All categories

3 years ago

Is this True or False ?

Mathematics

1 answer:

Svetradugi [14.3K]3 years ago

6 0

Answer:

Option B True

Step-by-step explanation:

we know that

A function relates <u>each element</u> of a set (input) with <u>exactly one</u> element of another set (output)

1) "...each element..." means that every element in X (input) is related to some element in Y (output)

2) "...exactly one..." means that a function is single valued. It will not give back 2 or more results for the same input

therefore

f(x) is a function

You might be interested in

What is an equation of the line that passes through the point ( − 5 , − 3 ) (−5,−3) and is parallel to the line 3 x + 5 y = 15 3

aivan3 [116]

Answer:

would it be 5y

Step-by-step explanation:

6 0

2 years ago

Calculus Problem

Roman55 [17]

The two parabolas intersect for

$8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2$

and so the base of each solid is the set

$B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}$

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, $|x^2-(8-x^2)| = 2|x^2-4|$ . But since -2 ≤ x ≤ 2, this reduces to $2(x^2-4)$ .

a. Square cross sections will contribute a volume of

$\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x$

where ∆x is the thickness of the section. Then the volume would be

$\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}$

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

$\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x$

We end up with the same integral as before except for the leading constant:

$\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx$

Using the result of part (a), the volume is

$\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}$

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

$\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x$

and using the result of part (a) again, the volume is

$\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}$

7 0

2 years ago

A contracting company rents a generator for 6 hours and a heavy duty saw for 6 hours total cost of $48 for another job the compa

Wewaii [24]

Answer:

the hourly rates are $8 and $10 respectively

Step-by-step explanation:

Given that

The generator rents for 6 hours and the total cost is $48

And, for another job The generator rents for 4 hours and the total cost is $40

We need to find out the hourly rates

For the first one

= $48 ÷ 6 hours

= $8

For the second one

= $40 ÷ 4 hours

= $10

Hence, the hourly rates are $8 and $10 respectively

6 0

3 years ago

A painting is 4 feet long.A photo frame is 10 inches long.How many inches longer is the painting then the photo frame?

Galina-37 [17]

Change 4 feet to inches
4 feet is 48 inches
48-10=38

3 0

3 years ago

A math class is having a discussion on how to determine if the expressions 4x-x+5 and 8-3x-3 are equivalent using substitution.

bixtya [17]

Answer:

option (b) is correct.

Both expressions should be evaluated with one value. If the final values of the expressions are the same, then the two expressions must be equivalent.

Step-by-step explanation:

Given : A math class is having a discussion on how to determine if the expressions 4x - x + 5 and 8 - 3x - 3 are equivalent using substitution.

We have to choose the correct method from the given options that the class has suggested.

Since we have to show the given expressions 4x - x + 5 and 8 - 3x - 3 are equivalent using substitution.

We will choose a single value of x and then evaluate both the given expression at that single value and if the output of both expression comes out to be same then the two expressions must be equivalent.

For example lets take x = 2,

Then expression 4x - x + 5 becomes 4(2) - 2 +5 = 8 - 2 + 5 = 6 + 5 = 11

also, expression 8 - 3x - 3 becomes 8 - 3(2) - 3 = 8- 6 - 3 = 8 - 9 = -1

thus, the value is not equal hence, the two expression are not equivalent.

Thus, option (b) is correct.

Both expressions should be evaluated with one value. If the final values of the expressions are the same, then the two expressions must be equivalent.

6 0

3 years ago

Read 2 more answers