Answer:
The set of all real values except 7
Step-by-step explanation:
We are given that,
Domain of the function f(x) is 'the set of all real values except 7'.
Domain of the function g(x) is 'the set of all real values except -3'.
It is required to find the domain of 
.
Now, we know that,
<em>The composition of functions 
and 
will be defined where the function is defined.</em>
Since, the domain of f(x) is 'the set of all real values except 7'.
Thus, the domain of is also 'the set of all real values except 7'.
Answer:
No solution
Step-by-step explanation:
1. Multiply the parenthesis by -10
2. Collect like terms
3. Cancel equal terms
4. You're left with -20=13, which is false. There is no solution.
where is point p???? ..................
The question is incomplete.Here is the complete question.
The load that can be supported by a rectangular beam varies jointly as the width of the beam and the square of its length, and inversely as the length of the beam. A beam 13 feet long, with a width of 6 inches and a height of 4 inches can support a maximum load of 800 pounds. If a similar board has a width of 8 inches and a height of 7 inches, how long must it be to support 1300 pounds?
Answer: It must be 392 inches or approximately 33 feet.
Step-by-step explanation: According to the question, the measures (width, length and height) of a beam and the weight it supports are in a relation of <u>proportionality</u>, i.e., if divided, the result is a constant.
For the first load:
width = 6in
height = 4in
length = 13ft or 156in
weight = 800lbs
Then, constant will be:
k = 1300
For the similar beam:
L = 49.8
L = 392in or 32.8ft
A similar board will support 1300lbs if it has 392 inches or 32.8 feet long.
To start it off, we have to find where the 3 meet - to find when 3e^x and 3e^(-x) meet, we start off with dividing both sides to get e^x=e^(-x) and e^x=1/e^x, multiplying both sides by e^x to get e^(2x)=1 and x=0. Plugging in x=1 for both equations, we get 3e and 3/e respectively. Graphing it out, we can see that it forms a weird shape, but if you draw a line at y=3, we can have 2 separate shapes, making it super easy! We have x as the radius since it's about the y axis and the equations (from a certain point) as the height
We have 2 integrals - 2π(∫(from 3 to 3e) (x)(3e^x)) and 2π(∫(from 3/e to 3) (x)(e^(-x)). We then get 2π (∫3xe^x+∫3xe^(-x)) as added up they make the area between the curves.For ∫3xe^x, For 3xe^x, which we can separate the 3 from and get xe^x, we use integration by parts to put x in for f and e^x as g in ∫fg'=fg-∫f'g, plugging it in to get xe^x-∫e^x, resulting in xe^x-e^x. Multiplying that by 3 (as we separated that earlier), we get 3xe^x-e^x
For ∫3xe^(-x), we can use the same technique for separating the 3 out, but for ∫xe^(-x), we can use put x in for f and g' as e^(-x), resulting in g being -e^(-x) by using u substitution and making -x u. Next, we get (x)(-e^(-x))+∫(-e)^(-x), and ∫(-e)^(-x)=e^(-x) in the same way -e^(-x) being the integral of e^(-x) was found.
Adding it all up for this, we get 3(-xe^(-x)-e^(-x)) as our solved integral.
Since 3xe^x-3e^x is just the solved integral and we need to find it on 3 to 3e, we plug in 3e for x and subtract it from plugging 3 into x to get ((9*e-3)*e^(3*e)-6*e^3). We need to multiply it by 2pi (since it's a cylindrical shell) to get (2pi(((9*e-3)*e^(3*e)-6*e^3))
For 3(-xe^(-x)-e^(-x)) , we can plug it in for 3 and 3/e (as the respective upper and lower bounds) to get 3*((e+3)*e^(-3*e^(-1)-1)-4*e^(-3)). Multiply that by 2pi to get 6pi*((e+3)*e^(-3*e^(-1)-1)-4*e^(-3)).
Add the two up to get 6pi*((e+3)*e^(-3*e^(-1)-1)-4*e^(-3))+(2pi(((9*e-3)*e^(3*e)-6*e^3)) in and it said
