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Veseljchak [2.6K]

3 years ago

14

A small rock falling from the top of a 124-ft-tall building with an initial downward velocity of –30 ft/sec is modeled by the eq

uation h(t) = –16t2 – 30t + 124, where t is the time in seconds. For which interval of time does the rock remain in the air?
t = 2
t > –2
t < 2
t > 2

WHICH ONE?? D:

1 answer:

adelina 88 [10]3 years ago

5 0

Answer:

Third option is correct.

Step-by-step explanation:

The given model is

$h(t)=-16t^2-30t+124$

Where, h(t) is heigth of rock after time t (in seconds).

The initial height of rock is 124 ft.

The leading coefficient is negative. It means it is a downward parabola.

First we have to the x-intercepts of the function.

$0=-16t^2-30t+124$

Using quadratic formula, we get

$t=\frac{-(-30)\pm \sqrt{(-30)^2-4(124)(-16)}}{2(-16)}$

$t=-3.8752$ and $t=2$

It means rock remains in the air between $-3.875$ .

The value of t can not be negative, therefore rock remains in the air between $0$ .

Third option is correct.

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Which pair of points have a slope of -3/5?

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Answer:

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Step-by-step explanation:

You have to use the slope formula $\frac{y_{2} - y_{1} }{x_{2} - x_{1} }$

( $x_{1}$ , $y_{1}$ ), ( $x_{2}$ , $y_{2}$ )

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(10, -2), (0, 4) $\frac{4 - -2 }{0- 10 }= \frac{6}{-10}$ you have to simplfy, the answer will be $\frac{3}{-5}$

(4, 2), (10, 4) $\frac{4 - 2 }{10 - 4 }= \frac{2}{6}$ you have to simplfy, the answer will be $\frac{1}{3}$

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3 years ago

An account grows at an annual interest rate of r⁡ ⁣, so it grows by a factor of x=1+r⁡ ⁣⁣ ⁡ each year. The function A(x)=800x

Paladinen [302]

Given:

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The below function gives the amount in the account after 4 years when the growth factor is x⁡ ⁣⁣.

$A(x)=800x^4+350x^3+500x^2+600x$

To find:

The total amount in the account if the interest rate for the account is 3% each year and initial amount.

Solution:

Rate of interest = 3% = 0.03

Growth factor : x = 1 + ⁡0.03 = 1.03

We have,

$A(x)=800x^4+350x^3+500x^2+600x$

Substitute x=1.03 in the given function, to find the total amount in the account if the interest rate for the account is 3% each year.

$A(1.03)=800(1.03)^4+350(1.03)^3+500(1.03)^2+600(1.03)$

$A(1.03)=800(1.12550881)+350(1.092727)+500(1.0609
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$A(1.03)=900.407048+382.45445+530.45+618$

$A(1.03)=2431.311498
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$A(1.03)\approx 2431.31
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Therefore, the total amount in the account is 2431.31 if the interest rate for the account is 3% each year.

For initial amount the rate of interest is 0.

Growth factor : x = 1 + ⁡0 = 1

Substitute x=0 in the given function to find the initial amount.

$A(1)=800(1)^4+350(1)^3+500(1)^2+600(1)$

$A(1)=800+350+500+600$

$A(1)=2250$

Therefore, 2250 was put into the account at the beginning.

3 0

3 years ago