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user100 [1]
3 years ago
15

For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 72 N acts on

a certain object, the acceleration of the object is 8 m/s^2. If the acceleration of the object becomes 10 m/s^2, what is the force?
Mathematics
1 answer:
Tems11 [23]3 years ago
3 0

Answer:

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.

For a moving object, the force acting on the object varies directly with the object's acceleration. Let F represent force and A represent acceleration, if we introduce a constant of variation, k, then the expression becomes

F = kA

When a force of 72 N acts on a certain object, the acceleration of the object is 8 m/s^2. This means that

72 = 8k

k = 72/8 = 9

The equation becomes

F = 9A

If the acceleration of the object becomes 10 m/s^2, then the force would be

F = 9 × 10

F = 90N

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Find the length of the segment that joins the points (-5, 4) and (6,-3).
Helen [10]

Answer:

\boxed {\boxed {\sf d=\sqrt{170} \ or \  d\approx 13.04}}}

Step-by-step explanation:

We are asked to find the length of a segment or the <em>distance</em> between the 2 points. The formula for distance is:

d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2

where (x₁ y₁) and (x₂, y₂) are the points. We are given the points ( -5, 4) and (6, -3). If we match the number and the corresponding variable, it is:

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  • y₁= 4
  • x₂= 6
  • y₂ = -3

Substitute the values into the formula.

d= \sqrt{(6--5)^2+(-3-4)^2

Solve inside the parentheses.

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  • -3-4= -7

d= \sqrt{(11)^2+(-7)^2

Solve the exponents.

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  • (-7)²= -7*-7= 49

d= \sqrt {(121)+(49)

Add.

d= \sqrt {170}

d=13.0384048104

Even though it's not specified, we could round to the nearest hundredth to make the answer more concise. The 8 in the thousandth place tells us to round the 3 to a 4 in the hundredth place.

  • 13.03<u>8</u>4048104

d\approx 13.04

The length of the segment is <u>√170</u> or approximately <u>13.04. </u>

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