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Over [174]
3 years ago
15

The gallons of water used to take a shower varies directly with the number of minutes in the shower. If a 6 minute shower uses 3

6 gallons of water, what is the constant of variation?
Mathematics
1 answer:
Lapatulllka [165]3 years ago
5 0
Answer:

You use 6 gallons of water per minute.

Explanation:

If you use 36 gallons in 6 minutes then you need to divide 6 by 36. 36/6=6. That would mean you use 6 gallons per minute.
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If y= 3x + 6, what is the minimum value of (x^3)(y)?
Rainbow [258]

Answer:

Given the statement: if y =3x+6.

Find the minimum value of (x^3)(y)

Let f(x) = (x^3)(y)

Substitute the value of y ;

f(x)=(x^3)(3x+6)

Distribute the terms;

f(x)= 3x^4 + 6x^3

The derivative value of f(x) with respect to x.

\frac{df}{dx} =\frac{d}{dx}(3x^4+6x^3)

Using \frac{d}{dx}(x^n) = nx^{n-1}

we have;

\frac{df}{dx} =(12x^3+18x^2)

Set \frac{df}{dx} = 0

then;

(12x^3+18x^2) =0

6x^2(2x + 3) = 0

By zero product property;

6x^2=0   and 2x + 3 = 0

⇒ x=0 and x = -\frac{3}{2} = -1.5

then;

at x = 0

f(0) = 0

and  

x = -1.5

f(-1.5) = 3(-1.5)^4 + 6(-1.5)^3 = 15.1875-20.25 = -5.0625


Hence the minimum value of (x^3)(y) is, -5.0625






3 0
3 years ago
A number is divided by 6.then 8 is added Mto the quotient. Next3 is subtracted from the sum.the result is 7. What is the number?
hjlf

(n/6 + 8) - 3 = 7

(n/6 + 8) - 3 + 3 = 7 + 3

n/6 + 8 - 8 = 10 - 8

n/6 = 2

(n/6)(6) = 2(6)

n = 12

6 0
3 years ago
HelPPP I need ANSWERS DUEE TOMORROW
aleksley [76]
7. 233
8. 4
9. 6
10. 5
11. 4
12. 7
13. 7
3 0
3 years ago
Map of field: 12 in × 15 in
alexdok [17]
Multiply the dimensions by 3 to convert to feet.

12 x 3 = 36 ft.

15 x 3 = 45 ft.

the dimensions are 36 ft. x 45 ft.
4 0
3 years ago
One survey estimates that,on average, the retail value of a mid sized car decreases by8% annually.if the retail value of a car i
Scrat [10]
Percentage by which the average value of mid sized car decreases each year = 8%
Retail value of a car today = v dollars
Amount of decrease in the value of the car after 1 year = (8/100) * v
                                                                                         = 2v/25 dollars
Then
The equation that represents the value of the car after 1 year = v - (2v/25) dollars
                                                                                                   = (25v - 2v)/25 dollars
                                                                                                   = 23v/25 dollars
So following this expression the value of the mid sized car can be easily determined after 1 year. I hope this is the answer you were looking for and the procedure is also clear to you.
5 0
3 years ago
Read 2 more answers
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