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3 years ago

Write the formula for the volume of a cone without using pi.

1 answer:

8 0

Given the radius and h, the volume of a cone can be found by using the formula: Formula: Vcone = 1/3 × b × h. b is the area of the base of the cone. Since the base is a circle, area of the base = pi × r2. Thus, the formula is Vcone = 1/3 × pi × r2 × h.

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What equation is graphed in this figure?

Ksivusya [100]

to get the equation of any straight line, we simply need two points off of it, let's use those two points in the picture below.

$(\stackrel{x_1}{0}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}}\implies \cfrac{3}{1}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_2=m(x-x_2) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_2}{5}=\stackrel{m}{3}(x-\stackrel{x_2}{1})$

keeping in mind that for the point-slope form, either point will do, in this case we used the second one, but the first one would have worked just the same.

7 0

2 years ago

Samantha has $48 to spend on used video games. Single player games cost $6 each and multi player games cost $12 each. What equat

storchak [24]

Answer:

The equation is

6x + 12y = 48

Step-by-step explanation:

Standard form another way of writing a linear equation. It is in the form

Ax + By = C

Total amount with Samantha = $48

Single player games = $6 each

Multi player games = $12 each

Let

Number of Single player games = x

Number of Multi player games = y

The number of single player games (x) and the number of multi player games (y) Samantha can buy is

6x + 12y = 48

That is price × quantity of single player games + price × quantity of multi player games = Total amount with Samantha

3 0

3 years ago

Where should the point P be chosen on line segment AB so as to maximize the angle θ? (Assume a = 4 units, b = 5 units, and c = 9

taurus [48]

From the figure, let the distance of point P from point A on line segment AB be x and let the angle opposite side a be M and the angle opposite side c be N.

Using pythagoras theorem,
$\tan M= \frac{a}{b-x} \\ \\ M=\tan^{-1}\left(\frac{a}{b-x}\right)$
and
$\tan N= \frac{c}{x} \\ \\ N=\tan^{-1}\left(\frac{c}{x}\right)$

Angle θ is given by
$\theta=180-M-N \\ \\ =180-\tan^{-1}\left(\frac{a}{b-x}\right)-\tan^{-1}\left(\frac{c}{x}\right)$

Given that a = 4 units, b = 5 units, and c = 9 units, thus
$\theta=180-\tan^{-1}\left(\frac{4}{5-x}\right)-\tan^{-1}\left(\frac{9}{x}\right)$

To maximixe angle θ, the differentiation of <span>θ with respect to x must be equal to zero.
i.e.
$\frac{d\theta}{dx} = -\frac{4}{x^2-10x+41} + \frac{9}{x^2+81} =0 \\ \\ -4(x^2+81)+9(x^2-10x+41)=0 \\ \\ -4x^2-324+9x^2-90x+369=0 \\ \\ 5x^2-90x+45=0 \\ \\ x^2-18x+9=0 \\ \\ x=9\pm6 \sqrt{2}$

Given that x is a point on line segment AB, this means that x is a positive number less than 5.

Thus
$x=9-6 \sqrt{2}=0.5147$

Therefore, The distance from A of point P, so that </span>angle θ is maximum is 0.51 to two decimal places.

6 0

3 years ago

Sophia started a lawn mowing business and charges a flat fee of $5.00 plus $3.50 per hour.

umka2103 [35]

Answer:

5 + 3.5h = 29.50

Step-by-step explanation:

The flat fee means that you will be paid the money with no change to it.

So you will not multiply it.

3.5h means that you are adding 3.50 every hour according to the question

So summary:

5+3.5h = 29.50

Evaluation:

5+3.5h = 29.50

24.50 = 3.5h

h = 7

Sofia worked 7 hours

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

4 0

3 years ago

Xavier can swim at a constant speed of 5/3 meters/second.

koban [17]

Answer:

Step-by-step explanation:

Well we can find how far he travels in 55 seconds if he swims at constant speed of 5/3 meters.

5/3 times 55 = approx. 91.66 meters

Therefore Xavier will not quality for the national Swim Meet because he didn't swim 100 meters in 55 seconds

7 0

2 years ago