Substitute and solve; 7(5f - 3n) -8 when n = 3 and f = 7

The students in Mr. Wilson's Physics class are making golf ball catapults. The

Mnenie [13.5K]

Answer:

Part a) About 48.6 feet

Part b) About 8.3 feet

Part c) The domain is $0 \leq x \leq 48.6\ ft$ and the range is $0 \leq y \leq 8.3\ ft$

Step-by-step explanation:

we have

$y=-0.014x^{2} +0.68x$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

where

x is the ball's distance from the catapult in feet

y is the flight of the balls in feet

Part a) How far did the ball fly?

Find the x-intercepts or the roots of the quadratic equation

Remember that

The x-intercept is the value of x when the value of y is equal to zero

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-0.014x^{2} +0.68x=0$

so

$a=-0.014\\b=0.68\\c=0$

substitute in the formula

$x=\frac{-0.68(+/-)\sqrt{0.68^{2}-4(-0.014)(0)}} {2(-0.014)}$

$x=\frac{-0.68(+/-)0.68} {(-0.028)}$

$x=\frac{-0.68(+)0.68} {(-0.028)}=0$

$x=\frac{-0.68(-)0.68} {(-0.028)}=48.6\ ft$

therefore

The ball flew about 48.6 feet

Part b) How high above the ground did the ball fly?

Find the maximum (vertex)

$y=-0.014x^{2} +0.68x$

Find out the derivative and equate to zero

$0=-0.028x +0.68$

Solve for x

$0.028x=0.68$

$x=24.3$

<em>Alternative method</em>

To determine the x-coordinate of the vertex, find out the midpoint between the x-intercepts

$x=(0+48.6)/2=24.3\ ft$

To determine the y-coordinate of the vertex substitute the value of x in the quadratic equation and solve for y

$y=-0.014(24.3)^{2} +0.68(24.3)$

$y=8.3\ ft$

the vertex is the point (24.3,8.3)

therefore

The ball flew above the ground about 8.3 feet

Part c) What is a reasonable domain and range for this function?

we know that

A reasonable domain is the distance between the two x-intercepts

so

$0 \leq x \leq 48.6\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 48.6 feet

A reasonable range is all real numbers greater than or equal to zero and less than or equal to the y-coordinate of the vertex

so

we have the interval -----> [0,8.3]

$0 \leq y \leq 8.3\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 8.3 feet

8 0

2 years ago

HELP PLEASE ASAP!! (10 pts)

Mandarinka [93]

Answer:

is there a question or picture?

8 0

2 years ago

e Carlos rented a truck for one day. There was a base fee of $ 20.99 , and there was an additional charge of 88 cents for each m

Sonja [21]

Let Base fee be X and No. of Miles be Y.

According to the question
Total Charge= (X+ 88Y)
251.55=20.99+ 0.88Y
Y= 251.55-20.99/0.88
Y= 262 miles

7 0

2 years ago

Read 2 more answers

Jack is learning how to save,spend,and give his money away. He has determined to give away 10% if his summer job earnings. If he

romanna [79]

Answer:

Jack earned $2560 this summer.

Step-by-step explanation:

Given:

Money given away = $256

Percentile of money give away = 10%

We need to find the total money he earned this summer.

Solution:

Let the total money he earned this summer be 'x'.

So we can say that;

Money given away is equal to Percentile of money give away multiplied by total money he earned this summer and then divided by 100.

framing in equation form we get;

$\frac{10}{100}\times x = 256\\\\\frac{x}{10}=256$

Now multiplying both side by 10 we get;

$\frac{x}{10}\times 10=256\times 10\\\\x=\$2560$

Hence Jack earned $2560 this summer.

6 0

2 years ago

Does the following represent growth or decay y=4x

kari74 [83]

Hey there! :D

We can plug in numbers to see if it does.

y=4(1)

y=4

y=4(2)

y=8

This represents growth. When the input (x) increase, the output (y) increases.

I hope this helps!
~kaikers

4 0

3 years ago