area of the square + Area of 4 semi-circles

                = 2916 + 4578.12

                = 7494.12 m².

The error made by Frank was that he subtracted the area of the square and the area of 4 semi-circles to find the area of the whole figure as (4578.12  - 2916  = 1662.12 ).

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Complete question:

Frank needs to find the area enclosed by the figure. The figure is made by attaching semicircles to each side of a 54 m​-by-54 m square. Frank says the area is 1662.12 meter squared. Find the area enclosed by the figure. Use 3.14 for pi. What error might Frank have​ made?

Yes, all three triangles RQS, QSR, and PRS are similar to triangle PQR.

Congruency of triangles refers to the condition in which two or more triangles have the same size and shape. In other words, if two or more triangles have congruent sides and angles, then they are said to be congruent.

The criteria for determining the congruency of triangles are based on the properties of sides and angles. There are various ways to show that two triangles are congruent, including the following:

Side-Side-Side (SSS) Congruence: If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

Side-Angle-Side (SAS) Congruence: If two sides and the angle between them in one triangle are equal to two sides and the angle between them in another triangle, then the two triangles are congruent.

Angle-Side-Angle (ASA) Congruence: If two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, then the two triangles are congruent.

Angle-Angle-Side (AAS) Congruence: If two angles and a side not between them in one triangle are equal to two angles and the corresponding side not between them in another triangle, then the two triangles are congruent.

Hypotenuse-Leg (HL) Congruence: If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Yes, all three triangles RQS, QSR, and PRS are similar to triangle PQR.

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Jacob's bean sprout grew 3.9 centimeters during the week.

What is measurements?

Measurements in math involve the assignment of numerical values to physical quantities, such as length, area, volume, mass, time, temperature, and so on. Measuring objects or events allows us to compare and quantify them, and is an essential part of mathematical problem-solving, as well as many other fields of study

Jacob's bean sprout grew 42 millimeters - 3 millimeters = 39 millimeters during the week.

To convert millimeters to centimeters, we need to divide by 10 since there are 10 millimeters in 1 centimeter.

So, the growth in centimeters is 39 millimeters ÷ 10 = 3.9 centimeters.

Therefore, Jacob's bean sprout grew 3.9 centimeters during the week.

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Answer:

Step-by-step explanation:

Let the three-digit number be represented as $abc$, where $a$ is the hundreds digit, $b$ is the tens digit, and $c$ is the units digit.

From the problem, we have two equations:

Equation 1: $2a=b+2$

Equation 2: $c=3a$

We can use these equations to solve for $a$, $b$, and $c$.

Starting with Equation 1, we can isolate $b$ to get $b=2a-2$.

Next, we can substitute Equation 2 into Equation 1 to get $2a=3a-6+2$, which simplifies to $a=8$.

Using this value of $a$, we can now find $b$ and $c$. From Equation 2, we have $c=3a=24$. And from Equation 1, we have $b=2a-2=14$.

Thus, the original three-digit number is $abc=824$.

When we reverse the digits to get $cba=428$, we increase the number by 594, so we have $cba=abc+594=824+594=1418$.

Therefore, the answer is $\boxed{824}$.

The probability that Sam will get a parking ticket given that he has to park in a no-parking zone on Monday is approximately 0.1308 or 13.08%.

We can use Bayes' theorem to solve this problem. Let A be the event that Sam gets a parking ticket and B be the event that Sam parks in a no-parking zone. Then, we want to find P(A|B), which is the conditional probability of A given B.

Bayes' theorem states that P(A|B) = P(B|A)*P(A)/P(B), where P(B|A) is the probability of B given A, P(A) is the prior probability of A, and P(B) is the prior probability of B.

From the problem, we know that P(A) = 0.07, P(B|A) = 1 (since if Sam parks in a no-parking zone, he will definitely get a parking ticket), and P(B|not A) = 0.50 (since if Sam finds a legal parking space, he has a 0.50 probability of parking in a no-parking zone).

To find P(B), we can use the law of total probability, which states that P(B) = P(B|A)*P(A) + P(B|not A)*P(not A), where P(not A) = 1 - P(A).

Therefore, P(B) = 10.07 + 0.50(1-0.07) = 0.5351.

Finally, we can use Bayes' theorem to find P(A|B):

P(A|B) = P(B|A)P(A)/P(B) = 10.07/0.5351 ≈ 0.1308.

Therefore, the probability that Sam will get a parking ticket given that he has to park in a no-parking zone on Monday is approximately 0.1308 or 13.08%.

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The surface integral of the dot product between the vector field F = 3i + 3j + 4k and the unit normal vector of the surface S is equal to zero.

To use Stokes' theorem to find the flux of the vector field F = 3i + 3j + 4k across the surface S, which is the part of the plane 3x + 2y + z = 1 in the first octant and oriented upward.

Stoke's theorem statement is “the surface integral of the curl of a function over the surface bounded by a closed surface will be equal to the line integral of the particular vector function around it.” Stokes theorem gives a relation between line integrals and surface integrals.

First, we need to parametirize the curve C that bounds the surface S. Since S is in the first octant, x, y, and z are all non-negative.

The boundary C consists of three line segments: (i) from (0, 0, 0) to (1/3, 0, 0), (ii) from (1/3, 0, 0) to (0, 1/2, 0), and (iii) from (0, 1/2, 0) to (0, 0, 0). Next, calculate the curl of F, which is the cross product of the del operator and F:
curl(F) = (∂Fz/∂y - ∂Fy/∂z)i - (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k = (0 - 0)i - (0 - 0)j + (0 - 0)k = 0.

Since curl(F) = 0, the line integral of F over C is also 0.

According to Stokes' theorem, the flux of F across S equals the line integral of F over C, which we found to be 0.

Therefore, the flux of the vector field F = 3i + 3j + 4k across the surface S is 0.

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To compare Ralph's and Frank's t-shirt companies, let's calculate the total cost of buying a certain number of t-shirts from each company.

1. Ralph's t-shirt company:

- Price per t-shirt: $5.00

- Shipping and design fee: $20.00

Total cost for Ralph's t-shirts = (number of t-shirts * $5.00) + $20.00

2. Frank's t-shirt company:

- Price per t-shirt: $10.00

- No additional fees

Total cost for Frank's t-shirts = number of t-shirts * $10.00

Now you can compare the total costs for each company depending on the number of t-shirts you want to buy.

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The limiting frictional force depends only on:

First, we need to find the total number of parts in the ratio 1:4:5:

1 + 4 + 5 = 10

This means that the string is divided into 10 equal parts. To find the length of each part, we divide the total length of the string by the number of parts:

80 cm ÷ 10 = 8 cm

Now, we can find the length of the longest piece, which is 5 times the size of each part:

8 cm x 5 = 40 cm

Therefore, the length of the longest piece is 40 cm.

Unfortunately, I cannot provide an answer to this question as it is incomplete. The given information ∫f(t)dt is not enough to determine the value of f(log e 5). More information about the function f would be needed, such as its explicit form or additional properties. Please provide more context or information to help me answer your question accurately.
Given that f is a function f:R → R that satisfies ∫f(t)dt, we need to find the value of f(log e 5).

By definition, log e 5 is the natural logarithm of 5, which can be written as ln(5). Therefore, we want to find the value of f(ln(5)).

However, without further information on the function f or the integral bounds, it's not possible to determine the exact value of f(ln(5)). Please provide more details about the function or the integral to get a specific answer.

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The function has a local maximum at x = -√(2/7) with value -3√14 and a local minimum at x = √(2/7) with value 3√14.

To find the local maximum and minimum of the function f(x) = 2x + 7x⁻¹, we need to find the critical points of the function and then use the second derivative test to determine if they are local maxima or minima.

First, we find the derivative of f(x):

f'(x) = 2 - 7x⁻²

Setting f'(x) = 0, we get:

2 - 7x⁻² = 0

Solving for x, we get:

x = ±√(2/7)

Next, we compute the second derivative of f(x):

f''(x) = 14x⁻³

At x = ±√(2/7), we have:

f''(±√(2/7)) = ±∞

Since f''(±√(2/7)) has opposite signs at the critical points, ±√(2/7), we conclude that f(x) has a local maximum at x = -√(2/7) and a local minimum at x = √(2/7).

To find the values of the local maximum and minimum, we plug them into the original function:

f(-√(2/7)) = 2(-√(2/7)) + 7/(-√(2/7)) = -3√14

f(√(2/7)) = 2(√(2/7)) + 7/(√(2/7)) = 3√14

Therefore, the function has a local maximum at x = -√(2/7) with value -3√14 and a local minimum at x = √(2/7) with value 3√14.

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Hi! I'd be happy to help you create a stem and leaf plot using the provided set of data for US History class test scores.

Step 1: Arrange the data in ascending order.

54, 56, 62, 65, 66, 70, 72, 72, 74, 85, 85, 88, 88, 88, 90, 91, 92, 97, 99

Step 2: Determine the range of the data.

The data ranges from 50s to 90s, so we will need 5 stems: 5, 6, 7, 8, and 9.

Step 3: Create the stem and leaf plot using the stems and corresponding leaves (the units digits of the data).

5 | 4 6
6 | 2 5 6
7 | 0 2 2 4
8 | 5 5 8 8 8
9 | 0 1 2 7 9

Here is the completed stem and leaf plot for the US History class test scores. The stems represent the tens digits (50s, 60s, 70s, 80s, 90s), and the leaves represent the units digits of the scores in each range.

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The mean is 7

The median is the middle value, which is 7.

Mean Absolute Deviation: 2

Step 3: Find the absolute deviation of each value from the mean:

|4-7.067|, |5-7.067|, |8-7.067|, |12-7.067|, |10-7.067|, |6-7.067|, |7-7.067|, |9-7.067|, |8-7.067|, |8-7.067|, |6-7.067|, |6-7.067|, |4-7.067|, |3-7.067|, |9-7.067|

These absolute deviations are: 3.067, 2.067, 0.933, 4.933, 2.933, 1.067, 0.067, 1.933, 0.933, 0.933, 1.067, 1.067, 3.067, 4.067, 1.933.

Step 4: Find the mean of these absolute deviations to find the mean absolute deviation:

Mean Absolute Deviation = (3.067+2.067+0.933+4.933+2.933+1.067+0.067+1.933+0.933+0.933+1.067+1.067+3.067+4.067+1.933) / 15 = 2

Step 5: Find the absolute deviation of each value from the median:

|4-8|, |5-8|, |6-8|, |6-8|, |6-8|, |7-8|, |8-8|, |8-8|, |8-8|, |9-8|, |9-8|, |10-8|, |12-8|, |8-8|, |3-8|

These absolute deviations are: 4, 3, 2, 2, 2, 1, 0, 0, 0, 1, 1, 2, 4, 0, 5.

Therefore, the absolute deviation from the median is 5.

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The values of the inverse trigonometric functions are 72°, 76° and 85°.

The range of the inverse trigonometric function is limited to a certain interval based on the domain of the original trigonometric function.

Its also important to identify the trigonometric ratio that corresponds to the given value.

The value on degree for inverse of sin (2/3) will be 41.81° which is 42°. Also, inverse of tan(4) is 76° using the calculator.

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Use a calculator to find the values of the inverse trigonometric functions. Round to the nearest degree.

inverse of sin (2/3)

inverse of tan(4)

inverse of tan (0.1)

The only even function among the given options is g(x) = 2x^2, so the answer is B) g(x) = 2x^2.

A function is even if it satisfies the property g(-x) = g(x) for all x.

Checking each of the given functions:

g(x) = (x - 1)^2 is not even, because g(-x) = (-x - 1)^2 = x^2 + 2x + 1, which is not equal to g(x) = (x - 1)^2.

g(x) = 2x^2 is even, because g(-x) = 2(-x)^2 = 2x^2 = g(x) for all x.

g(x) = 4x^2 is even, because g(-x) = 4(-x)^2 = 4x^2 = g(x) for all x.

g(x) = 2x is odd, because g(-x) = 2(-x) = -2x = -g(x) for all x.

Therefore, the only even function among the given options is g(x) = 2x^2, so the answer is B) g(x) = 2x^2.

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Answer:

A

Step-by-step explanation:

Simple interest gains interest only on the principal sum and so each year has the same interest. So, this example is not simple interest. Compound interest is calculated on the principal and the accumulated interest of the previous years. So, this is compound interest.

      Interest is 4%.

      [tex]A = P*(1 + R \%)^n[/tex]

Here A is the amount we receive after n years, P is the principal and R is the rate of interest.

        A = $1300 , R = 4%

            [tex]1300 = P * (1+0.04})\\\\1300 = P * 1.04\\\\\dfrac{1300}{1.04}=P\\\\\\\dfrac{130000}{104}=P[/tex]

            P = $ 1250

In the formula [tex]A(t) = Pe^{rt}[/tex] continuously compound interest P, r, and t stands for Principal, rate of interest, and time respectively, and A(t) stands for Amount after t amount of time.  If $200 is invested at an interest rate of 4% compounded continuously, then the amount after 3 years is $225.5.

The formula for Compound Interest at a continuous period of time is denoted by [tex]A(t) = Pe^{rt}[/tex]

where the Principal amount is multiplied by the exponential value of the interest rate and time passed.

Hence we are given here

P = $200, r = 4% = 0.04, and the amount to be calculated for t = 3 years

Hence we will find the amount by replacing these values to get

A(3) = 200 × e⁰°⁰⁴ ˣ ³

= $200 × e⁰°¹²

= $225.499

rounding it off to the nearest cent gives us

$225.5

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Correct Question

In the formula [tex]A(t) = Pe^{rt}[/tex] continuously compound interest P, r, and t stands for ______ , _______ , and __________ respectively, and A(t) stands for _______ .

So if $200 is invested at an interest rate of 4% compounded continuously, then the amount after 3 years is $__________. (Round your answer to the nearest cent.)

Using the Perpendicular Bisector Theorem, the distance from third base to home plate is 90 feet. This means that all the bases are equidistant from home plate, which is a fundamental property of a baseball diamond.

To find the distance from third base to home plate, we need to use the Perpendicular Bisector Theorem, which states that if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

First, we draw a baseball diamond with points A, B, C, and D labeled as described in the problem.

Next, we draw the line segment that joins first base (B) and third base (D), and we construct the perpendicular bisector of this segment by drawing a line through the midpoint of BD and perpendicular to BD. Let's label the point where the perpendicular bisector intersects the line that connects home plate (A) and second base (C) as E.

Since E lies on the perpendicular bisector of BD, it is equidistant from B and D. We know that first base (B) is 90 feet from home plate (A), so the distance from home plate to E must also be 90 feet. Therefore, the distance from third base (D) to home plate (A) is also 90 feet.

In conclusion, using the Perpendicular Bisector Theorem, we determined that the distance from third base to home plate is 90 feet.

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