MATHEMATICS HIGH SCHOOL

Find the two geometric means between 20 and 2500

Answers

Answer 1
Answer:

Answer:

The two geometric means between 20 and 2500 are 100 and 500.

Step-by-step explanation:

First of all we all should know about a geometric progression to solve this question.

A geometric progression is a series in which there is a first term a and all the next terms are calculated by multiplying the previous term by a common number r.

where a is known as first term and

r is known as common ratio.

In the question we are given a as 20 and we have to find out 2 terms after 20 and 4th term is given as 2500.

Formula for n^(th) term in a geometric progression is:

a_(n) = a* r^(n-1)

Here a_(4) = 2500

As per formula of n^(th) term:

a* r^(3) = 2500\n\Rightarrow 20 * r^(3) =2500\n\Rightarrow r^(3) = 125\n\Rightarrow r = 5

Now, 2nd term:

a_(2) = a * r\n\Rightarrow a_(2) = 20 * 5\n\Rightarrow a_(2) = 100

Now, 3rd term:

a_(3) = a * r^(2) \n\Rightarrow a_(3) = 20 * 5^(2)\n\Rightarrow a_(3) = 500

So, the two geometric means between 20 and 2500 are 100 and 500.

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Side a of a triangle is 4 cm longer than side b. Side c is twice as long as side b. What is the length of each side if the perimeter is 28 cm? Draw and label picture. Show all work with labeled answer.

Answers

Side a, b and c are 10cm , 6cm , 12cm

Given that;

Side a = 4 + Side b

Side c = 2(Side b)

Perimeter of triangle = 28 cm

Find:

Length of each side

Computation:

Assume;

Side b = q

Side a = 4 + q

Side c = 2q

So,

Perimeter of triangle = 28 cm

q + 4 + q + 2q = 28

4q = 24

q = 6

Side a = 10 cm

Side b = 6 cm

Side c = 12 cm

Learn more:

brainly.com/question/20955459?referrer=searchResults
a=b+4\nc=2b\na+b+c=28\n\nb+4+b+2b=28\n4b=24\nb=6\n\na=6+4\na=10\n\nc=2\cdot6\nc=12\n\n\boxed{a=10,b=6,c=12}

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Answers

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