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3 years ago

18.) A cylinder and a cone have the same radius and the same volume. How do the heights compare?

Mathematics

1 answer:

mart [117]3 years ago

6 0

Answer:

If a cone and a cylinder have the same base and the same height, then the volume of the cone is of the volume of the cylinder. For example, the cylinder and cone shown here both have a base with radius 3 feet and a height of 7 feet. The cylinder has a volume of cubic feet since .

Step-by-step explanation:

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A rocket is launched vertically from the ground with an initial velocity of 64. ft/sec Write a quadratic function that shows the

SpyIntel [72]

Answer:

a. s = 64t - 16t²

a. maximum height = 64 ft

b. time it took to reach maximum height = 2 s

c. total time it spent in the air = 4 s

Step-by-step explanation:

a. Using Newton's third equation of motion under gravity, s = ut - 1/2gt² where s = vertical height of rocket, t = time, u = initial velocity of rocket = 64 ft/s and g = acceleration due to gravity = 32 ft/s².

So, s = 64t - 1/2(32)t² = 64t - 16t²

The equation is thus s = 64t - 16t²

b. The maximum height is obtained when ds/dt = 0

ds/dt = d[64t - 16t²]/dt = 64 - 32t

64 - 32t = 0

32t = 64

t = 64/32 = 2 s

Substituting t = 2 into s, we have

s = 64(2) - 16(2)² = 128 - 64 = 64 ft

c. The amount tot time it took to reach maximum height is 2 s

d. The amount of time it was in the air is obtained when s = 0

s = 0 ⇒

64t - 16t² = 0

16t(4 - t) = 0

16t = 0 or 4 - t = 0

t = 0 or t = 4

So the rocket spends 4 s in the air.

The values of the different variable for a, b,c and d are indicated in the graph.

The point (2,64) indicated the time for maximum height 2 s and maximum height 64 ft.

The point (4,0) indicates the total time spent in the air 4 s

6 0

3 years ago

Please help!

horsena [70]

Answer:

Step-by-step explanation:

Part A,

99% sure this is D

Part B

It's probably about 4 feet tall.

Part C,

4 in. x 12 in.

2 in. x 24 in.

8 in. x 6 in.

3 in. x 16 in.

3 0

3 years ago

Read 2 more answers

If an island's only residents are penguins and bears, and if there are 21 heads and 50 feet on the island, how many penguins and

Ugo [173]

Answer:

The number of penguins on the island is 17 and the number of bears on the island is 4.

Step-by-step explanation:

We are given that an island's only residents are penguins and bears, and if there are 21 heads and 50 feet on the island.

Let the number of penguins on the island be 'x' and the number of bears on the island be 'y'.

Also, we know that bears and penguins both have one head, and the bear has 4 feet and the penguin has 2 feet.

So, according to the question;

The first condition states that there are 21 heads, that means;

x + y = 21

x = 21 - y ---------------- [equation 1]

The second condition states that there are 50 feet on the island, that means;

2x + 4y = 50

x + 2y = 25

21 - y + 2y = 25 {from equation 1}

y = 25 - 21

y = 4

Now, putting the value of y in equation 1, we get;

x = 21 - y

x = 21 - 4 = 17

Hence, the number of penguins on the island is 17 and the number of bears on the island is 4.

4 0

4 years ago

Marcus wrote an expression equivalent to 7(x+8). Liz wrote a different expression that has the same value as Marcus’ expression

Liono4ka [1.6K]

Try the app Gauthmath!!

5 0

3 years ago

Identify the standard form of the equation by completing the square.

OLEGan [10]

Answer:

$\dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1$

Step-by-step explanation:

Given equation:

$4x^2-9y^2-8x+36y-68=0$

This is an equation for a horizontal hyperbola.

To complete the square for a hyperbola

Arrange the equation so all the terms with variables are on the left side and the constant is on the right side.

$\implies 4x^2-8x-9y^2+36y=68$

Factor out the coefficient of the x² term and the y² term.

$\implies 4(x^2-2x)-9(y^2-4y)=68$

Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:

$\implies 4\left(x^2-2x+\left(\dfrac{-2}{2}\right)^2\right)-9\left(y^2-4y+\left(\dfrac{-4}{2}\right)^2\right)=68+4\left(\dfrac{-2}{2}\right)^2-9\left(\dfrac{-4}{2}\right)^2$

$\implies 4\left(x^2-2x+1\right)-9\left(y^2-4y+4\right)=36$

Factor the two perfect trinomials on the left side:

$\implies 4(x-1)^2-9(y-2)^2=36$

Divide both sides by the number of the right side so the right side equals 1:

$\implies \dfrac{4(x-1)^2}{36}-\dfrac{9(y-2)^2}{36}=\dfrac{36}{36}$

Simplify:

$\implies \dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1$

Therefore, this is the standard equation for a horizontal hyperbola with:

center = (1, 2)
vertices = (-2, 2) and (4, 2)
co-vertices = (1, 0) and (1, 4)
$\textsf{Asymptotes}: \quad y = -\dfrac{2}{3}x+\dfrac{8}{3} \textsf{ and }y=\dfrac{2}{3}x+\dfrac{4}{3}$
$\textsf{Foci}: \quad (1-\sqrt{13}, 2) \textsf{ and }(1+\sqrt{13}, 2)$

4 0

2 years ago