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2 years ago

What is the domain of the function f(x) = x^2 + 5?

Mathematics

1 answer:

Sophie [7]2 years ago

4 0

The domain is R so the first one is correct.

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The triangle T has vertices at (-2, 1), (2, 1) and (0,-1). (It might be an idea to

Firdavs [7]

Rewrite the boundary lines y = -1 - x and y = x - 1 as functions of y :

y = -1 - x ==> x = -1 - y

y = x - 1 ==> x = 1 + y

So if we let x range between these two lines, we need to let y vary between the point where these lines intersect, and the line y = 1.

This means the area is given by the integral,

$\displaystyle\iint_T\mathrm dA=\int_{-1}^1\int_{-1-y}^{1+y}\mathrm dx\,\mathrm dy$

The integral with respect to x is trivial:

$\displaystyle\int_{-1}^1\int_{-1-y}^{1+y}\mathrm dx\,\mathrm dy=\int_{-1}^1x\bigg|_{-1-y}^{1+y}\,\mathrm dy=\int_{-1}^1(1+y)-(-1-y)\,\mathrm dy=2\int_{-1}^1(1+y)\,\mathrm dy$

For the remaining integral, integrate term-by-term to get

$\displaystyle2\int_{-1}^1(1+y)\,\mathrm dy=2\left(y+\frac{y^2}2\right)\bigg|_{-1}^1=2\left(1+\frac12\right)-2\left(-1+\frac12\right)=\boxed{4}$

Alternatively, the triangle can be said to have a base of length 4 (the distance from (-2, 1) to (2, 1)) and a height of length 2 (the distance from the line y = 1 and (0, -1)), so its area is 1/2*4*2 = 4.

6 0

2 years ago

Write the product in its simplest form: 7xy3 . (-9xy)

Naddik [55]

The answer would be
-63x^2y^3

3 0

2 years ago

Use inductive reasoning to describe the pattern of each sequence. Then find the next two terms. 1, 2, 5, 6, 9,

juin [17]

It looks like the first 1 is the first problem, problem #1. (because of the period)
If this is the case, then the second sequence is 1, 0, -1, ...
1-1=0
0-1=-1
-1-1=-2
-2-1=-3
-3-1=-4
The sequence would then be 1, 0, -1, -2, -3, -4, ...

5 0

2 years ago

Read 2 more answers

you want to replace the carpet in the hallway. you checked with various stores and found that the best deal was given by a compa

Mrrafil [7]

I’m not sure, you should install photomath tho it should say

5 0

1 year ago

Sven has 11 more than twice as many customers as when he started selling newspapers. He now has 73 customers. How many did he ha

Andre45 [30]

Answer:

31 customers

Step-by-step explanation:

Let he had x customers when he started,

given that, 2x+11=73

=>2x=62.. Subtracting 11 from both sides

=> x=31 ...Dividing both sides by 2

Hence he had 31 customers when he started.

5 0

2 years ago