Mathematics, 10.01.2020 06:31, samanthashade8352

Aconical paper funnel of radius 4 and height 6 units is needed to make a good cup of coffee. if this funnel is made out of a sector of a circle, what must be the radius of this circle and what must be central angle of the sector?

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The radius of this circle is $2\sqrt{13}$ and the central angle of the sector is $\theta=\frac{2}{\sqrt{13}}\times360^\circ$ .

Step-by-step explanation:

Consider the provided information.

If a conical paper funnel is made out of a sector of circle then the radius of the sector becomes the slant height of the cone, and the length of the curved part of the sector becomes the circumference of the base of the cone.

First find the slant height: $l=\sqrt{r^2+h^2}$

$l=\sqrt{4^2+6^2}$

$l=\sqrt{16+36}$

$l=2\sqrt{13}$

Thus, the radius of the sector is $2\sqrt{13}$ which is same as the slant height of the cone.

Now, the circumference of the base of the cone is same as the length of the curved part.

$C=2\pi r$

$C=2\pi \times4=8\pi$

The length of the curved part = $\frac{\theta}{360\circ}\times2\pi r$

$\frac{\theta}{360\circ}\times2\pi \times2\sqrt{13}=8\pi$

$\frac{\theta}{360\circ}\times\sqrt{13}=2$

$\theta=\frac{2}{\sqrt{13}}\times360^\circ$

Hence, the radius of this circle is $2\sqrt{13}$ and the central angle of the sector is $\theta=\frac{2}{\sqrt{13}}\times360^\circ$ .

answered: Guest

360 different combinations

answered: Guest

step-by-step explanation:

i found the life tables for the year 2012.

life table of males at age 30. probability of dying between ages x and x+1

total population:

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old.

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497