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3 years ago

Please help mee with the question

Mathematics

1 answer:

brilliants [131]3 years ago

6 0

Answer:

5x-8y

Step-by-step explanation:

4x-9y+x+y

=4x+-9y+x+y

=(4x+x)+(-9y+y)

=5x+-8y

=5x-8y

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2 years ago

The area of a rectangle is 350 square meters. Find its width if its length is 50 meters

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Step-by-step explanation:

For a given rectangle,the area(A) is the product of its length and width

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n divided by 4 is equal to n/4

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3 years ago

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3 years ago

5. The combined perimeter of a circle and a square is 16. Find the dimensions of the circle and square

Tanya [424]

The dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively

Represent the side length of the square with s, and the radius of the circle with r.

So, the perimeter (P) and the area (A) of the shape are:

$P =4s + 2\pi r$

$A =s^2 + \pi r^2$

The perimeter is 16. So, we have:

$4s + 2\pi r = 16$

Divide through by 4

$s + 0.5\pi r = 4$

Make s the subject

$s = 4 - 0.5\pi r$

Substitute $s = 4 - 0.5\pi r$ in $A =s^2 + \pi r^2$

$A = (4 - 0.5\pi r )^2 + \pi r^2$

Expand

$A = 16 - 4\pi r + 0.25(\pi r)^2 + \pi r^2$

This gives

$A = 16 - 4\pi r + (0.25\pi^2 + \pi )r^2$

Differentiate with respect to r

$A' = 0 - 4\pi + 2(0.25\pi^2 + \pi )r$

$A' = - 4\pi + 2(0.25\pi^2 + \pi )r$

Set to 0

$- 4\pi + 2(0.25\pi^2 + \pi )r =0$

Add 4pi to both sides

$2(0.25\pi^2 + \pi )r =4\pi$

Divide both sides by 2

$(0.25\pi^2 + \pi )r =2\pi$

Make r the subject

$r =\frac{2\pi}{(0.25\pi^2 + \pi )}\\$

Factor out pi

$r =\frac{2\pi}{\pi(0.25\pi + 1 )}$

Cancel out the common factors

$r =\frac{2}{0.25\pi + 1 }$

Express pi as 3.14

$r =\frac{2}{0.25\times 3.14 + 1 }$

$r =\frac{2}{1.785}$

Divide

$r =1.12$

Recall that:

$s = 4 - 0.5\pi r$

This gives

$s =4 -0.5 \times \pi \times 1.12$

This gives

$s =4 -0.5 \times 3.14 \times 1.12$

$s =2.24$

Hence, the dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively