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3 years ago

PLEASE HELP ME IF YOUR RIGHT ILL GIVE BRIANLIEST!!!

Mathematics

2 answers:

IrinaK [193]3 years ago

5 0

Answer:

the answer is c.21 hope this helps

Juli2301 [7.4K]3 years ago

5 0

Answer:

c its 21 lol <33333333hsj fcb sndbd

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What's 4x + 3 = 2x + 17

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Answer:

x=7

Step-by-step explanation:

Move all terms containing x to the left side of the equation.

2x+3=17

Move all terms not containing x to the right side of the equation.

2x=14

Divide each term by 2 and simplify.

x=7

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3 years ago

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A 6 cm long spring extends to 9 cm when a 1 kg load is suspended from it. What would be its length if a 2 kg load were suspended

vampirchik [111]

Answer:

12 cm

Step-by-step explanation:

To calculate the length of a spring with a 2 kg load, compare the displacement of a 1 kg load and adjust accordingly.

When a 1 kg load is suspended from the spring, the spring which is 6 cm stretches to 9 cm. This is 3 cm longer due to the weight. If you attach a weight which is twice as much then the displacement will be twice as much. Instead of stretching an additional 3 cm, it will stretch 2*3 = 6 cm. Add this to the length of the spring and it stretches in total 6 + 6 = 12 cm.

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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):

Points (0,0) and (2,1):

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

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

Points (2,1) and (0,3):

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

Mass of the lamina that occupies region D is 4.

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:

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