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3 years ago

A cylinder has a volume of 157 cubic centimeters.

Mathematics

1 answer:

ziro4ka [17]3 years ago

5 0

Answer:

4.47100222

Step-by-step explanation:

157/2.5=62.8

62.8/pi= 19.98986085

square root the answer above and you get 4.47100222 for the radius

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(m+2)(m+3)=(m+2)(m-2)

Anastaziya [24]

(m+2)(m+3)= (m+2)(m-2)
⇒ m^2+ 3m+ 2m+ 6= m^2 -4
⇒ 5m+ 6= -4 (m^2 on both sides cancels out)
⇒ 5m= -4-6
⇒ 5m= -10
⇒ m= -10/5
⇒ m= -2

The final answer is m=-2~

6 0

3 years ago

The image of (-1, 2) reflected across the line y = -x is what?

Ann [662]

( -2, 1 ) is the image of ( -1,2 ) reflected across the line y=-x.

8 0

3 years ago

How would I solve this?

trasher [3.6K]

You had the right idea using the Pythagorean theorem to solve for b.

Problem is for that triangle to work, the 5 and the 2√2 would have to switch places. The length of a leg cannot be larger than the length of the hypotenuse for it to truly be a right triangle.

Pythagorean theorem only works for the right triangles. Only way to "solve this problem would be to bring in complex numbers.

5² + b² = (2√2)²

25 + b² = 2²(√2)²

25 + b² = 4(2)

25 + b² = 8

b² = 8 - 25

b² = - 17

b = √-17

b= (√17i)

Then the problem with THIS is a measurement/distance cannot be negative... which goes against exactly what that complex number i is.

8 0

3 years ago

Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5

zaharov [31]

Answer:

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}$ or $\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

$\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}$

Therefore, the solution is 31.

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as $\displaystyle \large{a_{n-1} \cdot r = a_n}$ meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as: