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3 years ago

13

Please help (x) = x2. What is g(x)?

1 answer:

Vera_Pavlovna [14]3 years ago

3 0

The answer is A-g(x)=-x^2-4

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560880

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3 years ago

What's the factory of 10

sergey [27]

Answer:

1,2,5,10

Step-by-step explanation:

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3 years ago

Read 2 more answers

20 Points + Brainliest for the answer and Explanation!!!

Vlad1618 [11]

Answer:

$P+Q=5x^2+4$

$Q-P=-x^2-4x+16$

Step-by-step explanation:

We are given

$P=3x^2+2x-6$

$Q=2x^2-2x+10$

Calculation of P+Q:

$P+Q=3x^2+2x-6+2x^2-2x+10$

now, we can combine like terms

$P+Q=3x^2+2x^2+2x-2x+10-6$

$P+Q=5x^2+0+4$

$P+Q=5x^2+4$

Calculation of Q-P:

$Q-P=2x^2-2x+10-(3x^2+2x-6)$

Firstly, we will distribute negative sign

$Q-P=2x^2-2x+10-3x^2-2x+6$

now, we can combine like terms

$Q-P=2x^2-3x^2-2x-2x+6+10$

$Q-P=-x^2-4x+16$

8 0

3 years ago

Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D is the trian

Alla [95]

Answer: mass (m) = 4 kg

center of mass coordinate: (15.75,4.5)

Step-by-step explanation: As a surface, a lamina has 2 dimensions (x,y) and a density function.

The region D is shown in the attachment.

From the image of the triangle, lamina is limited at x-axis: 0≤x≤2

At y-axis, it is limited by the lines formed between (0,0) and (2,1) and (2,1) and (0.3):

<u>Points (0,0) and (2,1):</u>

y = $\frac{1-0}{2-0}(x-0)$

y = $\frac{x}{2}$

<u>Points (2,1) and (0,3):</u>

y = $\frac{3-1}{0-2}(x-0) + 3$

y = -x + 3

Now, find total mass, which is given by the formula:

$m = \int\limits^a_b {\int\limits^a_b {\rho(x,y)} \, dA }$

Calculating for the limits above:

$m = \int\limits^2_0 {\int\limits^a_\frac{x}{2} {2(x+y)} \, dy \, dx }$

where a = -x+3

$m = 2.\int\limits^2_0 {\int\limits^a_\frac{x}{2} {(xy+\frac{y^{2}}{2} )} \, dx }$

$m = 2.\int\limits^2_0 {(-x^{2}-\frac{x^{2}}{2}+3x )} \, dx }$

$m = 2.\int\limits^2_0 {(\frac{-3x^{2}}{2}+3x)} \, dx }$

$m = 2.(\frac{-3.2^{2}}{2}+3.2-0)$

m = 2(-4+6)

m = 4

<u>Mass of the lamina that occupies region D is 4.</u>

<u />

Center of mass is the point of gravity of an object if it is in an uniform gravitational field. For the lamina, or any other 2 dimensional object, center of mass is calculated by:

$M_{x} = \int\limits^a_b {\int\limits^a_b {y.\rho(x,y)} \, dA }$

$M_{y} = \int\limits^a_b {\int\limits^a_b {x.\rho(x,y)} \, dA }$

$M_{x}$ and $M_{y}$ are moments of the lamina about x-axis and y-axis, respectively.

Calculating moments:

For moment about x-axis:

$M_{x} = \int\limits^a_b {\int\limits^a_b {y.\rho(x,y)} \, dA }$

$M_{x} = \int\limits^2_0 {\int\limits^a_\frac{x}{2} {2.y.(x+y)} \, dy\, dx }$

$M_{x} = 2\int\limits^2_0 {\int\limits^a_\frac{x}{2} {y.x+y^{2}} \, dy\, dx }$

$M_{x} = 2\int\limits^2_0 { ({\frac{y^{2}x}{2}+\frac{y^{3}}{3})}\, dx }$

$M_{x} = 2\int\limits^2_0 { ({\frac{x(-x+3)^{2}}{2}+\frac{(-x+3)^{3}}{3} -\frac{x^{3}}{8}-\frac{x^{3}}{24} )}\, dx }$

$M_{x} = 2.(\frac{-9.x^{2}}{4}+9x)$

$M_{x} = 2.(\frac{-9.2^{2}}{4}+9.2)$

$M_{x} = 18$

Now to find the x-coordinate:

x = $\frac{M_{y}}{m}$

x = $\frac{63}{4}$

x = 15.75

For moment about the y-axis:

$M_{y} = \int\limits^2_0 {\int\limits^a_\frac{x}{2} {2x.(x+y))} \, dy\,dx }$

$M_{y} = 2.\int\limits^2_0 {\int\limits^a_\frac{x}{2} {x^{2}+yx} \, dy\,dx }$

$M_{y} = 2.\int\limits^2_0 {y.x^{2}+x.{\frac{y^{2}}{2} } } \,dx }$

$M_{y} = 2.\int\limits^2_0 {x^{2}.(-x+3)+\frac{x.(-x+3)^{2}}{2} - {\frac{x^{3}}{2}-\frac{x^{3}}{8} } } \,dx }$

$M_{y} = 2.\int\limits^2_0 {\frac{-9x^3}{8}+\frac{9x}{2} } \,dx }$

$M_{y} = 2.({\frac{-9x^4}{32}+9x^{2})$

$M_{y} = 2.({\frac{-9.2^4}{32}+9.2^{2}-0)$

$M{y} =$ 63

To find y-coordinate:

y = $\frac{M_{x}}{m}$

y = $\frac{18}{4}$

y = 4.5

<u>Center mass coordinates for the lamina are (15.75,4.5)</u>

3 0

3 years ago

The sum of four<br>consecutive odd number is 8o. Find the number

yarga [219]

Answer:

<em>The sum of 4 consecutive odd number is 80</em>

<em>Let X be the first of these numbers</em>

<em>Then the next odd number is X+2</em>

<em>The third is X+4The fourth is X+6</em>

<em>All of these add up to 80</em>

<em>(X) + (X+2) + (X+4) + (X+6) = 80</em>

<em>Using the commutative and associative laws, let's transform this equation into</em>

<em>(X + X + X + X) + (2 + 4 + 6) = 804X + 12 = 80</em>

<em>Subtract 12 from both sides of the equation gives4X = 68</em>

<em>Divide both sides by 4 gives</em>

<em>X = 17</em>

<em>Going back to the original question:What are the 4 consecutive odd numbers: 17, 19, 21, 23Checking our answer:17 + 19 + 21 + 23 = 80 Correct!</em>

5 0

2 years ago