-2√ 20 + 3√ -18

I need help with the steps pls

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:

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:

[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

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:

Yes, (-3,9) makes the equation of y = -3x true

Step-by-step explanation:

y = -3x     (-3,9)

9 = -3(-3)

9 = 9

TRUE

Answer:

Move convo here

Step-by-step explanation:

Answer:

5:40

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

:)

Answer:

8

Step-by-step explanation:

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

You are a genius and not a stupid.

Answer:

50/50 chance

Step-by-step explanation:

Simple

Answer:

50% chance likely

Step-by-step explanation:

Answer:

-16

Step-by-step explanation:

3/4 = 0.75

0.75 x -16 = -12

Answer:

56.25 B (haha troll go brrr)

Step-by-step explanation:

the ratio of the triangle measurements are:

60/45=75/x

60x=3375

x=56.25, therefore the distance of the new bridge is 56.25

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:

no se

Step-by-step explanation:

The coordinate of the midpoint joining the two houses, since each unit on the coordinate is 50 units is (150, 250) and the distance walked to school is 254.95 yards

From the graph given :

The x - coordinate of the midpoint is 3 units from the origin = (3 × 50) = 150 yards

The y-coordinate of the midpoint is 5 units from the origin = (5 × 50) = 250 yards

Hence, the coordinate of the midpoint is (150, 250)

The distance walked to school :

Distance = √(y2 - y1)² + (x2 - x1)²

Distance = √(400 - 150)² + (300 - 250)²

Distance = √250² + 50²

Distance = 254.95 yards

Therefore, the distance the boys walk to school is 254.95 yards.

Learn more : https://brainly.com/question/20226272

Answer:

D I belive

Step-by-step explanation:

Answer:

i think its a

Step-by-step explanation:

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

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%.

Answer:

hi

Step-by-step explanation:

hell0

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:

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:

[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:

-2, -1, 0, 1, 2

Step-by-step explanation:

Answer:

p > d

c < p

Step-by-step explanation:

Answer:

the answer is d(<a=<b)

Step-by-step explanation:

because alternate interior angles are equal

Answer:

(0,-23)

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:

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