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Dimas [21]
4 years ago
14

Solve for K, the constant of variation, in a joint variation problem where y=520, x=5, z=6.5. Solution is?

Mathematics
1 answer:
Luden [163]4 years ago
6 0

Answer:

K = 676

Step-by-step explanation:

When y is directly proportional to x and inversely poportional to z

We have

y = kx/z

When y =520

x = 5

z = 6.5

K =?

We have

520 = k x 5/6.5

Cross multiply

520 x 6.5 = 5k

3380 = 5k

Divide both sides by 5

3380/5 = 5k/5

676 = k

k = 676

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Lester rents his vacation home for 6 months and lives in the home during the other 6 months of 2018. The gross rental income fro
zepelin [54]

Answer:

$ 500

Step-by-step explanation:

Data provided:

Gross rental income from the home = $ 4,500

Real estate taxes for the year = $ 800

Interest per year = $ 3,000

Utilities and maintenance expenses = $ 2,200

Depreciation expense = $ 4,000

Now, for 6 months

Real estate taxes for the year = $ 800 × 0.5 = $ 400  (0.5 as the for half a year i.e 6 months)

Interest per year = $ 3,000 × 0.5 = $ 1500

Utilities and maintenance expenses = $ 2,200 × 0.5 = $ 1,100

Depreciation expense = $ 4,000 × 0.5 = $ 2,000

Thus,

Total expenses for 6 months = $ 400 + $ 1500 + $ 1,100 + $ 2,000 = $ 5000

Therefore,

Net loss from renting his vacation home = Total expenses - Gross income

or

Net loss from renting his vacation home = $ 5000 - $ 4500 = $ 500

6 0
3 years ago
a cylinder has a volume of 24 cubic centimeters. The height of a cone with the same radius is two times the height of the cylind
Anastaziya [24]

Answer:

<h2>Volume of the cone is 16 cm³</h2>

Step-by-step explanation:

<h3 /><h3>We know that the volume of the cylinder is 24 cm³</h3><h3 /><h3>The formula for this cylinder is  24 = πr²h</h3><h3 /><h3>The cone has the same radius, but it's height is twice that of the cone, so the formula for the volume of the cone is</h3><h3 /><h3>V = (1/3)πr²(2h)                    it's 2h because it's height is twice the</h3><h3>                                                height of the cylinder</h3><h3 /><h3>We can rewrite the equation using the associative rule of multiplication...</h3><h3 /><h3>V = (2/3)(πr²h)</h3><h3 /><h3>We know from the formula for the cylinder that πr²h = 24 cm³, so substitute that in...</h3><h3 /><h3>V = (2/3)(24 cm³)</h3><h3 /><h3>Now simplify...</h3><h3 /><h3>V = 16 cm³</h3>
5 0
3 years ago
Write in y=mx+b form
MA_775_DIABLO [31]

Answer:

y = -2/3x

Step-by-step explanation:

To write in y=mx+b form, you need the y-intercept (b) and the slope (m).

The y-intercept is the point the line crosses the y-axis.  This line crosses the y-axis of (0, 0).  This makes the y-intercept equal to 0.

The slope is the rise of the line over the run of the line.  Pick two points from the line.  It doesn't matter which ones, you will get the right answer regardless.  

I picked (0, 0) and (-3, 2).  Subtract the x-values from each other, and subtract the y-values from each other.

-3 - 0 = -3  (x)

2 - 0 = 2  (y)

Divide the y by the x to find the slope.

2/-3 = -2/3

Plug in the slope and y-intercept into the equation.

y = mx + b

y = -2/3x + 0

y = -2/3x

6 0
3 years ago
Please help me with this
pochemuha

Answer:

Step-by-step explanation:

(-1)^{n} * 2^{n}

then

(-1)^{6} * 2^{6} =  64

4 0
3 years ago
The product of a whole number and unit fraction 2/3
anastassius [24]
Can you add the whole question I think it may be 6/4
5 0
3 years ago
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