Using the model of 7.77, how does the 7 in the tenths place compare to the 7 in the place to its left?

A rocket is launched straight up from the ground with an initial velocity of 192 feet per second. The equation for the height of

Ivenika [448]

The equation for the height of the rocket at time t given

$h= -16t^2+192t$

We have to find the time t, when the rocket reaches 560 feet.

That means we have to find t when h = 560 ft. we will place 560 in the place of h to find t now.

$h= -16t^2+192t$

$560 = -16t^2+192t$

In the right side, we can check -16 is the common factor. So we will take out -16 from the rigbht side.

$560 = -16(t^2 - 12t)$

To get rid of -16 from the right side and move it to left side, we will divide both sides by -16.

$560/-16 = -16(t^2-12t)/-16$

$-35 = t^2 -12t$

Now we will move -35 to the righ side by adding 35 to both sides.

$-35+35 = t^2-12t+35$

$0 = t^2 -12t+35$

$t^2-12t+35 = 0$

We will factorize thee left side to find the values of t now. We need to find a pair of factors of 35 that by adding them we will get -12.

The pair of factors of 35 are -5 and -7 and by adding -5-7 we will get -12.

$t^2-12t+35 =0$

$(t-5)(t-7) =0$

So by using zero product property we will get

$t-5 =0$

$t-5+5 = 0+5$

$t=5$

Also $t-7 =0$

$t-7+7 = 0+7$

$t=7$

So we have got the rocket reaches at 560ft when t = 5 seconds and also when t = 7 seconds.

Now part b.

When the rocket completes its trajectory and hits the ground then the height or h = 0. So we will place h = 0 there in the equation.

$h= -16t^2+192t$

$0= -16t^2 + 192 t$

$0 = -16(t^2-12t)$

$-16(t^2-12t) = 0$

We will move -16 to the other side by dividing it to both sides.

$-16(t^2-12t)/-16 = 0/-16$

$t^2-12t = 0$

We will take out the common factor t from the left side. By taking out t we will get,

$t(t-12) = 0$

We will use zero product property now. By using that we will get,

$t = 0$

ans also $t-12 = 0$

$t-12+12 = 0+12$

$t = 12$

When the rocket completes its trajectory and hits the ground the time t can not be 0. When t =0, the rocket starts the trajectory.

So when the rocket completes its trajectory and hits the ground ,

then t = 12seconds.

So we have got the required answers.

6 0

3 years ago

I don’t understand what to do on these question, some help would be nice (trigonometry)

Bumek [7]

Step-by-step explanation:

> find the angle of center circle:

cos~¹ 5/(5+12) = cos~¹ 5/17 = 72°

so the sector area of the shaded

region =

(360-72)/360 × 3.14 × 5²

= 288/360 × 78.5

= 62.8

> the height of triangle (red Line) =

4×tan 72° = 4× 3.078 = 12.31

the height of pyramid (green

Line) = √12.31²-8.5² =√74.16

= 8.61

so the volume of pyramid =

⅓×(17×8)×8.61 = 390.32

8 0

2 years ago

What sport do 7th graders prefer to play after school

stich3 [128]

Basketball was voted hugest

4 0

3 years ago

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Solve and simplify, typing the final answer as a fraction 1/4 ÷ 3/8

natita [175]

[ Answer ]

2 / 3

[ Explanation ]

1 * 8 / 4 * 3

8 / 12

Simplify:

2 / 3

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6 0

3 years ago

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Evaluate \dfrac j4 4 j ? start fraction, j, divided by, 4, end fraction when j=12j=12j, equals, 12.

cricket20 [7]

We need to evaluate the value of fraction $\frac{j}{4}$ .

We also given j=12.

In order to evaluate the value of fraction $\frac{j}{4}$ , we need to plug j=12.

Plugging j=12, we get

$\frac{j}{4}= \frac{12}{4}$

We have 12 in numerator and 4 in denominator.

We always divide top number by bottom number.

So, we need to divide 12 by 4.

On dividing 12 by 4 we get 3.

<h3>Therefore, $\frac{j}{4} = 3.$ </h3>

3 0

3 years ago

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