How to slove thisi need surface and radius

Mathematics

1 answer:

ahrayia [7]3 years ago

6 0

Answer:

e) Area of shaded part = a^2(1 - 0.25 π). Radius of the arc = 0.5a.

f) Area of shaded part = 0.5a^2( π - 2). Radius of the arcs = a.

Step-by-step explanation:

e) Area of shaded part = area of the square - area of the 2 semicircles

= a^2 - 2 * 0.5 π r^2

= a^2 - π (0.5a)^2

= a^2 - 0.25 a^2 π

= a^2(1 - 0.25π )

The radius of the semicircle is 0.5a.

f) Split the shaded area into 2 parts by drawing the diagonal of the square through the shaded area.

The area of one half = the area of the quarter circle - area of the triangle formed by the diagonal

= 0.25 π a^2 - 0.5a^2

= 0.25 a^2 π - 0.5a^2

= 0.25a^2( π - 2)

So the total area of the shaded area

= 2 * 0.25a^2( π - 2)

= 0.5a^2( π - 2).

You might be interested in

The standard IQ test has a mean of 97 and a standard deviation of 17. We want to be

densk [106]

Let's call our estimate x. It will be the average of n IQ scores. Our average won't usually exactly equal the mean 97. But if we repeated averages over different sets of tests, the mean of our estimate the average would be the same as the mean of a single test,

μ = 97

Variances add, so the standard deviations add in quadrature, like the Pythagorean Theorem in n dimensions. This means the standard deviation of the average x is

σ = 17/√n

We want to be 95% certain

97 - 5 ≤ x ≤ 97 + 5

By the 68-95-99.7 rule, 95% certain means within two standard deviations. That means we're 95% sure that

μ - 2σ ≤ x ≤ μ + 2σ

Comparing to what we want, that's means we have to solve

2σ = 5

2 (17/√n) = 5

√n = 2 (17/5)

n = (34/5)² = 46.24

We better round up.

Answer: We need a sample size of 47 to be 95% certain of being within 5 points of the mean