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4 years ago

8

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qr\sqrt4-x +\sqrt{4-x" align="absmiddle" class="latex-formula">

1 answer:

tankabanditka [31]4 years ago

8 0

$-2-x+\sqrt{-x+4}$

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Find the area of the surface. the part of the sphere x2 + y2 + z2 = 81 that lies above the plane z = 5.

IRISSAK [1]

<span>Here, we only need the upper hemisphere:
z = √(36 - x^2 - y^2).

Note that the cone and sphere intersect at z^2 + z^2 = 36 ==> z = √18
==> The region of integration is x^2 + y^2 + 18 = 36 ==> x^2 + y^2 = 18.

So via Cartesian Coordinates, the surface area equals
∫∫ √[1 + (z_x)^2 + (z_y)^2] dA
= ∫∫ √[1 + (-x/√(36 - x^2 - y^2))^2 + (-y/√(36 - x^2 - y^2))^2] dA
= ∫∫ √[1 + (x^2 + y^2)/(36 - x^2 - y^2)] dA
= ∫∫ √[36/(36 - x^2 - y^2)] dA
= ∫∫ 6 dA/√(36 - x^2 - y^2).

Converting to polar coordinates yields
∫(θ = 0 to 2π) ∫(r = 0 to √18) 6r dr dθ/√(36 - r^2)
= 2π ∫(r = 0 to √18) 6r(36 - r^2)^(-1/2) dr
= 2π * -3 * 2√(36 - r^2) {for r = 0 to √18}
= 12π (6 - 3√2)
= 36π (2 - √2).

I hope this helps! </span>

7 0

4 years ago

In a Gallup poll, 26.6% of 5000 people reported a Body Mass Index (BMI) greater than 30, which is classified as obese. The 5000

PSYCHO15rus [73]

Answer:

The 99% confidence interval for the proportion of the population who are obese is (0.25, 0.282)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 5000, \pi = 0.266$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.266 - 2.575\sqrt{\frac{0.266*0.734}{5000}} = 0.25$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.266 + 2.575\sqrt{\frac{0.266*0.734}{5000}} = 0.282$

The 99% confidence interval for the proportion of the population who are obese is (0.25, 0.282)

6 0

3 years ago

3 drinks and 2 pretzels costs $16, but 5 drinks and 5 pretzels costs $31.25. What is the price

Agata [3.3K]

Answer:

7.125

and 5.1

Step-by-step explanation:

6 0

3 years ago

The table represents a function.

Zarrin [17]

We have to complete the statement:

" The rate of change in the function y=x+4 is ______ the rate of change of the function represented in the table."

Let us consider the function represented in table.

The coordinates given in the table are:

(0,6) (2,8) (4,10) and (6,12)

Consider the first two coordinates (0,6) and (2,8)

$x_{1}=0 , y_{1}=6, x_{2}=2 , y_{2}=8$

Equation of line is given by $(y-y_{1})=m(x-x_{1})$

where 'm' is slope(rate of change) is given by the formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

So, $m = \frac{8-6}{2-0}=1$

So, equation of line is :

(y-6)= 1 (x-0)

y-6=x

y=x+6

Comparing it with standard equation of line y=mx+c with slope 'm'.

So, we get m(Rate of change)=1.

Now,

We will find the rate of change(slope) in the function y=x+4

Comparing it with standard equation of line y=mx+c with slope 'm'.

So, we get m(Rate of change)=1.

So, " The rate of change in the function y=x+4 is equal to the rate of change of the function represented in the table.

7 0

4 years ago

A video game shop is analyzing its sales performance using matrices. matrix a contains the unit sales data for each product cate

Marina86 [1]

Answer:

Matrix B should be subtracted from Matrix A.

Step-by-step explanation:

4 0

1 year ago