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maxonik [38]
3 years ago
11

PLEASE ANSWER Angela is a member of the swim team 7 member of the swim team are boys the other 8 members of the swims teams are

girls one member of Angela swim team wins a gold medal at the first swim meet what is the probability of the winning team member being a girl?
a 8/7
b 1/8
c 1/15
d 8/15
Mathematics
1 answer:
Marianna [84]3 years ago
8 0
1/15 Bc there's 15 on the team and only 1 is getting the medal
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Find the volume of the solid.
dmitriy555 [2]

In Cartesian coordinates, the region (call it R) is the set

R = \left\{(x,y,z) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } 2 \le z \le 4-x^2-y^2\right\}

In the plane z=2, we have

2 = 4 - x^2 - y^2 \implies x^2 + y^2 = 2 = \left(\sqrt2\right)^2

which is a circle with radius \sqrt2. Then we can better describe the solid by

R = \left\{(x,y,z) ~:~ 0 \le x \le \sqrt2 \text{ and } 0 \le y \le \sqrt{2 - x^2} \text{ and } 2 \le z \le 4 - x^2 - y^2 \right\}

so that the volume is

\displaystyle \iiint_R dV = \int_0^{\sqrt2} \int_0^{\sqrt{2-x^2}} \int_2^{4-x^2-y^2} dz \, dy \, dx

While doable, it's easier to compute the volume in cylindrical coordinates.

\begin{cases} x = r \cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \end{cases} \implies \begin{cases}x^2 + y^2 = r^2 \\ dV = r\,dr\,d\theta\,d\zeta\end{cases}

Then we can describe R in cylindrical coordinates by

R = \left\{(r,\theta,\zeta) ~:~ 0 \le r \le \sqrt2 \text{ and } 0 \le \theta \le\dfrac\pi2 \text{ and } 2 \le \zeta \le 4 - r^2\right\}

so that the volume is

\displaystyle \iiint_R dV = \int_0^{\pi/2} \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta \, dr \, d\theta \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta\,dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} r((4 - r^2) - 2) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} (2r-r^3) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \left(\left(\sqrt2\right)^2 - \frac{\left(\sqrt2\right)^4}4\right) = \boxed{\frac\pi2}

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1 year ago
30+5y_>4x I need the answer ASAP
Gre4nikov [31]
30+5y_>4x
5y_>4x-30
The answer is: y_>(4/5)x-6
5 0
2 years ago
The length of a square is 10 cm. Calculate the perimeter of the square A. 40cm² B. 400cm² C. 4ocm D. 414cm² I will mark you as b
noname [10]

Answer:

C. 40 cm

Step-by-step explanation:

length of side of square = s

perimeter = s + s + s + s = 4s

We use the formula P = 4s

P = 4 * 10 cm

P = 40 cm

Answer: The perimeter is 40 cm.

Notice that the perimeter is a sum of lengths, so its units are linear units such as cm, inches, feet, a unit of length.

An area has square units such as cm^2, in.^2, ft^2, etc.

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Vera_Pavlovna [14]

Answer:

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Step-by-step explanation:

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2 years ago
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Which formula is correct ?
larisa86 [58]

Answer:

The first answer choice

Step-by-step explanation:

Formula for volume of a rectangular pyramid is V=lwh/3

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