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2 years ago

Find the circumference of 8m using pie

Mathematics

1 answer:

KengaRu [80]2 years ago

8 0

Answer: C = 50.24m A = 200.96m^2

Step-by-step explanation:

Note that the area is in square meters, as the radius is in meters, and we are squaring the radius when calculating the area.

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Express p in terms of q if

Irina-Kira [14]

$p=x^2+\dfrac{1}{x^2}\\\\p=\dfrac{x^4}{x^2}+\dfrac{1}{x^2}\\\\p=\dfrac{x^4+1}{x^2}\qquad(*)$

$q=x+\dfrac{1}{x}\\\\q=\dfrac{x^2}{x}+\dfrac{1}{x}\\\\q=\dfrac{x^2+1}{x}\qquad\text{square both sides}\\\\q^2=\left(\dfrac{x^2+1}{x}\right)^2\\\\q^2=\dfrac{(x^2+1)^2}{x^2}\qquad\text{use}\ \ (a+b)^2=a^2+2ab+b^2\\\\q^2=\dfrac{(x^2)^2+2(x^2)(1)+1^2}{x^2}\\\\q^2=\dfrac{x^4+2x^2+1}{x^2}\\\\q^2=\dfrac{x^4+1}{x^2}+\dfrac{2x^2}{x^2}\\\\q^2=\dfrac{x^4+1}{x^2}+2\qquad\text{subtract 2 from both sides}\\\\q^2-2=\dfrac{x^4+1}{x^2}\\\\\text{From (*) we have}\\\\\boxed{p=q^2-2}$

8 0

3 years ago

A rectangular prism had a volume of 252 cubic centimeters. The length of the prism is 14 centimeters and the width of the prism

mojhsa [17]

<h2>Answer:</h2>

A prism is a solid object having two identical bases, hence the same cross section along the length. Prism are called after the name of their base. A rectangular prism is a solid whose base is a rectangle. Multiplying the three dimensions of a rectangular prism: length, width and height, gives us the volume of a prism:

$V=L\times W\times H$

FOR THE ORIGINAL PRISM WE HAVE THE FOLLOWING DIMENSIONS:

$L=14cm \\ \\ W=6cm \\ \\ H=3cm$

In fact, the volume is $252cm^3$ because:

$V=14\times 6\times 3 \therefore V=252cm^3$

Now the height of the prism was changed from 3 centimeters to 6 centimeters to create a new rectangular prism, therefore:

FOR THE NEW PRISM WE HAVE THE FOLLOWING DIMENSIONS:

$L=14cm \\ \\ W=6cm \\ \\ H=6cm$

So the new volume is:

$V=14\times 6\times 6 \therefore V=504cm^3$

<h3><em>What do we know about the volume of the new prism?</em></h3>

<em>Well, the volume has increased from </em> $252cm^3 \ to \ 504cm^3$ <em>and since</em> $504=2\times 252$ <em>we can say that the new volume is two times the original volume.</em>

8 0

3 years ago

Eva is making a pattern using these shapes can you arrange Evas shapes to make a symmetrical pattern

ratelena [41]

Answer:

pyramid, cone, sphere, cube

Step-by-step explanation:

A symmetrical pattern is one that is arranged in such a way that there is a progressive repetition of a pattern. Each pattern formed is the same with respect to each other.

Eva could form series symmetrical patterns with the shapes he has, which depends on the arrangement of the shapes to form desired pattern.

One simple pattern to be formed is;

pyramid, cone, sphere, cube

pyramid, cone, sphere, cube.

Thus, this would generate four symmetrical continuous patterns.

pyramid, cone, sphere, cube : pyramid, cone, sphere, cube : pyramid, cone, sphere, cube : pyramid, cone, sphere, cube.

6 0

3 years ago

1)The graph below shows a line segment XY:

Hitman42 [59]

The segment goes from point (-1, 3) to (1,-1)
Slope = rise / run = (-3 - 1) / (1 - (-1)) = -4 / 2 = -2
Slope = -2

5 0

4 years ago

Read 2 more answers

Lindsay is 5 years younger than Mark. Seven years ago, the sum of their ages was 31.

Rashid [163]

Answer:

The present age of Mark is 25 years.

And present age of Lindsay is 20 years.

Step-by-step explanation:

Let us assume:

The present age of Lindsay = l

The present age of Mark = m

⇒ Age of Lindsay seven years ago = (l -7) years

and Age of Mark seven years ago = (m -7) years

According to question:

Lindsay is 5 years younger than Mark ⇒ l = m - 5

Seven years ago, the sum of their ages was 31 ⇒ (l-7) + (m -7) = 31

So, the given set of equation are:

l = m - 5 ......... (1)

(l-7) + (m -7) = 31

⇒ ((m - 5) -7) + (m -7) = 32 (from (1)

or, m -12 + m - 7 = 31

or, 2m = 31 + 19 = 50

⇒ m = 50 / 2 = 25, or m = 25

Hence,the present age of Mark = 25 years

So,the present age of Lindsay = 25 - 5 = 20 years

7 0

3 years ago