1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lord [1]
3 years ago
6

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

Mathematics
1 answer:
Mnenie [13.5K]3 years ago
8 0

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

You might be interested in
You are renting a surfboard for the day. The surfboard rental fee is $25 with an additional charge of $7 per hour. You have at m
o-na [289]

Initial fee: $25

Per hour fee: $7

Your budget: $60

x = # of hours you can rent the surfboard

$25 + $7x ≤ $60

Subtract $25 from both sides.

$7x ≤ $35

Divide both sides by $7

x ≤ 5

You can rent the surfboard for less than or equal to 5 hours.

6 0
3 years ago
Margo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the cad
natka813 [3]

Answer:

a little late

205 1/5 is your answer

Step-by-step explanation:

break down the 3-D figure

Find area of triangle A=1/2bh

=1/2(8 inch)(6   9/10inch)

=1/2(8 inch)(69/10 inch)

=138/5 square inch

then multiply two because you have 2 triangles

=138/5 (2)  

= 276/5 square inch

= 55 1/5 sq.in

Find area of rectangle

A = lw

=6 1/4 in (8 in)

= 25/4 (8 in.)

= 50 sq. in.

then multiply by 3 because of the three rectangles

= 50 sq. inch (3)

= 150 sq. in.

Add all together

55 1/5 sq. inch + 150 sq. inch = 205 1/5 sq. inch

4 0
2 years ago
Write the formula for absolute value function if its graph has the vertex at point (0,6) and passes through the point (−1,−2).
valentinak56 [21]

First you need to find the slope of the line:

m =   \frac{y_2 - y_1}{x_2 - x_1}

m=6-(-2) / (-1)-0 =-8

equation of line is:

y=mx+b

y=-8x+6

for absolute value function:

if x<0

y=-8x+6

if x>0

y=+8x-6

8 0
3 years ago
When AB=3x+8 and GJ=2x+24 what is AB?
valina [46]

Answer:

AB= GJ ➗2

2x+24➗2= x+12

i'm not sure

4 0
3 years ago
HELP PLZZZZ! thank you
Setler79 [48]

1. Same length.

2.vertically opposite angle.

3.BAC =BDE

4.AC = DE

Hope this helps you ___!!❤

3 0
3 years ago
Other questions:
  • Write a rational number whose opposite and absolute value are the same.
    9·1 answer
  • MATH HELP. ^^<br><br> Answer the two pages below.
    6·1 answer
  • Suppose two random variables, X and Y are independent, which statement is false? a) P(X∣Y)=P(X) b) P(X∪Y)=P(X)+P(Y) c) P(X∩Y)=P(
    7·1 answer
  • Does this table represent a function? Why or why not?
    15·2 answers
  • How do you do the area and how to do it to the nearest tenth
    5·1 answer
  • Simplify 3(x+4)<br> A.3(x+4)<br> B.7x<br> C.12x<br> D.3X+12
    7·2 answers
  • can someone please give the answers the these 2 questions, ignore the blue dot one the fist questions i clicked it by accident
    14·1 answer
  • An item that regularly sells for a dollars is on sale for 35% off its regular price. Write an expression that shows the price in
    12·1 answer
  • On a trip from Indianapolis, Indiana, to Houston, Texas,
    6·1 answer
  • 50 POINTS! PLEASE ASAP, BRAINLIST
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!