At sunrise, the temperature was -12 °
1 answer:
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What is that $13,455.78? Something? I did this and got $13,122.76. Here's how I did it:
Use this formula
where A is the ending amount, P is the starting amount, n is the number of times it compounds a year, and t is the number of years. We have all we need to set it up:
First divide and add inside the parenthesis:
then multiply the exponents:
raise the value inside the parenthesis to the power of 260:
and finally multiply to get A = $13,122.76
Use this formula
First divide and add inside the parenthesis:
then multiply the exponents:
raise the value inside the parenthesis to the power of 260:
and finally multiply to get A = $13,122.76
Without loss of generality, we can assume the semicircle has a radius of 1 and is described by
y = √(1 - x²)
Then the shorter base has length 2x and the longer base has length 2. The area of the trapezoid is
A = (1/2)(2x+2)√(1-x²) = (1+x)√(1-x²)
Differentiating with respect to x, we have
A' = √(1-x²) + (1+x)(-2x)/(2√(1-x²)
Setting this to zero, we get
0 = (1-x²) +(1+x)(-x)
0 = 2x² +x -1
(2x-1)(x+1) = 0
x = {-1, 1/2} . . . . . -1 is an extraneous solution that gives minimum area
So, for x = 1/2, the area is
A = (1 + 1/2)√(1 - (1/2)² = (3/2)√(3/4)
A = (3/4)√3
Of course, if the radius of the semicircle is "r", the maximum area is
A = (r²·3·√3)/4
y = √(1 - x²)
Then the shorter base has length 2x and the longer base has length 2. The area of the trapezoid is
A = (1/2)(2x+2)√(1-x²) = (1+x)√(1-x²)
Differentiating with respect to x, we have
A' = √(1-x²) + (1+x)(-2x)/(2√(1-x²)
Setting this to zero, we get
0 = (1-x²) +(1+x)(-x)
0 = 2x² +x -1
(2x-1)(x+1) = 0
x = {-1, 1/2} . . . . . -1 is an extraneous solution that gives minimum area
So, for x = 1/2, the area is
A = (1 + 1/2)√(1 - (1/2)² = (3/2)√(3/4)
A = (3/4)√3
Of course, if the radius of the semicircle is "r", the maximum area is
A = (r²·3·√3)/4
Answer:
$200
Step-by-step explanation:
63 mph is 13 mph more than 50 mph, so the fine will be that for 13 mph over the speed limit. The fine corresponding to 13 mph over the limit is $200.
