Given:
The composite figure.
To find:
The volume of the given composite figure.
Solution:
Given composite figure contains a cuboid and a pyramid.
Length, breadth and height of the cuboid are 8, 6 and 4 respectively.
Volume of a cuboid is
Length and breadth of the pyramid is same as the cuboid, i.e., 8 and 6 respectively.
Height of pyramid = 10 - 4 = 6
Volume of a pyramid is
The volume of composite figure is
It can be written as
Therefore, the correct option is A.
The range is the set of all possible output, as you feed the function with all possible inputs. Since our inputs (domain) are -3, 0, 3, our outputs are
So, the range is
Answer:
The partial fraction decomposition is .
Step-by-step explanation:
Partial-fraction decomposition is the process of starting with the simplified answer and taking it back apart, of "decomposing" the final expression into its initial polynomial fractions.
To find the partial fraction decomposition of :
First, the form of the partial fraction decomposition is
Write the right-hand side as a single fraction:
The denominators are equal, so we require the equality of the numerators:
Expand the right-hand side:
The coefficients near the like terms should be equal, so the following system is obtained:
Solving this system, we get that .
Therefore,
Answer:
With the first four questions, all you need to do is find a value of x that gives you a zero value in any one of those brackets. Let's do it.
You said you finished 1, so let's skip it.
I can't give you a full answer for question 2, because you didn't capture the entire expression in the screenshot. I can see that the values 3 and 0.125 would give zero values, but I can't tell you the last.
For question three, we need to find x values where either 9x + 3 = 0, or x² - 9 = 0. There are three values that meet those conditions. You can solve it just by assigning a zero value and solving for x:
For the second term actually has two solutions, because a squaring a number also causes negatives to be converted to positives. Another way of seeing this is to notice that the second term is actually a difference of squares:
so in this case x could be -1/3, -3, or 3 to give a zero value.
For question four, you can only get a zero if you use imaginary numbers, as no real number can be squared to give you a negative. So the only answers to that are 5i, or -5i.
With questions five six seven and eight, we just need to make exceptions for zero denominators, so:
For question 5, you can x can be any real number except -4, 2 and 7
For 6, x can be anything but 3, 1/8th or 5
for 7, We again have that difference of squares, so the actual denominator is (9x + 3)(x + 9)(x - 9), meaning x can be anything but -1/3, -9, or 9
And finally for question 8, we again have a squaring, meaning that only an imaginary number will cause division by zero, meaning x can't be 5i or -5i.