Answer:
The value of c that satisfies the conclusion of the Mean Value Theorem applied to f on the interval [1,4] is approximately 0.1793.
Step-by-step explanation:
Given f(x) = 5cos²x² + ln(x + 1) - 3
The Mean Value Theorem applied to f on an interval [a, b] is given as
f'(x) = c = [f(b) - f(a)]/(b - a)
= [f(4) - f(1)]/(4 - 1)
c = [f(4) - f(1)]/3
f(4) = 5(cos4²)² + ln(5) - 3
= 3.2296
f(1) = 5(cos1²)² + ln(2) - 3
= 2.6916.
c = (3.2296 - 2.6916)/3
= 0.538/3
≈ 0.1793
Answer:
Week=25 Hours
Weekend= 5 Hours
Step-by-step explanation:
So we need to use the info they gave us and create two equations. Firstly we know how much he gets paid per hour during the week (x) and how much he gets paid on the weekend (y).
$20x+$30y=$650
We get this because we know the combined rates he is paid times the hours should add up to the amount he earned.
The next equation will be made off of the information that he worked 5 times as many hours during the week as on the weekend. This tells us that we will take the weekend hours (y) and multiply them by 5 in order to get the week hours (x).
x=5y Now, since we have one variable by itself, we can plug it in for x in the first equation.
20(5y)+30y=650 Our first step here is to distribute the 20 to the 5y in order to eliminate the parenthesis.
100y+30y=650 Next add the like terms together (100y+30y).
Now all we have to do to find y is divide by 130 on both sides to get y alone.
130y=650
________
130 130
y=5 Now to solve for x we just plug our y value into one of the equations above. I'm going to use the second equation.
x=5(5)
x=25
(2k, k) and (3k, 4k)
Slope = (4k - k )/(3k - 2k)
= 3k / k
= 3
Answer :
3
Answer:
59°, 71°
Step-by-step explanation:
This is a "sum and difference" problem. All problems of this type have the same answer: the larger of the two numbers is the average of those given.
Then the larger angle is (130 +12)°/2 = 71°. The smaller is 71° -12° = 59°.
_____
<em>More detailed solution</em>
There are several ways to get there using equations. You can, for example, let L represent the larger number. Then L - D will be the smaller one (where D represent the difference). The sum of the two numbers (S) is ...
L + (L -D) = S
2L = S + D . . . . collect terms, add D
L = (S+D)/2 . . . the larger number is the average of the sum and difference
Answer:
i know im late but its 42
Step-by-step explanation:
:/ i think
