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3 years ago

The height h, in feet of a model rocket t seconds after launch is given

Mathematics

1 answer:

Illusion [34]3 years ago

7 0

Answer:

h_max = 324.09 ft

Step-by-step explanation:

The correct equation is;

h = 245t - 16t²

We are told that as the rocket descends, it deploys

a recovery parachute when it reaches 325 feet above the ground.

Thus;

245t - 16t² = 325

Thus;

16t² - 245t + 325 = 0

Using quadratic formula, we have the roots as;

t = 1.47s or 13.85s

We will pick the higher value.

Thus;

Maximum height will occur at t = 13.85 s

Thus, plugging in 13.85 for t into h = 245t - 16t², we have;

h_max = 245(13.85) - 16(13.85)²

h_max = 324.09 ft

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How many dekameters are in 225 millimeters? Use the metric table to help answer the question.

Arada [10]

Answer:

0.0225 dekameters

hope it helps

Step-by-step explanation:

1 millimeter = 0.0001 dekameters

0.0001 x 225 = 0.0225

8 0

3 years ago

Read 2 more answers

Use the scale drawing and the scale factor to enlarge a square that has a side length of 12 in. Scale factor= 3 in:2m.

podryga [215]

Given:

The side of square = 12 in.

Scale factor of enlargement = 3 in : 2 m

To find:

The proportion that is use to solve the side length, x, of the enlarged square.

Solution:

Let, the side of length of enlarged square = x m

In case of enlargement the corresponding sides are proportional.

$\dfrac{3}{12}=\dfrac{2}{x}$

$3x=2\times 12$

$3x=24$

Divide both sides by 3.

$x=\dfrac{24}{3}$

$x=8$

Therefore, the required proportion is $\dfrac{3}{12}=\dfrac{2}{x}$ and the side length of the square after enlargement is 8 m.

4 0

2 years ago

What shape is created by the rotation and what is the

zlopas [31]

Answer:

<u>Option D: A cylinder with a circumference of about 50 units</u>

Step-by-step explanation:

The rest of the question is the attached figure.

The square shown has a perimeter of 32 units. The square is rotated about line k. What shape is created by the rotation and what is the approximate circumference of the base? Circumference of a circle: C = 2πr

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

Given: the perimeter of the square = 32

perimeter of a square is four times the length of its side

So, the side length of square = 32/4 = 8 units

The square is rotated about line k.

So, it will form a cylinder with radius 8 units.

Circumference of a circle = 2 π r

Where, r is the radius of the circle.

Circumference of the base is C = 2 π * 8

∴ C = 16π = 16 * 3.14

∴ C = 50.26548 ≈ 50

The shape is created by the rotation is a cylinder with a circumference of about 50 units.

<u>So, the answer option is D.</u>

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2 years ago

The cost of tuition increases each year by 2.6%.

djyliett [7]

Answer:

I think it is a) exponential

6 0

2 years ago

Find the derivative of the function at P 0 in the direction of A. f(x,y,z) = 3 e^x cos(yz), P0 (0, 0, 0), A = - i + 2 j + 3k

Alik [6]

The derivative of $f(x,y,z)$ at a point $p_0=(x_0,y_0,z_0)$ in the direction of a vector $\vec a=a_x\,\vec\imath+a_y\,\vec\jmath+a_z\,\vec k$ is

$\nabla f(x_0,y_0,z_0)\cdot\dfrac{\vec a}{\|\vec a\|}$

We have

$f(x,y,z)=3e^x\cos(yz)\implies\nabla f(x,y,z)=3e^x\cos(yz)\,\vec\imath-3ze^x\sin(yz)\,\vec\jmath-3ye^x\sin(yz)\,\vec k$

and

$\vec a=-\vec\imath+2\,\vec\jmath+3\,\vec k\implies\|\vec a\|=\sqrt{(-1)^2+2^2+3^2}=\sqrt{14}$

Then the derivative at $p_0$ in the direction of $\vec a$ is

$3\,\vec\imath\cdot\dfrac{-\vec\imath+2\,\vec\jmath+3\,\vec k}{\sqrt{14}}=-\dfrac3{\sqrt{14}}$

3 0

3 years ago