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Luba_88 [7]
3 years ago
5

In right angle ABC, angle C is the right angle, AC = 3 and AB = 5. Point D is on hypotenuse AB, such that DB = 1. Find the area

of the triangle DBC.

Mathematics
1 answer:
Ivan3 years ago
4 0
Look at the picture.

To find the area of triangle DBC we need to find its base, x, and its height, h.

Triangle ABC is a right triangle, so using the Pythagorean theorem we can find x.
(\hbox{one leg})^2+(\hbox{the other leg})^2=(\hbox{the hypotenuse})^2 \\
3^2+x^2=5^2 \\
9+x^2=25 \\
x^2=25-9 \\
x^2=16 \\
x=\sqrt{16} \\
x=4

Now look at triangles ABC and DBH. They both are right triangles and have the same angle α. That means they're similar and their corresponding sides are proportional. The ratio of the side opposite to angle α to the hypotenuse is the same in both triangles - so the ratio of h to 1 is the same as the ratio of 3 to 5.
\frac{h}{1}=\frac{3}{5} \\
h=\frac{3}{5}

The base x is 4, the height h is 3/5. Calculate the area:

A=\frac{xh}{2}=\frac{4 \times \frac{3}{5}}{2}=2 \times \frac{3}{5}=\frac{6}{5}

The area of triangle DBC is 6/5.

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Step-by-step explanation:

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What is the volume of a hemisphere with a radius of 2.1 m, rounded to the nearest tenth of a cubic meter?
Art [367]

Answer:

The volume of hemisphere is <u>19.4 cubic meter</u>.

Step-by-step explanation:

Given:

A hemisphere is with a radius of 2.1 m.

Now, to find the hemisphere volume with radius 2.1 m.

Radius\ (r) = 2.1 m.

So, we put formula to get the volume of hemisphere:

Volume=\frac{2}{3} \pi r^3\ \ \ \ \ (Taking\ the\ value\ of\ \pi =3.14)\\\\Volume=\frac{2}{3} \times 3.14\times 2.1^3\\\\Volume=\frac{2}{3} \times 3.14\times 9.26\\\\Volume=19.384\ cubic\ meter.

<u><em>Hence, the rounded to the nearest tenth of a cubic meter is 19.4 cubic meter.</em></u>

Therefore, the volume of hemisphere is 19.4 cubic meter.

3 0
3 years ago
How am I supposed to integrate this?
svlad2 [7]
6x^2-4x+1=6\left(x-\dfrac13\right)^2+\dfrac13\ge0

which means the parabola lies above the x-axis over its entire domain. This means the area is given by

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