The two lines don't change direction when they intersect, so that means the two angle measures are equivalent.
You could write .
To make this easier, you can move the numbers with variables to one side of the equation, and the numbers without variables to the other. Know that when a number is moved to the other side, it becomes the opposite of what it currently is.
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The value of x is 35.
Answer: 3026
30
Step-by-step explanation: Average sum of the female and male's test score is the sum of expected value of each gender:
Assuming x represents the random male selected and y represents the random female selected:
3026
The average sum of their scores is 3026.
Average difference is the difference between the expected value (mean) of each gender:
1528 - 1498
30
The average difference of their scores is 30.
The maximum volume of the box is 40√(10/27) cu in.
Here we see that volume is to be maximized
The surface area of the box is 40 sq in
Since the top lid is open, the surface area will be
lb + 2lh + 2bh = 40
Now, the length is equal to the breadth.
Let them be x in
Hence,
x² + 2xh + 2xh = 40
or, 4xh = 40 - x²
or, h = 10/x - x/4
Let f(x) = volume of the box
= lbh
Hence,
f(x) = x²(10/x - x/4)
= 10x - x³/4
differentiating with respect to x and equating it to 0 gives us
f'(x) = 10 - 3x²/4 = 0
or, 3x²/4 = 10
or, x² = 40/3
Hence x will be equal to 2√(10/3)
Now to check whether this value of x will give us the max volume, we will find
f"(2√(10/3))
f"(x) = -3x/2
hence,
f"(2√(10/3)) = -3√(10/3)
Since the above value is negative, volume is maximum for x = 2√(10/3)
Hence volume
= 10 X 2√(10/3) - [2√(10/3)]³/4
= 2√(10/3) [10 - 10/3]
= 2√(10/3) X 20/3
= 40√(10/27) cu in
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