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3 years ago

Do these ratios form a proportion?

Mathematics

2 answers:

nikklg [1K]3 years ago

6 0

Answer:

ha bhai.......yes..........

Georgia [21]3 years ago

3 0

Answer:

Yes these ratios do form a proportion :)

Step-by-step explanation:

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Caroline knows the height and the required volume of a cone-shaped vase she’s designing. Which formula can she use to determine

timama [110]

Answer:

Option B. $r=\sqrt{\frac{3V}{\pi h}}$

Step-by-step explanation:

we know that

The volume of a cone is equal to

$V=\frac{1}{3}\pi r^{2} h$

Solve for the radius r

That means-----> isolate the variable r

Multiply by 3 both sides

$3V=\pi r^{2} h$

Divide by $(\pi h)$ both sides

$r^{2}=\frac{3V}{\pi h}$

square root both sides

$r=\sqrt{\frac{3V}{\pi h}}$

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3 years ago

Let f(x) = xe−x if x ≥ 0 and f(x) = 0 if x < 0<br> Is f a probability density function?

Lynna [10]

Yes. $f(x)$ is a PDF if

• $f(x) \ge 0$ for all $x$ in the support; this is true, since $e^{-x}>0$ for all $x$ , and multiplying a positive number $x$ doesn't change this fact;

• the integral of $f(x)$ over its support is 1; this is also true, since

$\displaystyle \int_{-\infty}^\infty f(x) \, dx = \int_0^\infty xe^{-x} \, dx = 1$

which can be computed by parts.

3 0

1 year ago

If cos x=8/17, and 270° < x < 360°<br> what is cos(2x)?

svp [43]

Answer: $\bold{-\dfrac{161}{289}}$

<u>Step-by-step explanation:</u>

Given: cos x = $\dfrac{8}{17}$ , x is in Quadrant 4

Use Pythagorean Theorem to find sin x:

8² + y² = 17²

y² = 17² - 8²

y² = 289 - 64

y² = 225

y = 15

→ sin x = $-\dfrac{15}{17}$

Use the double angle formula to find cos (2x):

$cos (2x) = cos^2 x - sin^2 x\\\\.\qquad=\bigg(\dfrac{8}{17}\bigg)^2-\bigg(-\dfrac{15}{17}\bigg)^2\\\\\\.\qquad=\dfrac{64}{289}-\dfrac{225}{289}\\\\\\.\qquad=-\dfrac{161}{289}$