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2 years ago

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Evaluate the integral. ∫50∫25−x2√−25−x2√∫25−x2−z2√−25−x2−z2√1(x2+y2+z2)1/2dydzdx∫05∫−25−x225−x2∫−25−x2−z225−x2−z21(x2+y2+z2)1/2d

ydzdx

1 answer:

Kipish [7]2 years ago

4 0

Is that a valid question?

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Bernardo and Ogechi were asked to find an explicit formula for the sequence 1\,,\,8\,,\,64\,,\,512,...1,8,64,512,...1, comma, 8,

MatroZZZ [7]

Answer:

$h_{n}=1.(8)^{n-1}$ will be the correct formula for the given sequence.

Step-by-step explanation:

The given sequence is 1, 8, 64, 512...........

The given sequence is a geometric sequence having a common ratio (r) of

r = $\frac{\text{Second term}}{\text{First term}}$

r = $\frac{8}{1}=8$

Since explicit formula of a geometric sequence is given by

$T_{n}=a(r)^{n-1}$

where $T_{n}$ = nth term of the sequence

a = first term of the sequence

r = common ratio of the successive term to the previous term

Now we plug values of a and r in the formula to get the explicit formula for the given sequence.

$T_{n}=1.(8)^{n-1}$

Therefore, if Bernardo is saying that the formula of the sequence is

h(n) = $1.(8)^{n-1}$ then he is correct.

7 0

2 years ago

Read 2 more answers

Pleaseee help!!! If you can, answer both :))

kherson [118]

Okay the first one is what u did lol

6 0

2 years ago

How many terms are in the algebraic expression -7 + 12x4 - 5y8 + x?

Mazyrski [523]

Answer:

4

Step-by-step explanation:

Each mix of numbers and letters that is separated by a + or a - is a term.

5 0

2 years ago

In general, the probability that a blood donor has Type A blood is 0.40.Consider 8 randomly chosen blood donors, what is the pro

postnew [5]

Answer:

The probability that more than half of them have Type A blood in the sample of 8 randomly chosen donors is P(X>4)=0.1738.

Step-by-step explanation:

This can be modeled as a binomial random variable with n=8 and p=0.4.

The probability that k individuals in the sample have Type A blood can be calculated as:

$P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{8}{k} 0.4^{k} 0.6^{8-k}\\\\\\$

Then, we can calculate the probability that more than 8/2=4 have Type A blood as:

$P(X>4)=P(X=5)+P(X=6)+P(X=7)+P(X=8)\\\\\\P(x=5) = \dbinom{8}{5} p^{5}(1-p)^{3}=56*0.0102*0.216=0.1239\\\\\\P(x=6) = \dbinom{8}{6} p^{6}(1-p)^{2}=28*0.0041*0.36=0.0413\\\\\\P(x=7) = \dbinom{8}{7} p^{7}(1-p)^{1}=8*0.0016*0.6=0.0079\\\\\\P(x=8) = \dbinom{8}{8} p^{8}(1-p)^{0}=1*0.0007*1=0.0007\\\\\\\\P(X>4)=0.1239+0.0413+0.0079+0.0007=0.1738$

3 0

2 years ago

A rectangular solid with a square base has a volume of 5832 cubic inches. (Let x represent the length of the sides of the square

Aleks04 [339]

Answer:

a) 18 in x 18 in x 18 in

b) $S = 1944\ in2$

Step-by-step explanation:

a) Let's call 's' the side of the square base and 'h' the height of the solid.

The surface area is given by the equation:

$S = 2s^2 + 4sh$

The volume of the solid is given by the equation:

$V = s^2h = 5832$

From the volume equation, we have that:

$h = 5832/s^2$

Then, using this value of h in the surface area equation, we have:

$S = 2s^2 + 4s(5832/s^2)$

$S = 2s^2 + 23328/s$

To find the side length that gives the minimum surface area, we can find where the derivative of S in relation to s is zero:

$dS/ds = 4s - 23328/s^2 = 0$

$4s = 23328/s^2$

$4s^3 = 23328$

$s^3 = 23328/4 = 5832$

$s = 18\ inches$

The height of the solid is:

$h = 5832/(18)^2 = 18\ inches$

b) The minimum surface area is:

$S = 2(18)^2 + 4(18)(18)$

$S = 1944\ in2$

8 0

2 years ago