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3 years ago

A circle has circumference 27 cm. What is the area of the circle? Use 3.14 for .

Mathematics

1 answer:

ella [17]3 years ago

5 0

Circumference = 2πr = 27 cm

= 2 × 3.14 × r = 27

= 3.14 × r = 27/2

so, r = $\frac{27}{2}$ × $\frac{1}{3.14}$ = 4.2 cm

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3 years ago

Read 2 more answers

(b) If the sum of two consecutive odd numbers is 48, find the numbers.

Rudiy27

Answer:

23, 25

Step-by-step explanation:

let the first number be represented as A, since there are two odd numbers, the second number would be A + 2

A + A+2 = 48

2A + 2 = 48

2A = 48 - 2

2A = 46 ( divide both sides by 2)

A = 23

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= 23 + 2 = 25

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2 years ago

A rectangle has an area of 198 square meters and a width of 9 meters.

madreJ [45]

Answer:

The length of the triangle is 22.

Step-by-step explanation:

Area = width*length

length = area/width = 198/9 = 22

3 0

2 years ago

1. What are the solutions (coordinate points) to the system of equations?

Leto [7]

Question 1

The given system of equations is:

$y = {x}^{2} + 5x + 6 \\ y = 3x + 6$

Equate the two equations:

${x}^{2} + 5x + 6 = 3x + 6$

Rewrite in standard form:

${x}^{2} + 5x - 3x + 6 - 6 = 0$

${x}^{2} + 2x = 0$

$x(x + 2) = 0$

$x = 0 \: or \: x = - 2$

When we put x=0, in y=3x +6, we get:

$y = 3(0) + 6 = 6$

One solution is (0,6)

When we put x=-2, into y=3x+6, we get:

$y = 3( - 2) + 6 = 0$

Another solution is (-2,0)

The solutions are; (0,6) and (-2,0)

Question 2:

The function is

$f(x) = {x}^{6} - {x}^{4}$

Let us put x=-x,

$f( - x) = {( - x)}^{6} - {( - x)}^{4}$

This gives:

$f( - x) = {x}^{6} - {x}^{4}$

We can observe that:

$f(x) = f( - x)$

This is the property of an even function.

Question 3:

The given function is

$f(x) = {x}^{2} + 3x - 2$

The average rate of change of f(x) from x=a to x=b is given as:

$\frac{f(b) - f(a)}{b - a}$

This is the slope of the secant line connecting the two points on f(x)

From x=2 to x=6, the average rate of change

$= \frac{f(6) - f(2)}{6 - 2} \\ = \frac{ {6}^{2} + 3 \times 6 - 2 - {2}^{2} - 3 \times 2 + 2 }{4} \\ = \frac{36 + 18 - 4 - 6}{4} \\ = \frac{44}{4} \\ = 11$

The average rate of change is 11

3 0

3 years ago