Use the Chain Rule to find the indicated partial derivatives. w = xy + yz + zx, x = r cos(θ), y = r sin(θ), z = rθ; âw âr , âw âθ when r = 4, θ = Ï2

Answer:

[tex]m=\frac{11}{6}[/tex]

General Formulas and Concepts:

Pre-Alg

Alg I

Step-by-step explanation:

Step 1: Define

Point (-2, 7)

Point (4, 18)

Step 2: Solve for slope m

Answer:

dkdkfdodffffdsddddddddd

you have four years 1767 dollars in account

Answer:

10

Step-by-step explanation:

so x=true/false questions

y=multiple-choice questions

2x+4y=100

2x=y

plug in 2x for y in the first equation

2x+4(2x)=100

10x=100

x=10

y=20

The total questions would include 10 true/false questions and 20 multiple-choice questions.

We have Mr. Dudley who is writing a test for his mathematics class. The test will have true/false questions worth 2 points each and multiple-choice questions worth 4 points each for a total of 100 points. He wants to have twice as many multiple-choice questions as true/false questions.

We have to determine how many true/false questions and multiple-choice questions will be on the test.

The modelling of equation is done to derive a mathematical relation among the terms defined in a mathematical statement.

According to the question -

Assume that the number of true/false questions be x.

Assume that the number of multiple-choice questions be y.

Then -

y = 2x

Points for each true/false questions - 2 points

Points for each multiple-choice questions -  4 points

Total points of test = 100 points

Now,

Model the equation on the basis of above information -

2x + 4y = 100

2x + 4 (2x) = 100

2x + 8x = 100

10x = 100

x = 10

Therefore -

y = 2x = 2 x 10 = 20

Hence, the total questions would include 10 true/false questions and 20 multiple-choice questions.

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Answer:

4/5 of 3/4 = 3/5

2/3 of 1/4 = 1/6

Step-by-step explanation:

Answer:

[tex]Length =\frac{25}{4 + \pi}[/tex] and [tex]Width = \frac{50}{4+\pi}[/tex]

Step-by-step explanation:

This question is better understood with an attachment.

See attachment for illustration.

Given

Represent Perimeter with P

[tex]P = 25ft[/tex]

Required

Determine the dimension of the rectangle that maximizes the area

First, we calculate the perimeter of the rectangular part of the window.

From the attachment, the rectangle is not closed at the top.

So, The perimeter would be the sum of the three closed sides

Where

[tex]Width = 2x[/tex]

[tex]Length = y[/tex]

So:

[tex]P_{Rectangle} = y + y + 2x[/tex]

[tex]P_{Rectangle} = 2y + 2x[/tex]

Next, we determine the circumference of the semi circle.

Circumference of a semicircle is calculated as:

[tex]C = \frac{1}{2}\pi r[/tex]

From the attachment,

[tex]Radius (r) = x[/tex]

So, we have:

[tex]C = \frac{1}{2}2\pi * x[/tex]

[tex]C = \pi x[/tex]

So, the perimeter of the window is:

[tex]P = P_{Rectangle} + C[/tex]

[tex]P =2y + 2x + \pi x[/tex]

Recall that: [tex]P = 25[/tex]

So, we have:

[tex]25 =2y + 2x +\pi x[/tex]

Make 2y the subject

[tex]2y = 25 - 2x - \pi x[/tex]

Make y the subject:

[tex]y = \frac{25}{2} - \frac{2x}{2} - \frac{\pi x}{2}[/tex]

[tex]y = \frac{25}{2} - x - \frac{\pi x}{2}[/tex]

Next, we determine the area (A) of the window

A = Area of Rectangle + Area of Semicircle

[tex]A = 2x * y + \frac{1}{2}\pi r^2[/tex]

[tex]A = 2xy + \frac{1}{2}\pi r^2[/tex]

Recall that

[tex]Radius (r) = x[/tex]

[tex]A = 2xy + \frac{1}{2}\pi x^2[/tex]

Substitute [tex]\frac{25}{2} - x - \frac{\pi x}{2}[/tex] for y in [tex]A = 2xy + \frac{1}{2}\pi x^2[/tex]

[tex]A = 2x(\frac{25}{2} - x - \frac{\pi x}{2}) + \frac{1}{2}\pi x^2[/tex]

Open Bracket

[tex]A = 2x * \frac{25}{2} - 2x * x - 2x * \frac{\pi x}{2} + \frac{1}{2}\pi x^2[/tex]

[tex]A = 25x - 2x^2 - \pi x^2 + \frac{1}{2}\pi x^2[/tex]

[tex]A = 25x - 2x^2 - \frac{1}{2}\pi x^2[/tex]

To maximize area, we have to determine differentiate both sides and set A' = 0

Differentiate

[tex]A' = 25 - 4x - \pi x[/tex]

[tex]A' = 0[/tex]

So, we have:

[tex]0 = 25 - 4x - \pi x[/tex]

Factorize:

[tex]0 = 25 -x(4 + \pi)[/tex]

[tex]-25 =-x(4 + \pi)[/tex]

Solve for x

[tex]x = \frac{-25}{-(4+\pi)}[/tex]

[tex]x = \frac{25}{4+\pi}[/tex]

Recall that

[tex]Width = 2x[/tex]

[tex]Width = 2(\frac{25}{4+\pi})[/tex]

[tex]Width = \frac{50}{4+\pi}[/tex]

Recall that:

[tex]y = \frac{25}{2} - x - \frac{\pi x}{2}[/tex]

Substitute [tex]\frac{25}{4+\pi}[/tex] for x

[tex]y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{\pi (\frac{25}{4+\pi})}{2}[/tex]

[tex]y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{\frac{25\pi}{4+\pi}}{2}[/tex]

[tex]y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{25\pi}{4+\pi} * \frac{1}{2}[/tex]

[tex]y = \frac{25}{2} - \frac{25}{4+\pi} - \frac{25\pi}{2(4+\pi)}[/tex]

[tex]y = \frac{25(4+\pi) - 25 * 2 - 25\pi}{2(4 + \pi)}[/tex]

[tex]y = \frac{100+25\pi - 50 - 25\pi}{2(4 + \pi)}[/tex]

[tex]y = \frac{100- 50+25\pi - 25\pi}{2(4 + \pi)}[/tex]

[tex]y = \frac{50}{2(4 + \pi)}[/tex]

[tex]y = \frac{25}{4 + \pi}[/tex]

Recall that:

[tex]Length = y[/tex]

So:

[tex]Length =\frac{25}{4 + \pi}[/tex]

Hence, the dimension of the rectangle is:

[tex]Length =\frac{25}{4 + \pi}[/tex] and [tex]Width = \frac{50}{4+\pi}[/tex]

Answer:

It equals pizza 3’5.42 inch

Step-by-step explanation:

ANSWER

For 739, the answer is: prime anslo written as B

Step-by-step explanation:

739 is a prime number because it has only two distinct divisors: 1 and itself (739).

HAVE A GOOD DAY!

Answer:

its neither

Step-by-step explanation:

Answer:

C would be the correct number line

Step-by-step explanation:

5x ≥ - 17 - 3

5x ≥ -20

5x/5 ≥ -20/5

x ≥ 4

Answer:

Step 2: Missy did not multiply the area of each face by 2 before adding.

Step-by-step explanation:

I took the test :)

Answer:

12 x 12 = 144, 12 x 13 = 156

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

8*3

=24

4*5

=20

20+24

=44

Step-by-step explanation:

24=3n-15 or,25+15=3n or,39=3n or,39/3=n or,n=13 therefore the value of n is 13. I think this answer is helpful for you

Answer: n = 13

Step-by-step explanation:

24=3(n-5) - First  distribute the 3 to the n and the 5. Which you would than get 3n and -15

24=3n-15 - Now add the 15 to both sides which would cause it to cancel out on the left side of the equal side.

39=3n - Now divide the 3 from 3n on both sides of the equal side.

n=13 - Once you do that you will get n = 13. That is your answer!

Answer:

Step-by-step explanation:

Step(i):-

Given equation is sin x cos x = -1/4

                           [tex]2(2sinxcosx) = -1[/tex]

we know that trigonometry formula

                             2 sin x  cos x = sin 2x

                            2 ( sin 2 x) = -1

                                sin2x = -1/2

Step(ii):-

                            sin2x =    [tex]\frac{-1}{2} = sin (\pi +\frac{\pi}{6}[/tex]

Answer:

Hey man! Just saw this and that answer is not correct! I see how you were thinking tho. Here is how it should be graphed.

Step-by-step explanation:

I have marked the correct dots in green.

Answer:

A

B

C

Step-by-step explanation:

Answer:

20

Step-by-step explanation

Answer:

The ratio of their volumes is not the same 4:1, but [tex](4:1)^3[/tex] = 64:1.

Step-by-step explanation:

Measurements in Similar Figures

In similar figures, if the ratio of any of these corresponding lengths is expressed as a:b then the ratio of the other corresponding lengths can also be expressed as a:b.

In similar figures, if the ratio of any of these corresponding lengths is expressed as a:b then the ratio of the areas can be expressed as (a:b)^2 and the ratio of the volumes can be expressed as (a:b)^3.

We are given the ratio of the sides of two similar prisms as 4:1. The ratio of their volumes is not the same 4:1, but [tex]\mathbf{(4:1)^3}[/tex] = 64:1.

Answer:

If a graph is an Euler Circuit that mean that it can be traversed and begins and has all even verticies.  This allows you to start and stop at the same verticie.

Step-by-step explanation:

Answer:

7.64 in.

Step-by-step explanation:

The diameter of the circle whose circumference is 24 inches is 7.654 inches.

A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius).

Given:

The circumference of the circle, C = 24 inches,

Calculate the radius of the circle as shown below,

Circumference = [tex]2\pi r[/tex]

C = 2 × π r

r = 24 / 2π

r = 3.819

r = 3.82 inches

Calculate the diameter as shown below,

Diameter = 2 × r

Diameter = 2 × 3.82

Diameter = 7.639 inches

Thus, the diameter is 7.64 inches.

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Answer:

$8333.3

Step-by-step explanation:

The problem here is to find the principal that will yield an interest of $500 in a year at a rate of 6%.

   Interest  = [tex]\frac{PRT}{100}[/tex]  

P is the principal

R is the rate

T is the time

The time is 1 year;

      500  = [tex]\frac{P x 6 x 1}{100}[/tex]

           6P = 50000

             P  = [tex]\frac{50000}{6}[/tex]   = $8333.3

Answer:

1

Step-by-step explanation:

All numbers to the power of 0 are 1.

PLS GIVE BRAINLIEST

Answer:

Answer:

Well 3/4 & 5/12 are already simplified and in fraction form, if youre

looking for decimal form its gonna be .75 &.41

Step-by-step explanation:

Answer:

P(X ≥ 3) = 0.94538

Step-by-step explanation:

When flipping a coin, probability of getting a tail is p= 0.5.

Number of times flipped; n = 10

Now, this is a binomial probability distribution problem with the formula;

P(X = x) = C(n, r) × p^(x) × (1 - p)^(n - x)

Probability of getting at least 3 tails is;

P(X ≥ 3) = P(3) + P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10)

P(3) = C(10, 3) × 0.5³ × (1 - 0.5)^(10 - 3)

P(3) = 0.1172

P(4) = C(10, 4) × 0.5⁴ × (1 - 0.5)^(10 - 4)

P(4) = 0.2051

From online binomial probability calculator, we have the remaining as;

P(5) = 0.2461

P(6) = 0.2051

P(7) = 0.1172

P(8) = 0.0439

P(9) = 0.0098

P(10) = 0.00098

Thus;

P(X ≥ 3) = 0.1172 + 0.2051 + 0.2461 + 0.2051 + 0.1172 + 0.0439 + 0.0098 + 0.00098

P(X ≥ 3) = 0.94538

Answer:

$14300

Step-by-step explanation:

30% is the same as .3

They are raising 5k more to the 6k so 5000+6000= 11000

.3*11000= 3300...so the trustee is adding 3300 to the fund, making the total fund 3300+11000= $14300

Answer:  250 total kids and 140 girls

Step-by-step explanation:

%56=girls that means %44= boys  that means 110 is %44 of the number of kids is 110/44*100= 2.5*100=250kids  56%=girls that means %56 of 250 which is 140 girls