Point P is the center of the circle in the figure above. What is the value of x?

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

[tex]V = \frac{1}{3}\pi r^{2}h[/tex]

Differentiate the equation with respect to time t, such that

[tex]\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)[/tex]

[tex]\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)[/tex]

To differentiate the product,

Let r² = u, so that

[tex]\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)[/tex]

Then, using product rule

[tex]\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}][/tex]

Since [tex]u = r^{2}[/tex]

Then, [tex]\frac{du}{dr} = 2r[/tex]

Using the Chain's rule

[tex]\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}[/tex]

∴ [tex]\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})][/tex]

Then,

[tex]\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}][/tex]

Now,

From the question

[tex]\frac{dr}{dt} = 7 m/min[/tex]

[tex]\frac{dV}{dt} = 236 m^{3}/min[/tex]

At the instant when [tex]r = 99 m[/tex]

and [tex]V = 180 m^{3}[/tex]

We will determine the value of h, using

[tex]V = \frac{1}{3}\pi r^{2}h[/tex]

[tex]180 = \frac{1}{3}\pi (99)^{2}h[/tex]

[tex]180 \times 3 = 9801\pi h[/tex]

[tex]h =\frac{540}{9801\pi }[/tex]

[tex]h =\frac{20}{363\pi }[/tex]

Now, Putting the parameters into the equation

[tex]\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}][/tex]

[tex]236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)][/tex]

[tex]236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386][/tex]

[tex]708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}[/tex]

[tex]708 = 30790.75 \frac{dh}{dt} + 76.36[/tex]

[tex]708 - 76.36 = 30790.75\frac{dh}{dt}[/tex]

[tex]631.64 = 30790.75\frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt}= \frac{631.64}{30790.75}[/tex]

[tex]\frac{dh}{dt} = 0.021 m/min[/tex]

Hence, the rate of change of the height is 0.021 meters per minute.

Answer:

37.6%

Step-by-step explanation:

You can use find John's original earnings by taking 12% off of 5600. You can do this by doing 0.78 x 5600, and you get 4368.

Now, we can use John's orignal earning to find Musa's original earning. Knowing that their earning's correspond, you can use the proportion 5/3 = 5600/x. You can use cross products to solve:

4368 x 3 = 5x

13104 = 5x

2620.8 = x

Musa's original earnings was 2620.8.

If the sum of their new earnings is 9800, we can take of John's new earnings to find Musa's new earnings. 9800 - 5600= 4200. That means Musa's new earnings were 4200. To find the percentage, we can use the following equation, and then solve:

2620.8 = 4200x

.624 = x

That means that 2620.8 is 62.4% of 4200, and that it increased by 37.6%.

Answers:

u = 18

v = 20

========================================================

Work Shown:

The leg YZ is congruent to the left FH

This means YZ = FH and that leads to u+v-18 = 10u-8v

The hypotenuse ZX is congruent to the hypotenuse HG

This means ZX = HG and we get the equation 14v-14u+32 = v+u+22

----------------------

The system of equations we have so far is

u+v-18 = 10u-8v

14v-14u+32 = v+u+22

Let's get the equations into standard form

Start with the first equation

u+v-18 = 10u-8v

u+v = 10u-8v+18

u+v-10u+8v = 18

-9u+9v = 18

-9(u-v) = 18

u-v = 18/(-9)

u-v = -2

Note how we can solve for the variable u to get

u = v-2

which we'll use later

----------------------

Let's get the other equation into standard form as well

14v-14u+32 = v+u+22

14v-14u-v-u = 22-32

-15u+13v = -10

Now plug in u = v-2 and solve for v

-15u+13v = -10

-15(v-2) + 13v = -10

-15v+30+13v = -10

-2v+30 = -10

-2v = -10-30

-2v = -40

v = -40/(-2)

v = 20

Which means,

u = v-2

u = 20-2

u = 18

Answer:

5

Step-by-step explanation:

When dividing numbers by fractions, we can simply multiply the  umber by the reciprocal of the decimal. So,

4 ÷ 1/5 = 4 × (reciprocal of 1/5)

A reciprocal of a number is the same number written under 1. aka, 1 divided by that number, which simply is flipping the numerator and denominator of a number.

So the reciprocal of 1/5 is 5/1 = 5.

So 4 ÷ 1/5 = 4 × 5.

So your answer is 5.

hope it was useful!

Answer:

50/50 chance

Step-by-step explanation:

Simple

Answer:

50% chance likely

Step-by-step explanation:

Answer:

-2, -1, 0, 1, 2

Step-by-step explanation:

Answer:

D) x=5, x=-5.

Step-by-step explanation:

x^2-25=0

factor

(x+5)(x-5)=0

x+5=0, x-5=0,

x=0-5=-5,

x=0+5=5.

Answer:

It depends on the person mental state or past. But red often gives the person a sense of danger or fear

Step-by-step explanation:

Answer:

5:40

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

:)

Answer:

p > d

c < p

Step-by-step explanation:

Answer:

X=18, Y=6

Step by Step Explanation:

This is a little long winded.. Let's solve for Y first.

First looking at the problem, you can note a few things. First of all, there is an Isosceles triangle, and there is an equilateral triangle. Where they connect, there is a 90° angle.

Now, all equilateral triangles have the same angle measurement. 60°. Now, if you look where the right angle is, it is showing a 60° angle, a total of 90°, and an unknown area. So simply subtract. 90-60=30. Divide that by 5, and you have your answer of 6.

Now let's solve X. X is very simple. On an isosceles triangle, the two top sides are the same length. And one of the top sides is the same size as the equilateral triangle. And on equilateral triangles, all sides are the same.

So the 11 transfers over to the X side. So let's make a small equation. 11=X-7. To make it even, let's add 7 to both sides. 11+7=X+7-7. Simplify to get 18=X, which is your answer.

Answer:

X=18 y=6

Step-by-step explanation:

explain and solve

Answer:

The center circle of this question is (2,3)

Answer:

6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

10 + (-3.5) × 2 + (-9) ÷ (-3)

Step 2: Evaluate

Answer:

[tex]p=3[/tex]

Step-by-step explanation:

[tex]5p+3=18\\5p=15\\p=3[/tex]

Hope this helps plz hit the crown :D

Answer:

Are you solving for p , because if you are p = 3

Step-by-step explanation:

18 = 5p + 3

Subtract 3 from both sides

15 = 5p

Divide by 5 in both sides

p = 3

Answer:

8

Step-by-step explanation:

[tex]x - y \\ \\ = 6 - ( - 2) \\ \\ = 6 + 2 \\ \\ = 8[/tex]

You are a genius and not a stupid.

Answer:

80 ft/s

Step-by-step explanation:

Given that,

A ball is thrown vertically upward from the top of a 96-ft tower, with an initial velocity of 16 ft/sec. Its position function is given by :

[tex]s(t)=-16t^2 + 16t + 96[/tex] ...(1)

When it hits the ground, s(t) = 0

[tex]-16t^2 + 16t + 96=0\\\\t=3\ s[/tex]

At t = 3 s it will hit the fround.

We need to find its velocity when it hits the ground.

Differentiate equation (1) to find its velocity.

[tex]v=\dfrac{ds(t)}{dt}\\\\v=\dfrac{d(-16t^2 + 16t + 96)}{dt}\\\\v=-32t+16[/tex]...(2)

Put t = 3 in equation (2)

[tex]v=-32(3)+16\\\\v=-80\ ft/s[/tex]

Hence, when it will ground its velocity is 80 ft/s.

Answer:

8000

Step-by-step explanation:

7-7=0

2-2=0

6-6=0

take the 1 out of 14,000 and add that to the 4 as a ten so you get 14 and than subtract 6 to get 8

Answer:

Look for the incenter and place it there.

Step-by-step explanation:

Since there are three angles of 50°, 70° and 60°. If the designer is to place a sculpture on a round central position equidistant from all three walls, then he is looking for the incenter.

The incenter is simply the point where the bisectors of all the three angles intersect. This point is also the center of the largest circle that can be drawn inside the triangle where it touches all three sides of the triangle. Definitely, if the incenter is the middle of the circle that touches all the three sides, then the incenter will be equidistant from the three walls due to the fact that radius will always be the same in a circle.

This is why, he is to look for the incenter.

Answer:

[tex]3x^{2} -9x-30[/tex]

Step-by-step explanation:

(x - 5)(3x + 6)

[tex]3x^{2} +6x-15x-30\\3x^{2} -9x-30[/tex]

Answer:

3x² - 9x - 30

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

(x - 5)(3x + 6)

Step 2: Expand

Answer:

(0,-23)

Step-by-step explanation:

BS UDJD9AYW VS DHS EG EE S WCWVW W S FHRD DJE EHVEBE EBE

Answer:

hi

Step-by-step explanation:

hell0

Answer:

1.a

2.b

3.e

4.f

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

a

Answer:

I would say between 9 and 13

80% would be about 10 gallons and the remaining 20% would be like 3 gallons making it 13, but I don't think that it could hold more than 13 gallons, making the answer between 9 and 13

Step-by-step explanation: