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slavikrds [6]
3 years ago
13

The quotient of two numbers is 21. Their difference is 60.What are the two numbers?

Mathematics
1 answer:
goldenfox [79]3 years ago
4 0
The numbers are 63 and 3
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How many different perfect cubes are among the positive actors of 2021^2021
9966 [12]

Answer:

hope this helps :D

Step-by-step explanation:

Perfect cube factors:

If a number is a perfect cube, then the power of the prime factors should be divisible by 3.

Example 1:Find the number of factors of293655118 that are perfect cube?

Solution: If a number is a perfect cube, then the power of the prime factors should be divisible by 3. Hence perfect cube factors must have

2(0 or 3 or 6or 9)—– 4 factors

3(0 or 3 or 6)  —–  3  factors

5(0 or 3)——- 2 factors

11(0 or 3 or 6 )— 3 factors

Hence, the total number of factors which are perfect cube 4x3x2x3=72

Perfect square and perfect cube

If a number is both perfect square and perfect cube then the powers of prime factors must be divisible by 6.

Example 2: How many factors of 293655118 are both perfect square and perfect cube?

Solution: If a number is both perfect square and perfect cube then the powers of prime factors must be divisible by 6.Hence both perfect square and perfect cube must have

2(0 or 6)—– 2 factors

3(0 or 6) —– 2 factors

5(0)——- 1 factor

11(0 or 6)— 2 factors

Hence total number of such factors are 2x2x1x2=8

Example 3: How many factors of293655118are either perfect squares or perfect cubes but not both?

Solution:

Let A denotes set of numbers, which are perfect squares.

If a number is a perfect square, then the power of the prime factors should be divisible by 2. Hence perfect square factors must have

2(0 or 2 or 4 or 6 or 8)—– 5 factors

3(0 or 2 or 4 or 6)  —– 4 factors

5(0 or 2or 4 )——- 3 factors

11(0 or 2or 4 or6 or 8 )— 5 factors

Hence, the total number of factors which are perfect square i.e. n(A)=5x4x3x5=300

Let B denotes set of numbers, which are perfect cubes

If a number is a perfect cube, then the power of the prime factors should be divisible by 3. Hence perfect cube factors must have

2(0 or 3 or 6or 9)—– 4 factors

3(0 or 3 or 6)  —–  3  factors

5(0 or 3)——- 2 factors

11(0 or 3 or 6 )— 3 factors

Hence, the total number of factors which are perfect cube i.e. n(B)=4x3x2x3=72

If a number is both perfect square and perfect cube then the powers of prime factors must be divisible by 6.Hence both perfect square and perfect cube must have

2(0 or 6)—– 2 factors

3(0 or 6) —– 2 factors

5(0)——- 1 factor

11(0 or 6)— 2 factors

Hence total number of such factors are i.e.n(A∩B)=2x2x1x2=8

We are asked to calculate which are either perfect square or perfect cubes i.e.

n(A U B )= n(A) + n(B) – n(A∩B)

=300+72 – 8

=364

Hence required number of factors is 364.

8 0
3 years ago
Find the measures of interior angles. Find a and B.
olga nikolaevna [1]

Answer:

A = 68

B = 44

C = 68

Step-by-step explanation:

find x:

68 + x + x - 24 = 180

2x + 44 = 180

180 - 44 = 136

136 / 2 = 68

x = 68

_________________________

68 + 68 + 44 = 180

6 0
3 years ago
8 students want to share 6 candy bars equally. How much will each student get?
Crank

Answer: 1.3

Step-by-step explanation:

8 divided by 6 will equal 1.3 so each student will get 1.3

3 0
3 years ago
Read 2 more answers
A circle has a diameter of 26 units. What is the area of the circle to the nearest hundredth of a square unit? UseC=pi d
IrinaVladis [17]

Answer:

A circle diameter of 26 units is 530.93

I did the math in my head

4 0
3 years ago
How do i solve this im kinda confused
Bas_tet [7]

Answer:

A:2

B:-5

C:8

D:-147

Step-by-step explanation:

A: For this one, you can cancel out the negatives. Then just divide 14 by 7. Your final answer is 2. Final Answer : 2

B: This one you can forget about the negative for the first bit. Just divide 15 by 3 to get 5. Now the negative is only on one side of the equation so therefore we add the negative back into our answer. Final Answer : -5

C: Just divide 32 by 4 to get 8. No removal or substitution is needed for this one because both numbers are positive. Final Answer : 8

D: Multiply both numbers normally forgetting about the negative at first. 49 * 3 is 147. Now one of our numbers contain a negative so we plug back the negative into our answer. Final Answer : -147

5 0
2 years ago
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