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3 years ago

Help please this is due in couple minutes

Mathematics

1 answer:

agasfer [191]3 years ago

5 0

63 + 64 = 127
180 - 127 = 53
m<1 = 53°
m<2 = 53°
53 + 67 = 120
180 - 120 = 60
m<3 = 60°

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A candle in the shape of a circular cone has a base of radius r and a height of h that is the same length as the radius. which e

ladessa [460]

Answer:

$\frac{r(1-\sqrt{2})}{-3}$

Step-by-step explanation:

Volume of cone = $\frac{1}{3} \pi r^{2} h$

Since we are given that a circular cone has a base of radius r and a height of h that is the same length as the radius

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

= $\frac{1}{3} \pi r^{3}$

Surface area of cone including 1 base = $\pi r^{2} +\pi\times r \times \sqrt{r^2+h^2}$

Since r = h

So, area = $\pi r^{2} +\pi\times r \times \sqrt{r^2+r^2}$

= $\pi r^{2} +\pi\times r \times \sqrt{2r^2}$

= $\pi r^{2} +\pi\times r^2 \times \sqrt{2}$

Ratio of volume of cone to its surface area including base :

$\frac{\frac{1}{3} \pi r^{3}}{\pi r^{2} +\pi\times r^2 \times \sqrt{2}}$

$\frac{\frac{1}{3}r}{1+\sqrt{2}}$

$\frac{r}{3(1+\sqrt{2})}$

Rationalizing

$\frac{r}{3(1+\sqrt{2})} \times \frac{1-\sqrt{2}}{1-\sqrt{2}}$

$\frac{r(1-\sqrt{2})}{-3}$

Hence the ratio the ratio of the volume of the candle to its surface area(including the base) is $\frac{r(1-\sqrt{2})}{-3}$

8 0

3 years ago

Read 2 more answers

Which ordered pair is a solution of the equation y-4=7(x-6) A.(5,4) B.(6,5) C.(5,4)(6,5) D.Neither

Natasha_Volkova [10]

Answer:

D. Neither

Step-by-step explanation:

3 0

3 years ago

The point (-3,-1) is the midpoint of (x,y) and (5,4). Find the point (x,y).

nirvana33 [79]

Answer:

(-11, -6)

Step-by-step explanation:

Find the distance between the midpoint, (-3, -1) and (5, 4). This can be calculated by finding the difference between the x coordinates and y coordinates.

-3 - 5 = -8 (distance between x coordinates)

-1 - 4 = -5 (distance between y coordinates)

Find the point (x, y) by subtracting 8 from the midpoint's x value, and then subtracting 5 from the midpoint's y value.

-3 - 8 = -11

-1 - 5 = -6

So, the point (x, y) is (-11, -6)

4 0

3 years ago

You throw two four-sided dice. Let the random variable X represent the maximum value of the two dice. Compute E(X). Round your a

Troyanec [42]

Answer:

E(X)=3.125

Step-by-step explanation:

We are given that two four sided dice.

Then , the sample space

{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}

Total number of outcomes=16

Let the random variable X represent the maximum value of the two dice

Outcomes X P(X)

(1,1) 1 1/16

(1,2),(2,1),(2,2) 2 3/16

(1,3),(2,3),(3,1),(3,2),(3,3) 3 5/16

(1,4),(3,4) ,(2,4),(4,1),(4,2),(4,3),(4,4) 4 7/16

Using the probability formula

$P(E)=\frac{Favorable\;outcomes}{Total\;number\;of\;outcomes}$

Now,

$E(X)=\sum_{i=1}^{n}x_iP(x_i)$

$E(x)=1(1/16)+2(3/16)+3(5/16)+4(7/16)$

$E(x)=\frac{1+6+15+28}{16}$

$E(x)=\frac{50}{16}=3.125$

7 0

3 years ago

If m angle 1 = 42 and m angle 2 = 27, then m angle APC =

Arada [10]

I think that it's 111

4 0

3 years ago