Answer:
See explanation
Step-by-step explanation:
<u>Given:</u> XW is an altitude
m∠XWY=8x-6
<u>Prove:</u> x=2
<u>Solution:</u>
Statement Reason
1. XW is an altitude Given
2. m∠XWY = 90° Definition of altitude
3. m∠XWY = 8x - 6 Given
4. 8x - 6 = 90 Substitution property
5. 8x - 6 + 6 = 90 + 6 Addition property of equality
8x = 90
6. x = 12 Division property of equality
Let "a" and "b" be some number where:
a - b = 24
We want to find where a^2 + b^2 is a minimum. Instead of just logically figuring out that the answer is where a=b=12, I'll just use derivatives.
So we can first substitute for "a" where a = b+24
So we have (b+24)^2 + b^2 = b^2 +48b +576 + b^2
And that equals 2b^2 +48b +576
Then we take the derivative and set it equal to zero:
4b +48 = 0
4(b+12) = 0
b + 12 = 0
b = -12
Thus "a" must equal 12.
So:
a = 12
b = -12
And the sum of those two numbers squared is (12)^2 + (-12)^2 = 144 + 144 = 288.
The smallest sum is 288.
85 / 15 = 5 2/3
30 x 5 = 150
2/3 x 30 = 20
The answer is 170 seconds, or 2 minutes and 50 seconds
