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3 years ago

You ate 2⁄3 of the pizza. How many twelfths is that?

Mathematics

1 answer:

Kipish [7]3 years ago

5 0

You would multiply 2x4 and 3x4 and it would be 8/12 so that leaves you with 4 twelths left.

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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

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

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

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

$0 \leq x \leq 48.6\ ft$

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

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

Hal earns $5 a week doing chores for his parents. He also earns $10 a week for each dog, d, he walks.

sammy [17]

Answer:

Step-by-step explanation:

m = 5 + 10d

The variable "d" is the independent variable because its value does not depend on another variable. The variable "m" is the dependent variable because its value depends on the value of the variable "d"

3 0

2 years ago

A triangles interior angles are 32 and 64 what is the other one. I need this ASAP.

larisa86 [58]

Answer:

Step-by-step explanation:

This is because the angles should add up to 180. So 32 + 64 is 96. Then you subtract 96 from 180 to get 86.

7 0

3 years ago

What is the simplest form of the following expression?

S_A_V [24]

$\sqrt[3]{ \frac{12x ^{2} }{16y} } = \sqrt[3]{\frac{3x ^{2} }{4y} }$

7 0

3 years ago

Read 2 more answers

Without computing, decide whether the value of each expression is much smaller than one, closer to one, or much greater than one

d1i1m1o1n [39]

Answer:

C: closer to one

D: much smaller than one

E: much greater than one

F: much smaller than one

Step-by-step explanation:

3 0

2 years ago