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2 years ago

What are the measure of the other three angles formed by the intersection?

Mathematics

1 answer:

SVEN [57.7K]2 years ago

4 0

Answer:

∠1 = 48°

∠2 = 132°

∠3 = 48°

Step-by-step explanation:

∠1 = (360-132-132)/2 = 48°

∠2 = 132° because it is the alternate angle to 132°

∠3 = 48° because it is the alternate angle to ∠1

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A conical tank has an inside diameter of 20 ft and a height of 12 ft. The tank is filled with liquid to a height of 9 ft. How mu

Ierofanga [76]

Check the picture below

so.. if you notice, the diameter is 20, the radius is half that, the radius and height are at a ratio of 5:6, if the larger cone is filled up to 9ft, that means, the conical gap above, is 3ft in height

so, simply getting the volume of the larger cone filled up, with a height of 12, and then subtracting that conical gap, you'd end up with what's leftover, whatever the volume is at 9ft

$\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}\\\\
-------------------------------\\\\
\textit{volume of larger cone}\qquad V_l=\cfrac{\pi 10^2\cdot 12}{3}\implies \boxed{V_l=400\pi }
\\\\\\
\textit{volume of smaller cone}\qquad V_s=\cfrac{\pi \left( \frac{5}{2} \right)^2\cdot 3}{3}\implies \boxed{V_s=\cfrac{25\pi }{4}}
\\\\\\
\textit{volume of liquid up to 9ft}\qquad V_l-V_s=\cfrac{1575\pi }{4}\implies 393.75\pi$

5 0

3 years ago

Help me I've been stuck forever! it is an absolute value equation btw.

ehidna [41]

Answer:

${n=\frac{-11}{3} ,3}$

Step-by-step explanation:

Original problem: $2|n+7|=|4n+8|$

Get rid of the absolute value signs by breaking the problem down into two equations, the positive and negative cases.

The first case, the positive case, will be formed by just changing the absolute value symbols ( $|$ ) into parentheses.

$2(n+7)=(4n+8)$

The next case, the negative case, will be formed by changing the absolute value symbols into parentheses as well but the $(4n+8)$ will be multiplied by negative 1.

$2(n+7)=-(4n+8)$

Let's solve the first equation we created with the positive case. Start by getting rid of the parentheses on the right side of the equation.

$2(n+7)=4n+8$

Distribute 2 inside the parentheses.

$2n+14=4n+8$

Combine like terms by subtracting 2n and 8 from both sides of the equation.

$6=2n$

Isolate and solve for n by dividing both sides of the equation by 2.

$3=n$

One of the solutions is 3. Let's solve the second equation we created. Distribute the negative sign inside the parentheses on the right side of the equation.

$2(n+7)=-4n-8$

Now distribute 2 inside the parentheses on the left side of the equation.

$2n+14=-4n-8$

Combine like terms by adding 4n to both sides of the equation.

$6n+14=-8$

Subtract 14 from both sides of the equation.

$6n=-22$

Divide both sides of the equation by 6.

$n=\frac{-22}{6}$

This fraction can be simplified by dividing the top and bottom by 2 to $\frac{-11}{3}$ .

You can check for extraneous solutions by substituting 3 and $\frac{-11}{3}$ back into the original equation. There are no extraneous solutions in this particular problem.

This means that the two solutions of n are 3 and $\frac{-11}{3}$ .

$\boxed{n=\frac{-11}{3} ,3}$