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2 years ago

if 4 times a number is increased by 6, the result is less than 15 than the square of the number. find the number

Mathematics

1 answer:

iren [92.7K]2 years ago

7 0

Answer:

n = 7

n = -3

Step-by-step explanation:

4n+6 = n²-15

4n = n² - 21

n² - 4n - 21 = 0

(n-7)(n+3) = 0

n = 7

n = -3

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olga nikolaevna [1]

Answer:

Fraction of the original board left = $\frac{2}{15}$

Step-by-step explanation:

Let the length of the board is = l feet

Marty saws off $\frac{1}{5}$ of a wooden board.

Length of the board left = l - $(\frac{1}{5})l$

= $(\frac{4}{5})l$ feet

He saws off $\frac{3}{4}th$ of the remaining board,

Board left = $(\frac{4}{5})l-[(\frac{4}{5})l\times (\frac{3}{4})]$

= $\frac{4}{5}l-\frac{3}{5}l$

= $\frac{1}{5}l$ feet

He finally saws off $\frac{1}{3}$ rd of the remaining board.

Board left = $\frac{1}{5}l-[\frac{1}{5}\times \frac{1}{3}]l$

= $(\frac{1}{5}-\frac{1}{15})l$

= $\frac{2}{15}l$ feet

Fraction of the original board left = $\frac{\frac{2}{15}l}{l}$

= $\frac{2}{15}$

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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

$0.028x=0.68$

$x=24.3$

<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

if 4 times a number is increased by 6, the result is less than 15 than the square of the number. find the number​

if 4 times a number is increased by 6, the result is less than 15 than the square of the number. find the number