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denpristay [2]
3 years ago
10

The curves y = √x and y=(2-x) and the Cartesian axes form two distinct regions in the first quadrant. Find the volumes of rotati

on for each of the regions if rotating each around the horizontal axis and around the vertical axis. Construct the integral that represents the sum of the volumes of revolutions around the y-axis. Confirm that you get the same answer as when you revolve just the outer curve y=(2-x)'

Mathematics
1 answer:
makkiz [27]3 years ago
7 0

Answer:

Step-by-step explanation:

If you graph there would be two different regions. The first one would be

y = \sqrt{x} \,\,\,\,, 0\leq x \leq 1 \\

And the second one would be

y = 2-x \,\,\,\,\,,  1 \leq x \leq 2.

If you rotate the first region around the "y" axis you get that

{\displaystyle A_1 = 2\pi \int\limits_{0}^{1} x\sqrt{x} dx = \frac{4\pi}{5} = 2.51 }

And if you rotate the second region around the "y" axis you get that

{\displaystyle A_2 = 2\pi \int\limits_{1}^{2} x(2-x) dx = \frac{4\pi}{3} = 4.188 }

And the sum would be  2.51+4.188 = 6.698

If you revolve just the outer curve you get

If you rotate the first  region around the x axis you get that

{\displaystyle A_1 =\pi \int\limits_{0}^{1} ( \sqrt{x})^2 dx = \frac{\pi}{2} = 1.5708 }

And if you rotate the second region around the x axis you get that

{\displaystyle A_2 = \pi \int\limits_{1}^{2} (2-x)^2 dx = \frac{\pi}{3} = 1.0472 }

And the sum would be 1.5708+1.0472 = 2.618

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Travis spies an owl in a tall tree. He estimates the height of the tree to be 85 feet and the angle of elevation to the bird fro
anyanavicka [17]

Answer:

63.44 feet

Step-by-step explanation:

tan(68 degrees)= 85/y  

y tan (68 degrees)=85

y=85/tan(68 degrees) ( cross multiply)

y = 34.34 feet

tan (41 degrees)=85/x+y

(x+y)tan(41 degrees)=85

x+y=85/tan 41 degrees

x=85/tan(41 degrees) - y

x= 85/tan (41 degrees)-(34.34) (cross multiply)

Therefore, Travis stepped back 63.44 feet to gain a better view!

7 0
2 years ago
Evaluate 6x + 11 when x = 7
nlexa [21]

Answer:

53

Step-by-step explanation:

To evaluate 6x + 11, we must substitute the value of x.

Since we know that x = 7, it is easier to evaluate the expression;

6x + 11

6(7) + 11

Since 6 is outside the parenthesis, we must multiply everything inside the parenthesis by 6;

6(7) + 11

42 + 11

When you add the two numbers you get:

53

4 0
3 years ago
2564.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A
Leokris [45]

Answer:

We conclude that the board's length is equal to 2564.0 millimeters.

Step-by-step explanation:

We are given that a sample of 26 is made, and it is found that they have a mean of 2559.5 millimeters with a standard deviation of 15.0.

Let \mu = <u><em>population mean length of the board</em></u>.

So, Null Hypothesis, H_0 : \mu = 2564.0 millimeters    {means that the board's length is equal to 2564.0 millimeters}

Alternate Hypothesis, H_A : \mu \neq 2564.0 millimeters      {means that the boards are either too long or too short}

The test statistics that will be used here is <u>One-sample t-test statistics</u> because we don't know about the population standard deviation;

                             T.S.  =  \frac{\bar X-\mu}{\frac{s }{\sqrt{n}} }  ~  t_n_-_1

where, \bar X = sample mean length of boards = 2559.5 millimeters

            s = sample standard deviation = 15.0 millimeters

             n = sample of boards = 26

So, <em><u>the test statistics</u></em> =  \frac{2559.5-2564.0}{\frac{15.0 }{\sqrt{26}} }  ~   t_2_5

                                     =  -1.529    

The value of t-test statistics is -1.529.

Now, at a 0.05 level of significance, the t table gives a critical value of -2.06 and 2.06 at 25 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so <u><em>we have insufficient evidence to reject our null hypothesis</em></u> as it will not fall in the rejection region.

Therefore, we conclude that the board's length is equal to 2564.0 millimeters.

4 0
3 years ago
What is x squared 6x - 7 factorised?
lilavasa [31]
The factors would be (x +7) and (x - 1)
3 0
3 years ago
Can anyone rewrite quadratic function in standard form?
kati45 [8]

Answer:

hey I believe standard form would look like this:  f(x) = a(x - h)^2 + k

this is regular form f(x)=ax^2+bx+c or something like x^2+4x+4.

I think H and K are the vertex

hope this is close to what your looking for.

Step-by-step explanation:

I think it's x^2+6x-18

4 0
3 years ago
Read 2 more answers
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