Answer:
33 degrees
Step-by-step explanation:
114+2x =180 right?
so 2x = 180-114 = 66
then x = 33
SOLUTION:
A box has a square base of side x and height y where x,y > 0.
Its volume is V = x^2y and its surface area is
S = 2x^2 + 4xy.
(a) If V = x^2y = 12, then y = 12=x^2 and S(x) = 2x^2 C 4x (12=x2) = 2x2 + 48x^-1. Solve S'(x) = 4x - 48x-2 = 0 to
obtain x = 12^1/3. Since S(x/) ---> infinite as x ---> 0+ and as x --->infinite, the minimum surface area is S(12^1/3) = 6 (12)^2/3 = 31.45,
when x = 12^1/3 and y = 12^1/3.
(b) If S = 2x2 + 4xy = 20, then y = 5^x-1 - 1/2 x and V (x) = x^2y = 5x - 1/2x^3. Note that x must lie on the closed interval [0, square root of 10]. Solve V' (x) = 5 - 3/2 x^2 for x>0 to obtain x = square root of 30 over 3 . Since V(0) = V (square root 10) = 0 and V(square root 30 over 3) = 10 square root 30 over 9 , the
maximum volume is V (square root 30 over 3) = 10/9 square root 30 = 6.086, when x = square root 30 over 3 and y = square root 30 over 3 .
<span><span> r = -1/3 = -0.333
</span><span> r = 0</span></span>
The data value that is an outlier is 67
<h3>How to determine the outlier?</h3>
The dataset is given as:
83, 84, 85, 87, 89, 88, 67, 79, and 81
To determine the outlier, we select the data values that are relatively far from others
In the above dataset, the data element 67 is far from other data values
Hence, the data value that is an outlier is 67
Read more about outlier at:
brainly.com/question/3631910
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Yvaires directly as x means
y=kx
y varies inversly with z means
y=k/z
therfor
y=(kx^2)/z
k=constant of variation
6=(k9^2)/27
6=(k81)/27
6=3k
divide both sides by 3
2=k
the constant of variation is 2
