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3 years ago

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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?

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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3 years ago

The deck that Amos is building is in the shape of a parallelogram, DGRY. The measure of

weqwewe [10]

Complete Question:

The deck that Amos is building is in the shape of a parallelogram, DGRY. The measure of D is five-halves the measure of Y. Find the measure of each angle of the deck.

Answer:

$\angle G = \angle Y = 51.43 ^{\circ}$

$\angle D = \angle R = 128.57 ^{\circ}$

Step-by-step explanation:

Given

Shape: Parallelogram DGRY

Dimension: $\angle D = \frac{5}{2}\angle Y$

Required

Find the measure of each angle

D and R are opposite sides & G and Y are also opposite sides.

So, we have:

$\angle D = \angle R = \frac{5}{2}\angle Y$

and

$\angle G = \angle Y$

The sum of angles is given as:

$\angle D + \angle G + \angle R + \angle Y=360^{\circ}$

Substitute values for $\angle D, \angle G \ \& \angle R$

$\frac{5}{2}\angle Y + \frac{5}{2}\angle Y + \angle Y + \angle Y = 360^{\circ}$

Take LCM

$\frac{5\angle Y + 5\angle Y + 2\angle Y+ 2\angle Y}{2}= 360^{\circ}$

$\frac{14\angle Y}{2}= 360^{\circ}$

Multiply both sides by $\frac{2}{14}$

$\frac{2}{14} * \frac{14\angle Y}{2}= 360^{\circ} * \frac{2}{14}$

$\angle Y= 360^{\circ} * \frac{2}{14}$

$\angle Y= \frac{ 360^{\circ} *2}{14}$

$\angle Y= \frac{720^{\circ}}{14}$

$\angle Y= 51.43 ^{\circ}$

So:

$\angle G = \angle Y = 51.43 ^{\circ}$

$\angle D = \frac{5}{2}\angle Y$

$\angle D = \frac{5}{2} * 51.43^{\circ}$

$\angle D = \frac{5* 51.43^{\circ}}{2}$

$\angle D = \frac{257.15^{\circ}}{2}$

$\angle D = 128.57 ^{\circ}$

Hence:

$\angle D = \angle R = 128.57 ^{\circ}$

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3 years ago

The Punic Wars began in 264 B.C. and ended in 146 B.C. How long did the Punic Wars last??

pishuonlain [190]

Answer:

The first two wars were long—23 years and 17 years, separated by an interval of 23 years. The third war lasted nearly three years. It started 52 years after the end of the second war. All three wars were won by Rome, which subsequently emerged as the greatest military power in the Mediterranean Sea.

Step-by-step explanation:

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3 years ago

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If a line includes the points (8,0) and (20,12). What is its equation in slope-intercept form?

aev [14]

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

substitute the coordinates of the points (8, 0) and (20, 12) to the formula:

$m=\dfrac{12-0}{20-8}=\dfrac{12}{12}=1$

y = 1x + b = x + b

Put the coordinates of the point (8, 0) to the equation of a line:

0 = 8 + b <em>subtract 8 from both sides</em>

-8 = b

<h3>Answer: y = x - 8</h3>

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3 years ago

Help, ASAP! Please!!

Yuliya22 [10]

Answer:

a. Parallel

b. Not parallel

Step-by-step explanation:

Systems which have no solutions are parallel lines. These lines do not intersect and therefore have no solution. Remember, parallel lines have the same slope. Compare the slope in each equation when in y=mx+b format to see if they are parallel.

a. y= 2x + 3 y-2x=-3 becomes y = 2x - 3

m = 2 m= 2

The slopes are the same so these are parallel lines.

b. 3x + y = 2 becomes y= -3x + 2 y = 1/3 x + 1/2

m = -3 m= 1/3

The slopes are different so this is not parallel.

Since -3 and 1/3 are the negative reciprocals of each other. These lines are actually perpendicular.

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3 years ago