What is the independent variable, and the dependent variable? How do you know ?

1 answer:

4 0

Independent variable - It is a variable that stands alone and isn't changed by the other variables you are trying to measure.

for example, someone's age might be an independent variable. other factors (such as what they eat, how much they go to school, how much television they watch) aren't going to change a person's age.

dependent variable - It is something that depends on other factors.

for example, a test score could be a dependent variable because it could change depending on several factors such as how much you studied, how much sleep you got the night before you took the test, or even how hungry you were when you took it. usually when you are looking for a relationship between two things you are trying to find out what makes the dependent variable change the way it does.

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For the circle x^2 + y^2 = 100, a) State the radius at 6,8

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Read 2 more answers

(I've been trying to figure this out for 3 days and I really need help)

liq [111]

Check the picture below.

since the diameter of the cone is 6", then its radius is half that or 3", so getting the volume of only the cone, not the top.

$\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\cfrac{\pi (3)^2(4)}{3}\implies V=12\pi \implies V\approx 37.7$

now, the top of it, as you notice in the picture, is a semicircle, whose radius is the same as the cone's, 3.

$\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=3 \end{cases}\implies V=\cfrac{4\pi (3)^3}{3}\implies V=36\pi \\\\\\ \stackrel{\textit{half of that for a semisphere}}{V=18\pi }\implies V\approx 56.55$

well, you'll be serving the cone and top combined, 12π + 18π = 30π or about 94.25 in³.

pretty much the same thing, we get the volume of the cone and its top, add them up.

$\bf \stackrel{\textit{cone's volume}}{\cfrac{\pi (3)^2(8)}{3}}~~~~+~~~~\stackrel{\stackrel{\textit{half a sphere}}{\textit{top's volume}}}{\cfrac{4\pi 3^3}{3}\div 2}\implies 24\pi +18\pi \implies 42\pi ~~\approx~~131.95~in^$