The answer is -13.
Solution:
= |-4b - 8| + |-1 - b^2| + 2b^3
= |-4(-2) - 8| + |-1 - -2^2| + 2(-2)^3
= |8-8| + |-1+4| + 2(-8)
= |0| + |3| + (-16)
= -13
Answer:

Step-by-step explanation:
We have been given that an object oscillates 4 feet from its minimum height to its maximum height. The object is back at the maximum height every 3 seconds. We are asked to find the cosine function that can be used to model the height of the object.
We know that standard form of cosine function is
, where,
|A| = Amplitude,
Period =
,
C = Phase shift,
D = Vertical shift.
Since distance between maximum and minimum is 4, therefore, amplitude will be half of it, that is,
.
Since objects gets back to its maximum value in every 3 seconds, therefore, period of the function is 3 seconds. We know that period is given by
, therefore, we can write
, therefore,
.
We haven't been given any information about phase and mid-line, we can assume the values of C and D to be zero
.
Therefore, our function required function would be
.
0.75*3.5a = 2.625a
0.75*6b = 4.5b
2.625a - 4.5b is our final answer
Answer:
Final answer is approx
.
Step-by-step explanation:
using given information from the attached picture, we need to find the value of cos(H) so let's apply the formula of cosine.




Hence final answer is approx
.
Answer: x(x-4) = 140 This equation can be solve to find the length.
Step-by-step explanation:
If the width of the rectangle will be 4 less than the length and the length is represented by x then we could have the equation w=x - 4 for the width and the length is just x. And to find the area of a rectangle we multiply the length by the with so multiply x-4 by x for it to equal 140 because 140 is the area.
x(x-4) = 140 solve for x
- 4x = 140 subtract 140 from both sides
x^2 - 4x - 140 = 0 find a number that the product is 140 and the sum is -4
-14 and 10 works out.
- 14x + 10x - 140 = 0 factor by grouping
x(x -14) 10(x-14) = 0 factor out x-14
(x-14) ( x+10) = 0 set them both equal zero.
x-14= 0 or x+10 = 0
x = 14 or x= -10
Since -10 can't represent a distance, the answer is 14.
Check.
In this case the length is 14 and if the width is 4 less than the length then we will subtract 4 from 14.
14- 4 = 10 so the width is 10.
14 * 10 = 140