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3 years ago

What is the area of the square that shares a side with the third side of the triangle?

Mathematics

1 answer:

disa [49]3 years ago

3 0

Step-by-step explanation:

Cuz sides of square are same, we just find hypotenusa side of triangle (use Phytagoras Theorem) :

c² = a² + b²

c² = 2² + 4²

c² = 4 + 16

c² = 20

c = √20

Side of square is √20 units.

The area of square :

A = s²

= √20²

= √20 × √20

= 20 units²

So, the area of square is 20 units²

Hope it helpful and useful :)

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never [62]

Hey There!

80+70 is 150

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3 years ago

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Find the total weekly earnings for a waitress with a weekly salary of $257 plus a 4% commission on dinners, if the total worth o

ss7ja [257]

The waitress earns $425 weekly.

Work:
Use proportions.
x 4
------- = ------
4,200 100

4,200 x 4 = 16800
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3 years ago

A sphere of radius r is cut by a plane h units above the equator, where

Anika [276]

Consider the top half of a sphere centered at the origin with radius $r$ , which can be described by the equation

$z=\sqrt{r^2-x^2-y^2}$

and consider a plane

$z=h$

with $0$ . Call the region between the two surfaces $R$ . The volume of $R$ is given by the triple integral

$\displaystyle\iiint_R\mathrm dV=\int_{-\sqrt{r^2-h^2}}^{\sqrt{r^2-h^2}}\int_{-\sqrt{r^2-h^2-x^2}}^{\sqrt{r^2-h^2-x^2}}\int_h^{\sqrt{r^2-x^2-y^2}}\mathrm dz\,\mathrm dy\,\mathrm dx$

Converting to polar coordinates will help make this computation easier. Set

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\var\phi\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

Now, the volume can be computed with the integral

$\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_0^{\arctan\frac{\sqrt{r^2-h^2}}h}\int_{h\sec\varphi}^r\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta$

You should get

$\dfrac{2\pi}3\left(r^3\arctan\dfrac{\sqrt{r^2-h^2}}h-\dfrac{h^3}2\left(\dfrac{r\sqrt{r^2-h^2}}{h^2}+\ln\dfrac{r+\sqrt{r^2-h^2}}h\right)\right)$

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3 years ago

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natima [27]

Answer:

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Step-by-step explanation:

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Your father is planning to cook for 35 people using a recipe that specifies two and a half cups of sugar for each six people,

almond37 [142]

Your father will require 14.6 cups of sugar for the larger group

<h3>Ratio and proportions</h3>

From the question, we have that 2.5 cups of sugar can be used to make recipes for 6 people that is;

6 people = 2.5 cups of sugar

In order to calculate for 35 people, we will have;

35 people = x

Taking the ratio of the expressions

6/35 = 2.5/x

6x = 87.5

x = 87.5/6

x = 14.6

Hence your father will require 14.6 cups of sugar for the larger group

Learn more on ratio and proportions here: brainly.com/question/19994681

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2 years ago

What is the area of the square that shares a side with the third side of the triangle?​

What is the area of the square that shares a side with the third side of the triangle?