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telo118 [61]
3 years ago
8

Measuring Circles: Question 1

Mathematics
1 answer:
andreev551 [17]3 years ago
7 0

Answer:10.51inches

Step-by-step explanation:

circumference=66

Radius=circumference ➗ (2xπ)

Radius=66 ➗ (2x3.14)

Radius=66 ➗ 6.28

Radius=10.51inches

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Use induction to prove that 2? ?? for any integer n>0 . Indicate type of induction used.
Hoochie [10]

Answer with explanation:

The given statement is which we have to prove by the principal of Mathematical Induction

    2^{n}>n

1.→For, n=1

L H S =2

R H S=1

2>1

L H S> R H S

So,the Statement is true for , n=1.

2.⇒Let the statement is true for, n=k.

      2^{k}>k

                   ---------------------------------------(1)

3⇒Now, we will prove that the mathematical statement  is true for, n=k+1.

     \rightarrow 2^{k+1}>k+1\\\\L H S=\rightarrow 2^{k+1}=2^{k}\times 2\\\\\text{Using 1}\\\\2^{k}>k\\\\\text{Multiplying both sides by 2}\\\\2^{k+1}>2k\\\\As, 2 k=k+k,\text{Which will be always greater than }k+1.\\\\\rightarrow 2 k>k+1\\\\\rightarrow2^{k+1}>k+1

Hence it is true for, n=k+1.

So,we have proved the statement with the help of mathematical Induction, which is

      2^{k}>k

                 

   

3 0
3 years ago
Jane made a door frame for the house but does not have a tool to measure the angles. How can she check that the corner is 90 deg
Ainat [17]

The door frame is a rectangle. The diagonals of a rectangle are congruent. She can measure the two diagonals and make sure they are congruent.

3 0
3 years ago
Read 2 more answers
Please help me in answers 3 and 5
Mama L [17]
3. The correct answer is 2) 3m² - 6. 
(2m² + 3m - 4) + (m² - 3m - 2)   Given
2m² + m²   These numbers are like terms, because they both end in m².
3m²   Since m² can also be written as 1m², and 2 + 1 = 3, this is the sum of 2m² and m² (1m²).

3m + (-3m)   These numbers are like terms, because they both end in m. -3m is negative because it was being subtracted.
0   Since we're adding a negative, it's the same as subtracting something. 3m - 3m is 0.

-4 + (-2)   These numbers are like terms, because they are both simple integers with no variable. Once again, we're adding a negative because it was being subtracted.
-6   -4 + (-2) is the same as -4 - 2, which is -6. Remember that when you're subtracting from a negative, the number seems to become larger. For instance, 1 - 1 is 0, but -1 - 1 is -2.

3m² - 6   Put all of the terms together. We don't have to write out 0, because 0 is the same as nothing.

5. This one is a bit unclear, but I think that the correct answer is 2) II and IV. The slope formula can be written as y = mx + b, where m is the slope and b is the y-intercept, or the place where the line crosses the y-axis. In this equation, b is 2, which is a positive number, so the y-intercept shifts upward. This means that the answer is either 2 or 3. As for |x - 6|, the way this is written makes the equation somewhat confusing. I believe that the bars are meant as absolute value bars, which, put simply, turn negatives into positives. This means that this part is x + 6, so the line shifts to the right. However, if they were intended as parentheses, the line would shift to the left, because we're subtracting 6 from x. I'm almost certain those were intended as absolute value bars, though, so I think that the answer is 2.

Hope this helps!
4 0
3 years ago
Find the GCF of 30, 60, and 78.
Sloan [31]
The greatest common factor is six.
6 0
3 years ago
Read 2 more answers
Find the value of x. Then find the measure of each labeled angle.
Hunter-Best [27]

Answer:

x = 114°

Step-by-step explanation:

x + (x - 48) = 180

2x = 228

x = 114

114 - 48 = 66

7 0
3 years ago
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