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2 years ago

Long division 40.8 divided by 4

Mathematics

1 answer:

DanielleElmas [232]2 years ago

8 0

1 0 . 2

-----------

4| 40.8

- 4

----------

0 0.8

- 8

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

Hopefully you understand this lol

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Find the area of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximati

Y_Kistochka [10]

Hello from MrBillDoesMath!

Answer: 8 (Pi - sqrt(3))

Discussion:

The area of the shaded region is that of the semicircle minus the area of the triangle..

Area of semicircle = 1/2 * Pi * R^2

Where R^2 is the square of the radius of the circle. In our case, R ( = OC)

= 4 so the semicircle area is

(1/2) * Pi * (4^2) = (1/2) * Pi * 16 = 8 Pi

Area of triangle.

First of all, angle ACB is a right angle ( i.e. 90 degrees).

* This is the Theorem of Thales from elementary Plane Geometry. *

so by Pythagoras

AC^2 + BC^2 = AB^2

But CB = 4 (given) and AB = 4*2 = 8 ( the diameter is twice the radius).

Substituting these in Pythagoras gives

AC^2 + 4^2 = 8^2 or

AC^2 = 8^2 - 4^2- = 64 - 16 = 48

Hence AC = sqrt(48) = sqrt (16*3) = 4 * sqrt(3)

We are almost done! The area of the triangle is given by

(1/2) b * h = (1/2) BC * AC = (1/2) 4 * (4 * sqrt(3)) = 8 sqrt(3)

We conclude the area area of the shaded part is

8 PI - 8 sqrt(3) = 8 (Pi - sqrt(3))

Note that sqrt(3) is approx 1.7 so (PI - sqrt(3)) is a positive number, as it better well be!

Thank you,

MrB

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3 years ago

Ya'll please help me!!!!. The water was pumped out of a backyard pond, What is the domain of this graph????

saw5 [17]

Stuck on the same question and it looks like nobody cares to answer on this website

6 0

3 years ago

Read 2 more answers

As the figure shows Elton runs 500 m to point b first then he turns 110 degrees and runs another 350 m to point c how far is the

Solnce55 [7]

Answer:

658.24 m

Step-by-step explanation:

The figure makes a triangle with vertices abc.

Where ab = 500 m

bc = 350 m

The angle abc = 100°

Using the cosine rule we can find the distance ac.

ac² = 500²+350² - 2×500×350×cos100°

= 372,500 - -60,776.86

= 433,276.86

ac = √433,276.86

= 658.24 m

8 0

3 years ago

What is the surface area of the square pyramid? 6 square meters 16 square meters 28 square meters 49 square meters

jeyben [28]

16 square meters xd :0

3 0

3 years ago

To determine whether or not they have a certain desease, 304 people are to have their blood tested. However, rather than testing

Artyom0805 [142]

Answer:

The expected number of tests necessary for the entire group of 304 people is 180.0325

Step-by-step explanation:

Probability of person being positive = p = 0.04

Probability of person being negative = q = 1-0.04=0.96

Number of people in each group = 19

We will use binomial over here

Probability of no test positive :

$P(x=0) = ^{19}C_0 (0.04)^0 (0.96)^{19} =0.460419201958$

P( at least one tests positive) = 1-P( no one tests positive)= 1-0.460419201958= 0.539580798042

Expected number of tests for each group = 1(0.460419201958)+20(0.539580798042) = 11.2520351628

Number of groups = $\frac{\text{Total population}}{\text{no. of people in each group}}=\frac{304}{19}=16$

Expected number of tests necessary for the entire group of 304 people:

= $\text{Expected number of tests for each group} \times \text{No. of groups}$

= $11.2520351628 \times 16$

=180.0325

Hence The expected number of tests necessary for the entire group of 304 people is 180.0325

7 0

3 years ago