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Elden [556K]
3 years ago
5

A ball is projected in to the air. Its height at time t is given by the equation

Mathematics
1 answer:
Ksju [112]3 years ago
3 0
The equation gives the height of the ball. That is, h is the height of the ball. t is the time. Since we are looking for the time at which the height is 8 (h=8), we need to set the equation equal to 8 and solve for t. We do this as follows:

h=-16 t^{2} +60t+1
8=-16 t^{2} +60t+1
16 t^{2} -60t-1+8=0
16 t^{2} -60t+7=0

This is a quadratic equation and as it is set equal to 0 we can solve it using the quadratic formula. That formula is:
t= \frac{-bplus minus \sqrt{ b^{2}-4ac } }{2a}
You might recall seeing this as "x=..." but since our equation is in terms of t we use "t-=..."

In order to use the formula we need to identify a, b and c.
a = the coefficient (number in front of) t^{2} = 16.
b = the coefficient of t = -60
c = the constant (the number that is by itself) = 7

Substituting these into the quadratic formula gives us:
t= \frac{-(-60)plus minus \sqrt{ (-60)^{2}-4(16)(7) } }{2(16)}
t= \frac{60plus minus \sqrt{3600-448 } }{32}
t= \frac{60plus minus \sqrt{3152 } }{32}

As we have "plus minus" (this is usually written in symbols with a plus sign over a minus sign) we split the equation in two and obtain:
t=  \frac{60+56.1426}{32} =3.63
and
t=  \frac{60-56.1426}{32} =.12

So the height is 8 feet at t = 3.63 and t=.12

It should make sense that there are two times. The ball goes up, reaches it's highest height and then comes back down. As such the height will be 8 at some point on the way up and also at some point on the way down.


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Bas_tet [7]

Answer:

6. D.

7.  F.

8. A.

9. B.

10. C.

Step-by-step explanation:

6.     9 + (12 - 10)

       12 - 10 = 2

        9 + 2 = 11

7.      (20 - 15) x 2

        20 - 15 = 5

         5 x 2 = 10

8.      10 ÷ 5 + 7

         10 ÷ 5 = 2

          2 + 7 = 9

9.        6 + 2 x 3

           2 x 3 = 6

           6 + 6 = 12

10.        (2 x 4) + 8

             2 x 4 = 8

             8 + 8 = 16

Let me know if this helps!

4 0
2 years ago
I'm so confused, pls help
Vera_Pavlovna [14]

Answer:

x = 14      D

Step-by-step explanation:

(18x + 36) / 3 = 6x + 12

6x + 12 = -16 + 8x

-6x .                -6x

12 = -16 + 2x

+16 . +16

28 = 2x

/2 .   /2

14 = x

8 0
2 years ago
2. Us i ng the filled table above,
VARVARA [1.3K]

The price elasticity of demand of the pen will be -0.2.

<h3>How to compute the elasticity?</h3>

The demand and supply schedule will be:

Price Qd. Qs

$10. 250. 100

$20. 200. 90

$30. 180. 80

The price elasticity of demand from $1 to $2 will be:

= Percentage change in quantity demanded/percentage change in price

Percentage change in quantity demanded will be:

= (200 - 250)/250 × 100

= -20%

Percentage change in price will be:

= (20 - 10)/10 × 100

= 100%

Therefore, the elasticity of demand will be:

= -20/100

= - 0.2

The value gotten illustrates an inelastic demand.

In order to increase the total revenue, the price can be reduced as it will lead to more sales.

Learn more about PED on:

brainly.com/question/21105870

#SPJ1

<u>Complete question:</u>

Choose any product or service. Create the demand and supply schedule.

Calculate just one PED.

Is the demand elastic or inelastic?

What price change would you recommend to increase TR?

8 0
2 years ago
Ramapo College has a total of 25,000 students enrolling this year. 42% of
salantis [7]

Answer: im sorry im not sure but you can find the answer if you look it up

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Print Version
san4es73 [151]

Answer:

$9450

Step-by-step explanation:

We will use compound interest formula:

F=P(1+r)^t

Where

F is future amount [what we want to figure out]

P is present amount [9000]

r is rate of interest [since we want for 6 months, the annual interest divided by 2 is r. So r = 10/2 = 5% or 0.05]

t is the time [ the time period is for 6 months so t = 1 since we already converted the interest rate to 6 month chunk]

Putting in formula, we get:

F=P(1+r)^t\\F=9000(1+0.05)^1\\F=9000(1.05)\\F=9450

6 0
3 years ago
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