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Svet_ta [14]
3 years ago
13

For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 20 N acts on

a certain object, the acceleration of the object is 4 /ms2. If the force is changed to 50 N, what will be the acceleration of the object?
Mathematics
1 answer:
jeka943 years ago
7 0

The acceleration of the object will be 10 m/s²

Step-by-step explanation:

Direct variation is a relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other

  • If y varies directly with x, then y ∝ x
  • y = k x, where k is the constant of variation

For a moving object, the force acting on the object varies directly with the object's acceleration.

Assume that the force is F and the acceleration is a

∵ F ∝ a

∴ F = k a

∵ F = 20 newtons

∵ a = 4 m/s²

- Substitute these values in the equation above to find k

∵ 20 = k (4)

∴ 20 = 4 k

- Divide both sides by 4

∴ k = 5

- Substitute the value of k in the equation

∴ F = 5 a ⇒ equation of variation

∵ F = 50 Newtons

∵ F = 5 a

∴ 50 = 5 a

- Divide both sides by 5

∴ 10 = a

∴ a = 10 m/s²

The acceleration of the object will be 10 m/s²

Learn more:

You can learn more about variation in brainly.com/question/10708697

#LearnwithBrainly

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Which graph represents y=^3sqrt x-5​
Lelechka [254]

Answer:

4

Step-by-step explanation:

Graph 4

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3 years ago
Can someone help me with this
mash [69]

The center of the circle is (h,k) = (-2,-3)

The radius of the circle is r = 2

The standard form of equation of the circle is

{(x + 2)}^{2}  +  {(y + 3)}^{2}  = 4

<h3>How to find the center, radius and standrad form of the circle?</h3>

The general form of equation of the circle is

{(x - h)}^{2}  +  {(y - k)}^{2}  =  {r}^{2}

Here, (h,k) means centre of the circle.

r means radius of the circle.

given that coordinate points of centre of circle is (-2,-3).

Hence the (h,k) = (-2,-3)

<h3>How to find the radius of the circle?</h3>

Now to find the radius of the circle

The distance from a circle's centre to its circumference is its radius.

The distance from a circle's centre (-2,-3) to its circumference (0,-3) is its radius.

using the formula, distance between the two points to obtain radius.

d =  \sqrt{(x1 - x2) {}^{2}  +  {(y1 - y2)}^{2} }  \\ r =  \sqrt{ {( - 2 - 0)}^{2} +  {( - 3 - ( - 3))}^{2}  }  \\ r =  \sqrt{ {( - 2)}^{2} +  {( - 3 + 3)}^{2}  }  \\ r =  \sqrt{ {4}^{2} + 0 }  \\ r =  \sqrt{4}  \\ r = 2

<h3>How to find the standard form of equation of the circle?</h3>

(h,k) = (-2,-3)

r = 2

subtitue the (h,k) and r values to get the standard form of equation of the circle.

(x - h) {}^{2}  +  {(y - k)}^{2}  =  {r}^{2}

{(x - ( - 2))}^{2}  +  {(y - ( - 3))}^{2} =  {r}^{2}

{(x + 2)}^{2}  +  {(y + 3)}^{2}  = 4

Learn more about circle, refer:

brainly.com/question/24810873

#SPJ9

5 0
1 year ago
A total of $5000 is invested: part at 9% and the remainder at 14%. How much is invested at each rate if the annual interest is $
IceJOKER [234]

9514 1404 393

Answer:

  • $200 at 14%
  • $4800 at 9%

Step-by-step explanation:

Let x represent the amount invested at 14%. Then 5000-x is the amount invested at 9%. The interest earned is ...

  (14%)x +(9%)(5000 -x) = 460

  0.05x +450 = 460 . . . . . . . . . . simplify

  0.05x = 10 . . . . . . . . . . . . . . subtract 450

  x = 200 . . . . . . . . . . . . . . divide by 0.05

  5000-x = 5000-200 = 4800

$200 was invested at 14%; $4800 was invested at 9%.

7 0
3 years ago
A coordinate plane with a line passing through (0, negative 3), (2, 0), and (4, 3). Which equation represents the graphed functi
Talja [164]

Answer:

y=\frac{3}{2}x-3

Step-by-step explanation:

we have the points

(0,-3),(2,0) and (4,3)

step 1

Find the slope

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

we take

(0,-3),(2,0)

substitute the values in the formula

m=\frac{0+3}{2-0}

m=\frac{3}{2}

step 2

Find the equation of the line in slope intercept form

y=mx+b

we have

m=\frac{3}{2}

b=-3 -----> the point (0,-3) is the y-intercept

substitute

y=\frac{3}{2}x-3

The graph in the attached figure

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3 years ago
Read 2 more answers
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