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2 years ago

12

Solve the system of equations -x - 2y = 11 and -3x - 2y = -7

1 answer:

rjkz [21]2 years ago

4 0

Answer: (9,-10) or x=9...y=-10

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An atrium is being designed to house an exhibit of tropical birds. The atrium must enclose 250,000 cubic feet of space, and the

9966 [12]

The <em>proposed</em> design of the atrium (<em>V < V'</em>) is possible since its volume is less than the <em>maximum possible</em> atrium.

<h3>Can this atrium be built in the rectangular plot of land?</h3>

The atrium with the <em>maximum allowable</em> radius (<em>R</em>), in feet, is represented in the image attached. The <em>real</em> atrium is possible if and only if the <em>real</em> radius (<em>r</em>) is less than the maximum allowable radius and therefore, the <em>real</em> volume (<em>V</em>), in cubic feet, must be less than than <em>maximum possible</em> volume (<em>V'</em>), in cubic feet.

First, we calculate the volume occupied by the maximum allowable radius:

<em>V' =</em> (8 · π / 3) · (45 ft)³

<em>V' ≈</em> 763407.015 ft³

The <em>proposed</em> design of the atrium (<em>V < V'</em>) is possible since its volume is less than the <em>maximum possible</em> atrium. $\blacksquare$

To learn more on volumes, we kindly invite to check this verified question: brainly.com/question/13338592

3 0

1 year ago

Jessica is a custodian at Oracle Arena. She waxes 20 m² of the floor in = of an hour. Jessica

Wewaii [24]

The complete question is as follows:

Jessica is a custodian at Oracle Arena. She waxes 20 $\mathbf{m^{2}}$ of the floor in $\mathbf{\frac{3}{5}}$ of and hour. At this rate, how many square meters can she wax per hour ?

Answer:

$\mathbf{\frac{100}{3}\approx33.33 \ m^{2} \ per \ hour}$

Step-by-step explanation:

$\textrm{rate}=\frac{\textrm{Area waxed in square meter}}{\textrm{Time taken to wax in hours}}$

$\textrm{rate}=\frac{20 \ \textrm{m}^{2}}{\frac{3}{5} \ \textrm{hours}}$

$\textrm{rate}=\frac{20\times5}{3}$

$\mathbf{rate=\frac{100}{3}\approx33.33 \ m^{2} \ per \ hour}$

8 0

3 years ago

Can you please help me on this question -4x+7y=3

inna [77]

Answer:

Y=(3+4x)/7

Step-by-step explanation:

3 0

2 years ago

Please solve 5 f <br> (Trigonometric Equations)<br> #salute u if u solved it

Zanzabum

Answer:

$\beta=45\degree\:\:or\:\:\beta=135\degree$

Step-by-step explanation:

We want to solve $\tan \beta \sec \beta=\sqrt{2}$ , where $0\le \beta \le360\degree$ .

We rewrite in terms of sine and cosine.

$\frac{\sin \beta}{\cos \beta} \cdot \frac{1}{\cos \beta} =\sqrt{2}$

$\frac{\sin \beta}{\cos^2\beta}=\sqrt{2}$

Use the Pythagorean identity: $\cos^2\beta=1-\sin^2\beta$ .

$\frac{\sin \beta}{1-\sin^2\beta}=\sqrt{2}$

$\implies \sin \beta=\sqrt{2}(1-\sin^2\beta)$

$\implies \sin \beta=\sqrt{2}-\sqrt{2}\sin^2\beta$

$\implies \sqrt{2}\sin^2\beta+\sin \beta- \sqrt{2}=0$

This is a quadratic equation in $\sin \beta$ .

By the quadratic formula, we have:

$\sin \beta=\frac{-1\pm \sqrt{1^2-4(\sqrt{2})(-\sqrt{2} ) } }{2\cdot \sqrt{2} }$

$\sin \beta=\frac{-1\pm \sqrt{1^2+4(2) } }{2\cdot \sqrt{2} }$

$\sin \beta=\frac{-1\pm \sqrt{9} }{2\cdot \sqrt{2} }$

$\sin \beta=\frac{-1\pm3}{2\cdot \sqrt{2} }$

$\sin \beta=\frac{2}{2\cdot \sqrt{2} }$ or $\sin \beta=\frac{-4}{2\cdot \sqrt{2} }$

$\sin \beta=\frac{1}{\sqrt{2} }$ or $\sin \beta=-\frac{2}{\sqrt{2} }$

$\sin \beta=\frac{\sqrt{2}}{2}$ or $\sin \beta=-\sqrt{2}$

When $\sin \beta=\frac{\sqrt{2}}{2}$ , $\beta=\sin ^{-1}(\frac{\sqrt{2} }{2} )$

$\implies \beta=45\degree\:\:or\:\:\beta=135\degree$ on the interval $0\le \beta \le360\degree$ .

When $\sin \beta=-\sqrt{2}$ , $\beta$ is not defined because $-1\le \sin \beta \le1$

4 0

2 years ago

Plzzzzzzzzzzzzzzz help

mash [69]

Increasing on:
(−∞,1)
Decreasing on:
(1,∞)

5 0

1 year ago