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Tasya [4]
3 years ago
5

What is the domain and range?

Mathematics
1 answer:
ycow [4]3 years ago
8 0

Answer:

Domain- the set of possible values of the independent variable or variables of a function.

Range- the set of values that a given function can take as its argument varies.

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In the Venn diagram, consider U = {whole numbers 1-100}
Dmitry [639]
The question is what numbers satisfy A ∩ C.

The symbol ∩ means intersection, .i.e. you need to find the numbers that belong to both sets A and C. Those numbers might belong to the set C or not, because that is not a restriction.

Then lets find the numbers that belong to both sets, A and C.

Set A: perfect squares from A to 100:

1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100

=> A = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}

Set C: perfect fourths

1^4 = 1
2^4 = 16
3^4 = 81

C = {1, 16, 81?

As you see, all the perfect fourths are perfect squares, so the intersection of A and C is completed included in A. this is:

A ∩ C = C or A ∩ C = 1, 16, 81

On the other hand, the perfect cubes are:

1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 81

B = {1, 8, 27, 81}

That means that the numbers 1 and 81 belong to the three sets, A, B, and C.

In the drawing you must place the number 16 inside the region that represents the intersection of A and C only, and the numbers 1 and 81 inside the intersection of the three sets A, B and C.
6 0
3 years ago
Read 2 more answers
The spherical balloon is inflated at the rate of 10 m³/sec. Find the rate at which the surface area is increasing when the radiu
rjkz [21]

The balloon has a volume V dependent on its radius r:

V(r)=\dfrac43\pi r^3

Differentiating with respect to time t gives

\dfrac{\mathrm dV}{\mathrm dt}=4\pi r^2\dfrac{\mathrm dr}{\mathrm dt}

If the volume is increasing at a rate of 10 cubic m/s, then at the moment the radius is 3 m, it is increasing at a rate of

10\dfrac{\mathrm m^3}{\mathrm s}=4\pi (3\,\mathrm m)^2\dfrac{\mathrm dr}{\mathrm dt}\implies\dfrac{\mathrm dr}{\mathrm dt}=\dfrac5{18\pi}\dfrac{\rm m}{\rm s}

The surface area of the balloon is

S(r)=4\pi r^2

and differentiating gives

\dfrac{\mathrm dS}{\mathrm dt}=8\pi r\dfrac{\mathrm dr}{\mathrm dt}

so that at the moment the radius is 3 m, its area is increasing at a rate of

\dfrac{\mathrm dS}{\mathrm dt}=8\pi(3\,\mathrm m)\left(\dfrac5{18\pi}\dfrac{\rm m}{\rm s}\right)=\dfrac{20}3\dfrac{\mathrm m^2}{\rm s}

4 0
3 years ago
at a small school, one male and one female are selected to represent the student body at the PTSCA meetings. if there are 41 mal
I am Lyosha [343]

It is given that there are 41 males and 48 females in the small school.

So, the number of ways a male student can be chosen from 41 males is ^{41}C_1

Likewise, the number of ways a female student can be chosen from 48 females is ^{48}C_1.

Thus, the total number of ways in which 2-person combinations are possible to represent the student body at the PTSAC meetings will be given by:

^{41}C_1\times ^{48}C_1=1968


7 0
3 years ago
Which is colder -3 -12 -8 -15
8_murik_8 [283]

Answer:

-15 is colder than the others

Step-by-step explanation:

It is colder because it is in the negatives but it also has a higher absolute value

4 0
3 years ago
Imagine that you are buying a car and needed a loan for $20,000. Your interest rate is 5% and you want to pay it off in 6 years.
Pepsi [2]

Answer:

Step-by-step explanation:

let each

8 0
3 years ago
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