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2 years ago

Which inequality is represented by this graph?

Mathematics

2 answers:

Whitepunk [10]2 years ago

7 0

c is the correct answer

Firdavs [7]2 years ago

6 0

Answer:

B is the answer i got 90%

Step-by-step explanation:

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Find the volume of the solid obtained by rotating the region bounded by the given curves about the speciﬁed axis. x+y = 3, x = 4

Ad libitum [116K]

The intersection between the curves are
3, 0
0, 3
The volume of the solids is obtained by
V = ∫ π [ (4 - (y-1)²)² - (3 - y)²] dy with limits from 0 to 3
The volume is
V = 108π/5 or 67.86

4 0

3 years ago

A rectangular floor of area 21.6 m2 is going to be tiled. Each tile is rectangular, and has an area of 576 cm2. An exact number

saveliy_v [14]

Answer:

Area of floor = 21.6m2

area of tile = 576cm2=0.0576m2

now,

number of tiles = 21.6/0.0576

= 375

7 0

3 years ago

Read 2 more answers

The functio p(x)= x(x-5)(x-2)(x+3) has four zeros. What is the smallest zero.

loris [4]

Answer:

x = 5 or x = 2 or x = 0 or x = -3 thus 0 is the smallest root

Step-by-step explanation:

Solve for x:

x (x - 5) (x - 2) (x + 3) = 0

Split into four equations:

x - 5 = 0 or x - 2 = 0 or x = 0 or x + 3 = 0

Add 5 to both sides:

x = 5 or x - 2 = 0 or x = 0 or x + 3 = 0

Add 2 to both sides:

x = 5 or x = 2 or x = 0 or x + 3 = 0

Subtract 3 from both sides:

Answer: x = 5 or x = 2 or x = 0 or x = -3

8 0

3 years ago

Consider the following differential equation. x^2y' + xy = 3 (a) Show that every member of the family of functions y = (3ln(x) +

Veronika [31]

Answer:

Verified

$y(x) = \frac{3Ln(x) + 3}{x}$

$y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{x}$

Step-by-step explanation:

Question:-

- We are given the following non-homogeneous ODE as follows:

$x^2y' +xy = 3$

- A general solution to the above ODE is also given as:

$y = \frac{3Ln(x) + C }{x}$

- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.

Solution:-

- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.

$y' = \frac{\frac{d}{dx}( 3Ln(x) + C ) . x - ( 3Ln(x) + C ) . \frac{d}{dx} (x) }{x^2} \\\\y' = \frac{\frac{3}{x}.x - ( 3Ln(x) + C ).(1)}{x^2} \\\\y' = - \frac{3Ln(x) + C - 3}{x^2}$

- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:

$-\frac{3Ln(x) + C - 3}{x^2}.x^2 + \frac{3Ln(x) + C}{x}.x = 3\\\\-3Ln(x) - C + 3 + 3Ln(x) + C= 3\\\\3 = 3$

- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.

- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

$y( 1 ) = \frac{3Ln(1) + C }{1} = 3\\\\0 + C = 3, C = 3$

- Therefore, the complete solution to the given ODE can be expressed as:

$y ( x ) = \frac{3Ln(x) + 3 }{x}$

- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

$y(3) = \frac{3Ln(3) + C}{3} = 1\\\\y(3) = 3Ln(3) + C = 3\\\\C = 3 - 3Ln(3)$