MATH HELP. Find the constant of variation k for the stated condition. y varies directly as x, and y = 44 when x = 2. k=?

Question

Question #2
Find the constant of variation k for the stated condition.
y varies inversely as the square of x, and y = 3 when x = 3.
k = ?

question #3
Translate the statement of variation into an equation; use k as the constant of variation.
a varies inversely as the square of b.
a = ?

question #4
Translate the statement of variation into an equation, and use k as the constant of variation.
y varies directly as the cube of x.
y = ?


question #5
Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car one day and paid $98 for 210 miles. On another day she rented a car from the same agency and paid $140 for 350 miles. Find the linear function f(x) (where x is in miles and f(x) is in dollars) that the agency could use to determine its daily rental charges.
f(x) =


**Just answer the ones you can...and please put which question it belongs to like 1,2,3... thanks

Answer 1

Question #1

Find the constant of variation k for the stated condition. y varies directly as x, and y = 44 when x = 2. k=?



y = kx

When x=2,

.....y = 2k = 44 ⇒

.....k = 22.......................ANS

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Question #2

Find the constant of variation k for the stated condition.

y varies inversely as the square of x, and y = 3 when x = 3.

k = ?



y = (1/k) x²

When x = 3

.....y = (1/k) 3² = 3

.....9/k = 3

.....9 = 3k

.....k = 3................ANS

-----------------------------------

Question #3

Translate the statement of variation into an equation; use k as the constant of variation.

a varies inversely as the square of b.

a = ?



a = (1/k) b²..............ANS

-------------------

Question #4

Translate the statement of variation into an equation, and use k as the constant of variation.

y varies directly as the cube of x.

y = ?



y = kx³.........................ANS

---------------------

Question #5

Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car one day and paid $98 for 210 miles. On another day she rented a car from the same agency and paid $140 for 350 miles. Find the linear function f(x) (where x is in miles and f(x) is in dollars) that the agency could use to determine its daily rental charges.



f(x) = kx + C

When x = 210,

.....f(210) = 210k + C = 98.........[1]



When x = 350,

.....f(350) = 350k + C = 140.......[2]



// We need to solve for C; Rewrite [1] and [2] solving for C

.....f(210) = 210k + C = 98.........[1]

.....C = -210x + 98...................[1a]



.....f(350) = 350k + C = 140.......[2]

.....C = -350k + 140...............[2a]



// Now since both [1a] and [2a] are solved for C,

// set [1a] = [2a] and solve for k

.....-210k + 98 = -350k + 140

.....140k = 42

.....k = 42/140

.....k = 0.3



// Lastly, go back and solve for C using either [1a] or [2a]

.....C = -210k + 98...................[1a]

.....C = -210(0.3) + 98

.....C = 35



So, the linear function f(x) (where x is in miles and f(x) is in dollars) that the agency could use to determine its daily rental charges is



f(x) = 0.3x + 35...................ANS

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Answer 2

y varies directly as x, and y = 44 when x = 2. k=?

y = kx

44 = k•2

k = 22



y varies inversely as the square of x, and y = 3 when x = 3.

y = k/x²

3 = k/3²

k = 3•9 = 27



a varies inversely as the square of b

a = k/b²



y varies directly as the cube of x

y = kx³



Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car one day and paid $98 for 210 miles. On another day she rented a car from the same agency and paid $140 for 350 miles. Find the linear function f(x) (where x is in miles and f(x) is in dollars) that the agency could use to determine its daily rental charges.



Cost = C + kx

98 = C + k210

140 = C + k350

two equations in two unknowns



98 = C + k210

140 = C + k350



C = 98 – k210

C = 140 – k350

98 – k210 = 140 – k350

k(350 – 210) = 140 – 98

k = 42/140 = 6/20 = 3/10



now we have

C = 140 – (3/10)350

C = 140 – 105 = 35



equation is

Cost = 35 + 0.3x



check

Cost = 35 + 0.3x

Cost = 35 + 0.3•210 = 35+70 = 105 ok



Cost = 35 + 0.3x = 35 + 0.3•350 = 35 + 105 = 140 ok

Answer 3

==== All Questions answered (came back to the 1st one, since it was in your question and not the

(details)

Question 1

Find the constant of variation k for the stated condition. y varies directly as x, and y = 44 when x = 2. k=?

y =kx

44 = k2

k = 44/2 = 21

==== answer

k = 21

Question #2

Find the constant of variation k for the stated condition.

y varies inversely as the square of x, and y = 3 when x = 3.

(Inversely means divided by)



k = ?

y = (k)/ √ ̅(x)

3 = (k) / √ ̅(3)

=== answer

k = 3(√ ̅(3))

=== checking answer

y = 3(√ ̅(3)) / √ ̅(x)

y = 3(√ ̅3)) / √ ̅(3) = 3





question #3

Translate the statement of variation into an equation; use k as the constant of variation.

a varies inversely as the square of b.

a = ?

=== answer

a = k / √ ̅(b)



question #4

Translate the statement of variation into an equation, and use k as the constant of variation.

y varies directly as the cube of x.

y = ?

What does this mean? The cube of x

I know what x cubed means (x^3)

I know what the cube root of x cube root of (X)



===== answer

depending on what you mean by the cube of x

y = kx^3

or

y = k X cube_root(x)



question #5

Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car one day and paid $98 for 210 miles. On another day she rented a car from the same agency and paid $140 for 350 miles. Find the linear function f(x) (where x is in miles and f(x) is in dollars) that the agency could use to determine its daily rental charges.

F = fixed amount

f(x) = mx + F

This gives this 1st equation

98 = m(210) + F

F = 98 -210m

It always gives 2nd equation

140 = m(350) + F

now substitute "98-210m" for F

140 = 350m + (98 - 210m) = 140m + 98



140-98 = 140m

42 = 140m

m = 42/140 = (factor out 2/2) = 21/70 =(factor out 7/7) 3/10

m = 0.30

140 = m(350) + F

now plug m= 0.30 back into the equation

140 = 0.30(350) + F

140 = 105 + F

F = 140 -105 = 35

==== answer

f(x) = 0.30x + 35



===== checking

f(210) = 0.30*210+ 35 = 98 (works)

f(350) = 0.30*350 + 35= 140 (works)