Find the perimeter of the quarter-circle. Give your answer to the nearest whole number.

Mathematics

2 answers:

Nikitich [7]3 years ago

8 0

Yes correct yay ! :)

Bezzdna [24]3 years ago

6 0

Answer:

The perimeter of the quarter-circle is 200 cm.

Step-by-step explanation:

Given that the angle of quarter-circle is 90°. So using Length of Arc formula, you are able to find the length of curve :

$arc = \frac{θ}{360} \times 2 \: \pi \: r$

Let r be radius = 56 cm,

Let θ = 90°

$arc = \frac{90}{360} \times 2 \times\pi \times 56$

$= \frac{1}{4} \times 2 \times \pi \times 56$

$= \frac{1}{2} \times \pi \times 56$

$= 28\pi \: cm$

We have already found the arc. Next we have to add up together to find the perimeter :

$p = 56 + 56 + 28\pi$

$p = 112 + 28\pi$

$p = 200 \: cm \: (3s.f)$

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Let g(x) = 2x and h(x)= x^2 -4. find (g o h)(0)

finlep [7]

The answer is -8

====================================================

Explanation:

There are two ways to get this answer

Method 1 will have us plug x = 0 into h(x) to get
h(x) = x^2 - 4
h(0) = 0^2 - 4
h(0) = 0 - 4
h(0) = -4
Then this output is plugged into g(x) to get
g(x) = 2x
g(-4) = 2*(-4)
g(-4) = -8 which is the answer
This works because (g o h)(0) is the same as g(h(0)). Note how h(0) is replaced with -4
So effectively g(h(0)) = -8 which is the same as (g o h)(0) = -8

-----------------------

The second method involves a bit algebra first
Start with the outer function g(x). Then replace every x with h(x). On the right side, we will replace h(x) with x^2-4 because h(x) = x^2-4

g(x) = 2x
g(x) = 2( x )
g(h(x)) = 2( h(x) ) ... replace every x with h(x)
g(h(x)) = 2( x^2-4 ) ... replace h(x) on the right side with x^2-4
g(h(x)) = 2x^2-8
(g o h)(x) = 2x^2-8

Now plug in x = 0
(g o h)(x) = 2x^2-8
(g o h)(0) = 2(0)^2-8
(g o h)(0) = 2(0)-8
(g o h)(0) = 0-8
(g o h)(0) = -8

Regardless of which method you use, the answer is -8

5 0

3 years ago

Triangle ABC is similar to triangle PQR, as shown below:

natita [175]

Answer:

$\frac{q}{b}=\frac{r}{c}$