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3 years ago

E = MV^2 ÷ 2 + mgh, Make V Subject of the formula

Mathematics

1 answer:

Stels [109]3 years ago

4 0

Answer:

$\red{ \bold{ V = \sqrt{\frac{2(E - mgh)}{M}}}}$

Step-by-step explanation:

$E = MV^2 ÷ 2 + mgh \\ \\ E - mgh = MV^2 ÷ 2 \\ \\ 2(E - mgh)= MV^2 \\ \\ \frac{2(E - mgh)}{M}=V^2 \\ \\ \sqrt{\frac{2(E - mgh)}{M}} = V \\ \\ \red{ \bold{ V = \sqrt{\frac{2(E - mgh)}{M}}}}$

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When CA= 3x-1 and SR=5x+4, what is CA?

avanturin [10]

Answer:

CA=17

Step-by-step explanation:

From given picture we see that A and C are the mid points of sides QR and QS respectively.

We know that line joining mid points of the two sides of triangle is always half of the length of the third side.

So that means:

2*CA=SR

2(3x-1)=5x+4

6x-2=5x+4

6x-5x=4+2

x=6

plug value of x into CA=3x-1

CA=3*6-1=18-1=17

Hence final answer is CA=17

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3 years ago

ricardo purchased a bunk bed for his children fora sale price of $276.25. The sale price was 65% of the original price. Calculat

nikklg [1K]

Use the formula S=P-PD

S is sale price, original price is P, and PD is discounted percent,

276.25=P-P(.65), I turned the percent into a decimal.

276.25=P(1-.65)

276.25=P(.35)

Now cross multiply.

$\frac{276.26}{.35}=\frac{P(.35)}{.35}\\\\P=\frac{276.26}{.35}=789.31$

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3 years ago

Plus $5 per day. The fee for the game booth is $50 plus $7 per day.

Marta_Voda [28]

Question:

A company sets up a food booth and a game booth at the county fair. The fee for the food booth is $100 plus $5 per day. The fee for the game both is $50 plus $7 per day. Write an expression for how much both will cost for the same number of days.

Answer:

105 times 15= 1575

57 times 20= 1140

1140+1575= 2715

(2715)(d)= x

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2 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

The recycling and reuse industry employs approximately 1,025,000 more workers than the waste management industry. Together they

NARA [144]

Answer:

Step-by-step explanation:

The recycling and reuse industry employs approximately 1,025,000 more workers than the waste management industry. This means that

Number of workers employed by The recycling and reuse industry = the number of workers employed by the waste management industry + 1,025,000

Let y = the number of workers employed by the waste management industry. Therefore

x = y + 1,025,000 - - - - - - 1

Since total = 1,275,000

x + y = 1,275,000 - - - - - - -2

Substituting equation 1 into equation 2, it becomes

y + 1,025,000 + y = 1,275,000

2y = 1,275,000 - 1,025,000

y = 250000/2 = 125000

x = y + 1,025,000 = 125000 + 1,025,000 = 1150000

The recycling and reuse industry employs 1150000 workers

The waste management industry employs 125000 workers

7 0

3 years ago

E = MV^2 ÷ 2 + mgh, Make V Subject of the formula​

E = MV^2 ÷ 2 + mgh, Make V Subject of the formula