Answer:
a) The function is constantly increasing and is never decreasing
b) There is no local maximum or local minimum.
Step-by-step explanation:
To find the intervals of increasing and decreasing, we can start by finding the answers to part b, which is to find the local maximums and minimums. We do this by taking the derivatives of the equation.
f(x) = ln(x^4 + 27)
f'(x) = 1/(x^2 + 27)
Now we take the derivative and solve for zero to find the local max and mins.
f'(x) = 1/(x^2 + 27)
0 = 1/(x^2 + 27)
Since this function can never be equal to one, we know that there are no local maximums or minimums. This also lets us know that this function will constantly be increasing.
Answer:
<em>3 3/4 feet</em>
Step-by-step explanation:
Given
Perimeter of the garden = 20ft
If he wants the length of the garden to be 2 1/2 longer than its width, then;
L = 2 1/2 + W
L is the length
W is the width
Perimeter of the garden = 2(L+W)
P20 = 2(5/2 + W+W)
20 = 5 + 2W+2W
20 - 5 = 4W
15 = 4W
W = 15/4
<em>W = 3 3/4 ft</em>
<em>Hence the width of the garden is 3 3/4 feet</em>
Answer:
a) 0.6636
b) 0.0951
c) 0,9474
d) 0.0047
e) 0.9957
f) 0.1308
Step-by-step explanation:
We look in tables z values and then we see carefully aereas inside normal curve
a) P[- 1.46 < z < 0.63 ] point 1.46 from table 0.0721 this s th area from value -1.46 to the left . And the value z = 0.63 corresond to the area 0.7357 which includes the area between 1.46 to the left tail, then we have to subtarct and get 0.6636 .
P[- 1.46 < z < 0.63 ] = 0.6636 66.36 %
b) P [ 0 < z < 1.31 ] we just need the area for point 1.31 that is 0.0951
P [ 0 < z < 1.31 ] = 0.0951 9.51 %
c) P [z > - 1.62 ] = 1 - 0.0526
P [z > - 1.62 ] = 0,9474 94.74 %
d) P[z < - 2.6 ] = 0.0047 0.47 %
e) P [ z < 2.63 ] = 1 - 0.0043
P [ z < 2.63 ] = 0.9957 99.57 %
f) P [ -2.58 < z < -1.1 ] = 0.1357 - 0.0049 =
P [ -2.58 < z < -1.1 ] = 0.1308 13.08 %
Answer: B; 2≤x≤8
Step-by-step explanation:
Do left part first: 0≤3x-6, 2≤x
Now do right part: 3x-6≤18, x≤8
Now combine into double inequality: 2≤x≤8
