It’s the first one if it’s not then my bad g
I’m pretty sure it is 57?
Answer:
D. right 4, down 8
Step-by-step explanation:
The usual transformations applied to functions are ...
f(x) ⇒ f(x -h) . . . . translation right h units
f(x) ⇒ f(x) +k . . . . translation up k units
f(x) ⇒ k·f(x) . . . . . vertical scaling by a factor of k; reflection over x-axis when k < 0
f(x) ⇒ f(x/k) . . . . . horizontal scaling by a factor of k; reflection over y-axis when k < 0
In the above, "scaling" will be expansion when |k| > 1, compression when |k| < 1.
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Your transformation is ...
x^2 ⇒ (x -4)^2 -8
f(x) ⇒ f(x -4) -8
This is translation with h=4 and k=-8. That is, it is translation right 4 units and down 8 units.
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<em>Additional comment</em>
Like much of math, it is all about matching patterns.
Answer: The correct option is second, i.e. ,"2 times the integral from 0 to 1 of the quantity x cubed minus 3 times x squared plus 2 times x, dx".
Explanation:
The given equation is,
It can be written as,
Find the zeros of the equation. Equation the function equal to 0.
So, the three zeros are 0, 1 and 2.
The graph of the equation is shown below.
From the given graph it is noticed that the enclosed by the curve and x- axis is lies between 0 to 2, but the area from 0 to 1 lies above the x-axis and area from 1 to 2 lies below the x-axis. So the function will be negative from 1 to 2.
The area enclosed by curve and x-axis is,
![A=\int_{0}^{1}f(x)dx+\int_{1}^{2}[-f(x)]dx](https://tex.z-dn.net/?f=A%3D%5Cint_%7B0%7D%5E%7B1%7Df%28x%29dx%2B%5Cint_%7B1%7D%5E%7B2%7D%5B-f%28x%29%5Ddx)
From the graph it is noticed that the area from 0 to 1 is symmetric or same as area from 1 to 2. So the total area is the twice of area from 0 to 1.
![A=2\int_{0}^{1}[x^3-3x^2+2x]dx](https://tex.z-dn.net/?f=A%3D2%5Cint_%7B0%7D%5E%7B1%7D%5Bx%5E3-3x%5E2%2B2x%5Ddx)
Therefore, The correct option is "2 times the integral from 0 to 1 of the quantity x cubed minus 3 times x squared plus 2 times x, dx".
Answer:
Only one.
Step-by-step explanation:
Given that there are 25 cookie of the same type in a cookie jar.
We have to select 4 cookies from these 25.
Since they are all the same type, they are identical.
The question is
How many ways can you choose 4 cookies from a cookie jar containing 25 cookies of all the same type?
There is no difference if we take any four cookies from these 25.
Hence no of different ways = 1
Only one is the answer.
