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3 years ago

Given cube inscribed in sphere with edges √243 cm. Find the volume of sphere

Mathematics

1 answer:

g100num [7]3 years ago

3 0

Answer:

10,300.77 cm³

Step-by-step explanation:

Radius = ½(diameter)

Diagonal:

sqrt[243 + 243]

sqrt(486)

Diameter

sqrt(486 + 243)

Radius: 27/2

Volume of sphere:

4/3 × pi × r³

4/3 × 3.14 × (27/2)³

10300.77 cm³

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A road perpendicular to a highway leads to a farmhouse located d miles away. An automobile traveling on this highway passes thro

pshichka [43]

Answer:

$\frac{dh}{dt}=\frac{30r}{\sqrt{d^{2}+900}}$

Step-by-step explanation:

A road is perpendicular to a highway leading to a farmhouse d miles away.

An automobile passes through the point of intersection with a constant speed $\frac{dx}{dt}$ = r mph

Let x be the distance of automobile from the point of intersection and distance between the automobile and farmhouse is 'h' miles.

Then by Pythagoras theorem,

h² = d² + x²

By taking derivative on both the sides of the equation,

$(2h)\frac{dh}{dt}=(2x)\frac{dx}{dt}$

$(h)\frac{dh}{dt}=(x)\frac{dx}{dt}$

$(h)\frac{dh}{dt}=rx$

$\frac{dh}{dt}=\frac{rx}{h}$

When automobile is 30 miles past the intersection,

For x = 30

$\frac{dh}{dt}=\frac{30r}{h}$

Since $h=\sqrt{d^{2}+(30)^{2}}$

Therefore,

$\frac{dh}{dt}=\frac{30r}{\sqrt{d^{2}+(30)^{2}}}$

$\frac{dh}{dt}=\frac{30r}{\sqrt{d^{2}+900}}$

3 0

3 years ago

Find the vertex of the following equation y= (x+9)^2+8

Olegator [25]

(-9,8) is the answer (h,k) is the equation

8 0

3 years ago

A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historic

Rina8888 [55]

Answer:

The probability that none of the LED light bulbs are defective is 0.7374.

Step-by-step explanation:

The complete question is:

What is the probability that none of the LED light bulbs are defective?

Solution:

Let the random variable X represent the number of defective LED light bulbs.

The probability of a LED light bulb being defective is, P (X) = p = 0.03.

A random sample of n = 10 LED light bulbs is selected.

The event of a specific LED light bulb being defective is independent of the other bulbs.

The random variable X thus follows a Binomial distribution with parameters n = 10 and p = 0.03.

The probability mass function of X is:

$P(X=x)={10\choose x}(0.03)^{x}(1-0.03)^{10-x};\ x=0,1,2,3...$

Compute the probability that none of the LED light bulbs are defective as follows:

$P(X=0)={10\choose 0}(0.03)^{0}(1-0.03)^{10-0}$

$=1\times 1\times 0.737424\\=0.737424\\\approx 0.7374$

Thus, the probability that none of the LED light bulbs are defective is 0.7374.

6 0

3 years ago

Step 3: Solving a system of equations to make comparisons between men and women

zysi [14]

I am also not able to solve thi s question

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3 years ago

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USPshnik [31]

Answer:

5, 5+ 5(1/5) 5 is the number

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