suppose that y is proportional to the 4th power of x and that y=13 when x=2 what is y when x=5
To solve this question, we can set up a proportion by using the given information.
Since "y is proportional to the 4th power of x," we can write the equation as:
y = kx^4
where k is the constant of proportionality.
Given that y = 13 when x = 2, we can substitute these values into the equation:
13 = k(2^4)
13 = 16k
To find the value of k, we divide both sides of the equation by 16:
k = 13/16
Now, we can use this value of k in the equation to find y when x = 5:
y = (13/16)(5^4)
y = (13/16)(625)
y = 406.25
Therefore, when x = 5, y is approximately 406.25.
suppose that y is inversely proportional to the cube of x and that y = 18 when x =20 what is y when x =5 round your answer to two decimal places if necessary
To solve this question, we can use the inverse proportion formula:
y = k/x^3
where k is the constant of proportionality.
Given that y = 18 when x = 20, we can substitute these values into the equation:
18 = k/(20^3)
18 = k/8000
To find the value of k, we multiply both sides of the equation by 8000:
k = 18 * 8000
k = 144000
Now, we can use this value of k in the equation to find y when x = 5:
y = 144000/(5^3)
y = 144000/125
y = 1152
Therefore, when x = 5, y is equal to 1152.
To find the value of y when x=5, given that y is proportional to the 4th power of x, we can set up a proportion:
(y₁ / x₁^4) = (y₂ / x₂^4)
where y₁ and x₁ are the initial values, and y₂ and x₂ are the final values.
Given that y=13 when x=2, we have y₁=13 and x₁=2. We want to find y₂ when x₂=5.
Plugging in the values, we have:
(13 / 2^4) = (y₂ / 5^4)
Simplifying the equation, we get:
(13 / 16) = (y₂ / 625)
To find y₂, we can cross-multiply:
13 * 625 = 16 * y₂
8125 = 16y₂
Now, solve for y₂ by dividing both sides by 16:
y₂ = 8125 / 16
Calculating the value, we have:
y₂ = 507.8125
Therefore, when x=5, y≈507.8125.