Please helpp with thiss

Find the volume of the given solid: Bounded by the cylinder y^2+z^2=4 and the planes x = 2y, x = 0, z = 0 in the first octant.

rodikova [14]

The solution would be like this for this specific problem:

V = ∫ dV 
= ∫0→2 ∫ 0→π/2 ∫ 0→ 2·r·sin(φ) [ r ] dzdφdr 
= ∫0→2 ∫ 0→π/2 [ r·2·r·sin(φ) - r·0 ] dφdr 
= ∫0→2 ∫ 0→π/2 [ 2·r²·sin(φ) ] dφdr 
= ∫0→2 [ -2·r²·cos(π/2) + 2·r²·cos(0) ] dr 
= ∫0→2 [ 2·r² ] dr 
= (2/3)·2³ - (2/3)·0³ 
= 16/3

So the volume of the given solid is 16/3. I am hoping that these answers have satisfied your query and it will be able to help you in your endeavors, and if you would like, feel free to ask another question.

3 0

3 years ago

A gray crayon is made with 5\text{ mL}5 mL5, space, m, L of black wax for every 6\text{ mL}6 mL6, space, m, L of white wax.

zloy xaker [14]

The correct answers are B and C.

Since the mixture requires 5 mL of black wax and 6 mL of white wax, we want multiples of these numbers; specifically, we need multiples that are the same number of times away.

A does not work; 10 is 5*2 and 24 is 6*4. These won't be in the same ratio.

B works; 15 is 5*3 and 18 is 6*3. These have the same ratio.

C works; 35 is 5*7 and 42 is 6*7. These have the same ratio.

D does not work; 26 is not a multiple of 6.

E does not work; 45 is 5*9 and 48 is 6*8. These will not have the same ratio.

8 0

3 years ago

Read 2 more answers

Please help mee, (30 points will give brainliest!!!)

Vadim26 [7]

Answer:

-4

+3

12

-0.5, 12.25

x = -0.5

Step-by-step explanation:

The x intercepts are the values of x when y = 0 ie the roots of the equation
$-x^2 -x +12 = 0$

or

$x^2 + x - 12 = 0$

We can re-write the above as:
(x+4) (x-3) = 0
This gives the two roots as x = -4 and x = +3. Leftmost (smallest) root is -4 and rightmost(largest) root is +3

y intercept is when x = 0. Plugging into the original equation, y value at x = 0 is 12

Vertex x value is given by the formula -b/2a where a is the coefficient of x^2 and b the coefficient of x

Here a = -1, b= -1 so vertex x value = - (-1)/(-1).2 = - 1/2 = -0.5

Plugging this value of x into the original function gives the vertex y value
$y = - (0.5^{2}) - (-0.5) + 12\\= -0.25 + 0.5 + 12 = 12.25$

The line of symmetry is the vertical line corresponding to the vertex x value so line of symmetry is at x = -0.5

The graph of the quadratic function shows these values