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3 years ago

What is the approximate volume of a cone with a diameter of 14 cm and a height of 9 cm.

Mathematics

1 answer:

Burka [1]3 years ago

4 0

Answer:

461.81

Step-by-step explanation:

diameter=14 , so radius is diameter/2=7

height=9

V= πr2 h /3=461.81

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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

Kristen has 64 coins in her bank. She has $9.25 in dimes and quarters. How many dimes and quarters does she have?

Stella [2.4K]

D= # of dimes
q= # of quarters

QUANTITY EQUATION:
d + q= 64

COST EQUATION:
0.10d + 0.25q= $9.25

STEP 1:
multiply quantity equation by -0.10 to be able to eliminate the d term in step 2

(-0.10)(d + q)= (-0.10)(64)
-0.10d - 0.10q= -6.40

STEP 2:
add equation from step 1 to cost equation to eliminate the d term and solve for q

Add
0.10d + 0.25q= $9.25
-0.10d - 0.10q= -6.40

0.15q= 2.85
divide both sides by 0.15

q= 19 quarters

STEP 3:
substitute q value in step 2 into either original equation to find d value

d + q= 64

d + 19= 64
subtract 19 from both sides

d= 45 dimes

CHECK:
0.10d + 0.25q= $9.25
0.10(45) + 0.25(19)= 9.25
4.50 + 4.75= 9.25
9.25= 9.25

ANSWER: There are 45 dimes and 19 quarters.

Hope this helps! :)

7 0

3 years ago

What is the correct answer?

murzikaleks [220]

Answer:

160

Step-by-step explanation:

The top right quadrant is 90 and the given is 70, adding them equal 160. It is the only option that is greater than 90 degrees anyway.

7 0

3 years ago

Mr. Fowler's science class grew two different varieties of

Zanzabum

Answer: A

Step-by-step explanation:

The average height of a variety a is greater but varies less than a variety b

5 0

2 years ago

I need help with 1 and 2 please :)

marin [14]

#1 is the third one down (x+3)^2 + (y-2)^2 = 9

8 0

3 years ago