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Lady bird [3.3K]
2 years ago
8

The sides of a right triangle form an arithmetic sequence with the difference d. Find the area of an inscribed circle in terms o

f d.
Mathematics
1 answer:
pantera1 [17]2 years ago
3 0

Answer:

The sides of a right triangle form an arithmetic sequence with the difference is described below in detail.

Step-by-step explanation:

Let's denominate the first term aa and the obvious difference dd. Therefore, your course enhances:

a, a+d, a+2da, a+d, a+2d

Now, these three terms form the sides of a right triangle. Since a+2da+2d is the highest (considering d > 0), we can state that it is the hypothenuse.

applying the Pythagorean Theorem:

a2+(a+d)2=(a+2d)2a2+(a+d)2=(a+2d)2

a2+a2+2ad+d2=a2+4ad+4d2a2+a2+2ad+d2=a2+4ad+4d2

3d2−a2+2ad=03d2−a2+2ad=0

(3d−a)(d+a)=0(3d−a)(d+a)=0

Therefore, your solutions are

3d=a3d=a

andd=−ad=−a

So if a = 3, d = 1. Therfore, one potential  sequence is 3, 4, 5.

Similarly, if a = 6, then d = 2, so another potential sequence is 6, 8, and 10

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Why can you NOT combine 3x and 5x^2 ?
diamong [38]
Although they are the same variable, you cannot add two variables raised to different powers. 3x^1 + 5x^2 cannot work, but 3x^2 + 5x^2 can. Also, if you are multiplying them, they would combine to be 15x^3, as 3 and 5 (The coefficients) multiply together and x^2 times x^1 = x^3.

I hope that helps.
7 0
3 years ago
10. A company finds that 45% of first-time visitors to its website do not buy any of its products. If there are 75 first-time vi
vekshin1

Using the binomial distribution, it is found that the probability that exactly 36 of them buy a product is of 0.044.

For each first-time visitor, there are only two possible outcomes, either they buy a product, or they do not. The probability of a first-time visitor buying a product is independent of any other first-time visitor, hence the binomial distribution is used to solve this question.

<h3>What is the binomial distribution formula?</h3>

The formula is:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

In this problem:

  • 45% of first-time visitors to its website do not buy any of its products, hence 55% buy, that is, p = 0.55.
  • There are 75 first-time visitors on a given day, hence n = 75.

The probability that exactly 36 of them buy a product is P(X = 36), hence:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 36) = C_{75,36}.(0.55)^{36}.(0.45)^{39} = 0.044

More can be learned about the binomial distribution at brainly.com/question/24863377

8 0
1 year ago
Peter is planting a rectangular garden. The length is 15 yards longer than the width. Jorge is planting a square garden. The sid
const2013 [10]

If the width of peter's garden is 32 yards, the ratio of the areas is 47: 32

<h3>Area of a rectangle.</h3>

area of rectangle = lw

where

  • l = length
  • w = width

Therefore,

Peter rectangular garden

  • l = 15 + x

Jorge is planting a square garden. The sides of Jorge's garden are equal to the width of Peter's garden.

Therefore,

  • x = side of Jorge garden

The ratios are as follows;

(15 + x)x : x²

Therefore, if the width of peter's garden is 32 yards, the ratio of the areas is as follows:

(15 + 32)32 : 32²

1504: 1024

752: 512

376: 256

94:64

47: 32

learn more on rectangle here: brainly.com/question/23881202

#SPJ1

7 0
1 year ago
375000000 divided by 1570000000
Zielflug [23.3K]

Answer: 0.238853503185

(I obviously used a calculator.)

If you rounded this answer, it would be 0.24. Hope this helps!

8 0
3 years ago
Read 2 more answers
find the number of possible combinations choose one of three books and one of eight CDs to bring on a bus trip
SVEN [57.7K]
There is a possibility of 24 combinations I believe
6 0
3 years ago
Read 2 more answers
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