Can you solve it?
find h. (system of equations)

Answer:

1.a

2.b

3.e

4.f

Step-by-step explanation:

Answer:

p > d

c < p

Step-by-step explanation:

Answer:

-2, -1, 0, 1, 2

Step-by-step explanation:

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:

The percent error of the cyclist's estimate is 5.63%

Step-by-step explanation:

Percentages

The cyclist estimates he will bike 80 miles this week, but he really bikes 75.5 miles.

The error of his estimate in miles can be calculated as the difference between his estimate and the real outcome:

Error = 80 miles - 75.5 miles = 4.5 miles

To calculate the error as a percent, we divide that quantity by the original estimate and multiply by 100%:

Error% = 4.5 / 80 * 100 = 5.625%

Rounding to the nearest hundredth:

The percent error of the cyclist's estimate is 5.63%

Answer:

45° and 12

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

(8)

The polygon has n = 8, that is 8 exterior angles, thus

exterior angle = 360° ÷ 8 = 45°

(9)

The number of sides n is

n = 360 ÷ 30 = 12

Answer:

45° 12 sides

Step-by-step explanation:

1) Every polygons interior angles is equal to 180 times two less than the amount of sides it has (i.e 180•(4-2)=360:quadrilateral) So applying that here we have eight sides so 180(8-2)=1080. Now divide that by 8 to get the measure of one angle and subtract it from 180 to get the exterior angle 45°

2) if the exterior angle is 30° then the interior angle is 150°. For this part i guess and checked but you can refer to the equation above. (180(x-2)=y/150)

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:

B because 3*3=9 And 3*1=3 so it would be 3(3y-1) foil the answer

Step-by-step explanation:

The answer is B, I took the test.

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:

5:40

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

:)

Answer:

3143

Step-by-step explanation:

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:

126

Step-by-step explanation:

72/4=18 hot dogs sold per day

18*7=126 hot dogs in a week.

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

Explanation:

The point (0,0) means x = 0 and y = 0 pair up together.

Recall that any point is always of the form (x,y).

If we plug x = 0 and y = 0 into the equation, we end up with,

y = 3x

0 = 3*0

0 = 0

We get the same thing on both sides, so we have a true equation.

Since we have a true equation, we've shown that  (0,0) is a solution.

Visually this indicates (0,0) is on the line y = 3x. Put another way, the line y = 3x goes through the origin.

Answer:

Step-by-step explanation:

true false true false

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:

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:

50/50 chance

Step-by-step explanation:

Simple

Answer:

50% chance likely

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:

[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: C. (2, -4)

Step-by-step explanation:

Take into consideration that y is less than or equal to -2. The only option in which the y value is less than or equal to -2 is option C., thus C would correctly solve the system of inequalities.

Answer:

A. 63/100

Step-by-step explanation:

100-37= 63.

Answer:

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

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

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