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3 years ago

Find the dimensions of the rectangle with maximum area that can be inscribed in a circle of radius 10.

Mathematics

1 answer:

Ilia_Sergeevich [38]3 years ago

5 0

Answer:

Step-by-step explanation:

That will be a square with a diagonal of 20

side length of 20sin45

and area of (20sin45)² = 200 units²

prove it you say?

Area of a rectangle is base times height

A = bh

With a radius of 10, the diagonals of any rectangle inscribed will be 20 units

20² = b² + h²

h = $\sqrt{400 - b^2}$

A = bh

A = b $\sqrt{400 - b^2}$

Area will be maximized when the derivative is set to zero

dA/db = $\sqrt{400 - b^2}$ - b²/ $\sqrt{400 - b^2}$

0 = $\sqrt{400 - b^2}$ - b²/ $\sqrt{400 - b^2}$

b²/ $\sqrt{400 - b^2}$ = $\sqrt{400 - b^2}$

b² = 400 - b²

2b² = 400

b² = 200

b = $\sqrt{200}$

h = $\sqrt{400 - b^2}$

h = $\sqrt{400 - \sqrt{200}^2 }$

h = $\sqrt{200}$

A = bh

A = $\sqrt{200}$ • $\sqrt{200}$

A = 200 units²

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A manufacturer claims that its cleaning product is best because over half of the cleaning services surveyed used the product. Wh

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Answer:

D. Only one cleaning product was asked about in the survey.

Any given company can use more than one cleaning product or even use a combination of different cleaning products. The question was not specific enough, since it should have probably asked which cleaning products are used and which ones are used more frequently.

Step-by-step explanation:

the other options are wrong because:

A. Only 50 cleaning services were surveyed. ⇒ This actually would increase the validity of the claim because it satisfies the the condition for a valid confidence interval [np and n(1 - p) are larger than 10]-
B. Cleaning services were selected at random. ⇒ This actually would increase the validity of the claim.
C. A well-known company conducted the survey. ⇒ This actually would increase the validity of the claim.

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3 years ago

Solve for x and y simultaneously if: x+4=2y and y2-xy+21=0

salantis [7]

Answer:

Step-by-step explanation:

x=−10, y=−3

x=10, y=7

y=7,x=10

y=−3,x=−10

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3 years ago

Using the numbers -4, 10, 8, 2, -3, -5, create two expressions that equal 6.

blondinia [14]

Expressions:

10 + (-4)
-4 + 8 + 2

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4 years ago

The price of a toy usually costing £50 is increases to £65 work out the percentage increase

Vesna [10]

Answer:

30%

Step-by-step explanation:

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3 years ago

Read 2 more answers

Tim must read 2 books from a list of 7 recommended books for his summer reading program. In how many different ways can Tim choo

Marianna [84]

There are 21 ways Tim choose 2 books from the 7 recommended book

Solution:

Given that Tim must read 2 books from a list of 7 recommended books for his summer reading program

To find: different ways can Tim choose 2 books from the 7 recommended books

This is a combination problem

A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected

The formula for combinations is:

$n C_{r}=\frac{n !}{r !(n-r) !}$

where n represents the number of items, and r represents the number of items being chosen at a time

Here we have to choose 2 books from 7 books

Therefore, n = 7 and r = 2

Substituting values in above formula, we get

$\begin{aligned}&7 C_{2}=\frac{7 !}{2 !(7-2) !}\\\\&7 C_{2}=\frac{7 !}{2 ! \times 5 !}\end{aligned}$

For a number n, the factorial of n can be written as,

$n !=n \times(n-1) \times(n-2) \dots \dots \times 2 \times 1$

Therefore, we get

$7 C_{2}=\frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 5 \times 4 \times 3 \times 2 \times 1}\\\\7C_2 = 7 \times 3 = 21$

Thus there are 21 ways Tim choose 2 books from the 7 recommended book

7 0

3 years ago