I can't remember on how to figure out the answer.. Please help.

Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your

love history [14]

If we substitute $x=r\cos\theta$ and $y=r\sin\theta$ , we get $r^2=x^2+y^2$ , so that

$z=\cos(x^2+y^2)=\cos(r^2)$

which is independent of $\theta$ , which in turn means the surface can be treated like a surface of revolution.

Consider the function $f(t)=\cos(t^2)$ defined over $0\le t\le1$ . Revolve the curve $C$ described by $f(t)$ about the line $t=0$ . The area of the surface obtained in this way is then

$\displaystyle2\pi\int_C\mathrm dS=2\pi\int_0^1\sqrt{1+f'(t)^2}\,\mathrm dt$

$=\displaystyle2\pi\int_0^1\sqrt{1+(-2t\sin(t^2))^2}\,\mathrm dt$

$=\displaystyle2\pi\int_0^1\sqrt{1+4t^2\sin^2(t^2)}\,\mathrm dt\approx7.4144$

4 0

3 years ago

Construct the cumulative frequency distribution for the given data.

tino4ka555 [31]

Answer:

Age Frequency Cumulative Frequency

Less than 30 27 27

Less than 40 37 27 + 37 = 64

Less than 50 1 1 64 + 11 = 75

Less than 60 3 75 + 2 = 77

Less than 70 5 77 + 5 = 82

Less than 80 1 82 + 1 = 83

Less than 90 2 83 +2 = 85

Step-by-step explanation:

Given:

The Frequency Distribution table of ages of best actresses when award was won

To find:

Construct the cumulative frequency distribution

Solution:

In order to construct cumulative frequency distribution for the given data, each frequency from above table is added to the sum of the previous frequencies. For example, frequency for Less than 40 is 37 and the previous frequency (less than 30) is 27 so in order to calculate cumulative frequency 27 i.e. previous frequency is added to 37 (frequency of less than 30). The complete table is given above.

4 0

3 years ago

Find all the real square roots of 0.0004.

chubhunter [2.5K]

Hey!!

the answer is 0.02 !.

if helped, brainliest

5 0

3 years ago

Read 2 more answers

So I'm in an online class of geometry and one of the units is trig. but no matter how long i keep learning or trying to learn th

Arturiano [62]

Answer and explanation:

There are six main trigonometric ratios, namely: sine, cosine, tangent, cosecant, secant, cotangent.

Those ratios relate two sides of a right triangle and one angle.

Assume the following features and measures of a right triangle ABC

right angle: B, measure β
hypotenuse (opposite to angle B): length b

angle C: measure γ
vertical leg (opposite to angle C): length c

horizontal leg (opposite to angle A): length a
angle A: measure α

Then, the trigonometric ratios are:

sine (α) = opposite leg / hypotenuse = a / b

cosine (α) = adjacent leg / hypotenuse = c / b

tangent (α) = opposite leg / adjacent leg = a / c

cosecant (α) = 1 / sine (α) = b / a

secant (α) = 1 / cosine (α) = b / c

cotangent (α) = 1 / tangent (α) = c / b

Then, if you know one angle (other than the right one) of a right triangle, and any of the sides you can determine any of the other sides.

For instance, assume an angle to be 30º, and the lenght of the hypotenuse to measure 5 units.

sine (30º) = opposite leg / 5 ⇒ opposite leg = 5 × sine (30º) = 2.5

cosine (30º) = adjacent leg / 5 ⇒ adjacent leg = 5 × cosine (30º) = 4.3

Thus, you have solved for the two unknown sides of the triangle. The three sides are 2.5, 4.3, and 5.

7 0

3 years ago

On a Sunday night, there are four people on a bus. The bus has five stops left before it end sits route. Suppose each person wil

allochka39001 [22]

There are two possible outcomes of this experiment either success p or failure q. It has a given number of trials and all trials are independent therefore it is binomial probability distribution.

1- 5 ways

2- 5/16

3- 1/16

4- 1/16

In the question given above n= 5 p =1/2 q= 1/2 r is the given point.

Part 1:

The number of ways in which different people get off the bus can be calculated using combinations since the order is not essential. Therefore

nCr= 5C4= 5 ways

2. Part 2:

The probability that all four people get off the bus on the first stop is given by :

P (x= 1)= 5C1 (1/2)^0(1/2)^4= 5(1/2)^4= 5/16

3. Part 3:- The probability that all four people get off the bus on the same stop.

P (x= x)= 5C5 (1/2)^0(1/2)^4= 1(1/2)^4= 1/16

4. Part 4- The probability that exactly three of the four people get off the bus on the same stop.

P (x= x)= 5C5 (1/2)^3(1/2)^1= 1(1/2)^4= 1/16

For binomial distribution click

brainly.com/question/15246027

brainly.com/question/13542338

3 0

3 years ago