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2 years ago

14

If 50 pounds of weight is located at point x and 100 pounds at point z, how much weight must be located at point y to balance th

e plank?

2 answers:

tatyana61 [14]2 years ago

7 0

Answer:

50

Step-by-step explanation:

will be your answer

Troyanec [42]2 years ago

6 0

It will have to be 50

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A stone is dropped into a barrel of water and sinks to the bottom. The ball is completely covered by water. By how much does the

Rom4ik [11]

Answer:

Answer: 5/12 or approx. 0.42

Step-by-step explanation:

The ball will displace as much water as its volume.

Meaning, the volume of the ball and the volume of the increase in water in the barrel will be equal.

Volume of a sphere:

$V_s=\frac{4}{3} \pi r^3$

The radius is half the diameter. The diameter of the sphere is 10, thus:

$r = d/2 = 10/2 = 5$

5^3 = 5*5*5 = 25*5 = 125

$V_s=\frac{4}{3} \pi * 5^3=\frac{4}{3} \pi * 125$

The volume of a cylinder, which will be the shape of the increase in water, is the following:

$V_c=\pi r^2 h$

We know the radius r, as we know the diameter.

$r=d/2=40/2=20$

$V_c=\pi r^2 h=\pi h * 20^2 = \pi h * 400$

We are looking for the height of the cylinder, h, as that will be the height of the water rise.

Since we know these 2 volumes are the same, we'll set them equal to each other and solve the equation:

$V_s = V_c$

$\frac{4}{3} * 125 * \pi = 400 * h * \pi$

We can get rid of pi by dividing both sides by pi:

$\frac{4}{3} * 125 = 400 * h$

And now divide both sides by 400:

$\frac{4}{3} * \frac{125}{400}= h$

Just reversing it and putting h to the left:

$h = \frac{4}{3} * \frac{125}{400} = \frac{4 * 125}{3 * 400}$

I see that I can divide both the numerator and the denominator by 4:

$h =\frac{125}{3 * 100}= \frac{125}{300}$

I'll now divide both the numerator and the denominator by 25 to simplify the expression:

$h=\frac{125}{300} =\frac{125 / 25}{300 / 25} = \frac{5}{12}$

Answer: The water rises by 5/12 (five twelfths).

If I want an approximate decimal answer, I can simply run this expression in a calculator:

$\frac{5}{12}$ ≈ $0.416666667$ ≈ $0.42$

7 0

2 years ago

5y-6=3y-20 how do i solve this problem

rusak2 [61]

Minus 3y both sides
2y-6=-20
add 6 to both sids
2y=-14
divide 2
y=-7

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2 years ago

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Chuck has a gross pay of $815.70. By how much will Chuck’s gross pay be reduced if he has the following items withheld? federal

tangare [24]

Chuck has a gross pay of $815.70. His gross pay will be reduced by:

Federal tax of $56;
Social Security tax that is 6.2% of his gross pay;
Medicare tax that is 1.45% of his gross pay;
State tax that is 19% of his federal tax.

Let's count:

1. gross pay of $815.70 - 100%,

Social Security tax of $x - 6.2%.

Then

$\dfrac{815.70}{x}=\dfrac{100}{6.2} ,\\ \\815.70\cdot 6.2=x\cdot 100,\\ \\x=\dfrac{815.70\cdot 6.2}{100} =50.5734.$

2. gross pay of $815.70 - 100%,

Medicare tax of $y - 1.45%.

Then

$\dfrac{815.70}{y}=\dfrac{100}{1.45} ,\\ \\815.70\cdot 1.45=y\cdot 100,\\ \\y=\dfrac{815.70\cdot 1.45}{100} =11.82765.$

3. Federal tax of $56 - 100%,

State tax $z - 19%.

Then

$\dfrac{56}{z}=\dfrac{100}{19} ,\\ \\56\cdot 19=z\cdot 100,\\ \\z=\dfrac{56\cdot 19}{100} =10.64.$

4. Chuck’s gross pay will be reduced by

$\$56+\$50.5734+\$11.82765+\$10.64=\$129.04105\approx \$129.04.$

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2 years ago

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Peter is at a lumber yard. He gets 2 free boxes of nails for every 10 boards he buys. Write an expression for the number of boxe

Sati [7]

A. The number of 10-boards Peter bought is equal to n divided by 10. Then, each of the 10-boxes will get two boxes of nails. The number of boxes of nails that Peter will have after buying n boards will be,

N = (2)(n/10)

Simplifying,

<em> N = n/5</em>

b. If the number of boards are 90 then,

N2 = (90/10)(2)(100 nails/box)
N2 = 1800

Answer: 1800

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2 years ago

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Grace read 9 books in 3 months what was her rate of reading Books per month

Lorico [155]

Answer:

3 books per month

Step-by-step explanation:

9 books ÷ 3 months = 3 books per month :)

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2 years ago

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