- f-¹(x) = 69/5y
- f-¹(x) = 13 + 4y/(y + 10)
<h3>How to determine the inverse </h3>
The steps involved in determining the inverse of a function are;
- Replace f(x) with y in the equation describing the function
- Interchange x and y
- Solve for y
- Replace y by f-1(x)
If f(x) = 4/5x + 13
y = 4/5y + 13
y = 4 + 65 /5y
f^-1 = 4 + 65 /5y
f^-1(x)= 69/5y
If f(x)= 3/x+10 + 4
y = 3/y + 10 + 4
y = 3 + 4y + 10/(y + 10)
y = 13 + 4y/(y + 10)
f^-1(x) = 13 + 4y/(y + 10)
Thus, the inverse of the functions is 69/5y and 13 + 4y/(y + 10)
Learn more about functions here:
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Answer:
a) r(t) = 0.783t radians
b) h(t) = 30cos(0.783*t) feet
Step-by-step explanation:
The situation is depicted in the picture attached
<h3>(see picture)
</h3>
Since the angular speed is constant, to find an expression for the angle r(t) in radians we just cross-multiply using the fact that 1 min = 60 seconds
4.7 radians __________ 60 seconds
r(t) radians ____________ t seconds
The height h(t) after t seconds is given by
h(t) = 30cos(r(t)) ===>
h(t) = 30cos(0.783*t) feet
Answer: 92
Step-by-step explanation:
Formula : Sum of first n numbers = Average x n
Given: Average score on first 6 tests= 84
A score on all 8 tests = 86
Then, Sum of first 6 numbers = 84 x 6 = 504
Sum of first 8 numbers = 86 x 8 = 688
Sum of two last numbers = (Sum of first 8 numbers) - (Sum of first 6 numbers)
= 688-504
=184
Average of last two numbers = (Sum of two last numbers )÷2
= 184÷2
= 92
Hence, the average of your last two test scores = 92.
First, let's find the X Intercept
You are going to have to set y to 0
-8x + 4(0) = 24
Any time you multiple a number by 0, the answer is 0
-8x (+ 0) = 24
Now we are going to divide each side by -8
-8x/-8 = 24/-8
x = -3
Now let's find the Y Intercept
You are going to have to set x to 0 like we did with the first one
(-8(0)) + 4y = 24
4y/4 = 24/4
y = 6
Your intercept is (-3,6)
on a horizontal number line . numbers to the left are less than numbers to the right .. numbers to the right are less than numbers to the left