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3 years ago

PLEASE HELP!!! 20 PTS!!!

Mathematics

1 answer:

Ahat [919]3 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

The area (A) of a triangle is calculated using the formula

A = $\frac{1}{2}$ bh ( b is the base and h the perpendicular height )

let b = x then h = 4x ( 4 times the length of the base ), then

$\frac{1}{2}$ × x × 4x = 24

$\frac{1}{2}$ × 4x² = 24

2x² = 24 ( divide both sides by 2 )

x² = 12 ( take the square root of both sides )

x = $\sqrt{12}$ = $\sqrt{4(3)}$ = 2 $\sqrt{3}$ , hence

base = 2 $\sqrt{3}$ and height = 8 $\sqrt{3}$

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Suppose that Stephen is the quality control supervisor for a food distribution company. A shipment containing many thousands of

solmaris [256]

Answer:

what subject is this in

Step-by-step explanation:

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3 years ago

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

$0.028x=0.68$

$x=24.3$

Alternative method

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

3 years ago

144 = -12 (x + 5) find x Show work.

kumpel [21]

Answer:

-17 =x

Step-by-step explanation:

144 = -12 (x + 5)

Divide each side by -12

144/-12 = -12 (x + 5)/-12

-12 = x+5

Subtract 5 from each side

-12-5 =x+5-5

-17 =x

3 0

3 years ago

Read 2 more answers

Find measure dbc 19 22 23 161 HELP !!!

uysha [10]

∠DBC = 19° since the two angles have to add up to 180, if x = 23, then 23 -4 = 19 for the right, and 7 x 23 = 161, and 161 + 19 = 180.

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3 years ago

What is 12% of 36?(finding a part of a whole)

Luden [163]

Answer:

4.32 is 12% of 36

Step-by-step explanation:

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3 years ago