What is (f−g)(x)?

At a playground, a child slides down a slide that makes a 42° angle with the horizontal direction. the coefficient of kinetic fr

enyata [817]

Assuming metric units, metre, kilogram and seconds

Best approach: draw a free body diagram and identify forces acting on the child, which are:
gravity, which can be decomposed into normal and parallel (to slide) components
N=mg(cos(theta)) [pressing on slide surface]
F=mg(sin(theta)) [pushing child downwards, also cause for acceleration]
m=mass of child (in kg)
g=acceleration due to gravity = 9.81 m/s^2
theta=angle with horizontal = 42 degrees

Similarly, kinetic friction is slowing down the child, pushing against F, and equal to
Fr=mu*N=mu*mg(cos(theta))
mu=coefficient of kinetic friction = 0.2

The net force pushing child downwards along slide is therefore
Fnet=F-Fr
=mg(sin(theta))-mu*mg(cos(theta))
=mg(sin(theta)-mu*cos(theta)) [ assuming sin(theta)> mu*cos(theta) ]

From Newton's second law,
F=ma, or
a=F/m
=mg(sin(theta)-mu*cos(theta)) / m
= g(sin(theta)-mu*cos(theta)) [ m/s^2]

In case imperial units are used, g is approximately 32.2 feet/s^2.
and the answer will be in the same units [ft/s^2] since sin, cos and mu are pure numbers.

3 0

4 years ago

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GIVING BRAINIEST IF RIGHT!! ANSWER FAST PLEASE

mojhsa [17]

Answer:

I think its B.) Yes, because the ratios simplify to the same number., sorry if it's wrong

Step-by-step explanation:

50/10 = 1/5

60/12 = 1/5

70/14 = 1/5

80/16 = 1/5

They all simplify to the same proportion.

6 0

3 years ago

2.21586210 rounded to four decimal places

Vadim26 [7]

Answer:

Sorry I really don't know :(

Step-by-step explanation:

Very sorry

7 0

4 years ago

If line GH is perpendicular to line HJ, then GJ is ____ HJ.

valentinak56 [21]

Option A: >

Solution:

Given a triangle GHJ.

The line GH is perpendicular to line HJ.

This means the triangle is a right angled triangle.

In ΔGHJ, GH is the base of the triangle and

HJ is a height of the triangle.

Then the third side must be the hypotenuse of the right triangle.

We know that by the Pythagoras theorem,

$(\text {Hypotenuse})^2=(\text{Base})^2+(\text{Height})^2$

$(\text {GJ})^2=(\text {GH})^2+(\text {HJ})^2$

This clearly shows that the hypotenuse is greater than the height.

⇒ GJ > HJ

Option A: > is the correct answer.

If line GH is perpendicular to line HJ, then GJ is > HJ.

3 0

3 years ago

How many solutions does the system have?

Usimov [2.4K]

Answer:

x= -9/7

y= -38/7

so it has A. exactly one solution

Step-by-step explanation:

Substitute into one of the equations: 5x+1= -2x-8

Rearrange unknown terms to the left side of the equation: 5x+2x=-8-1

Combine like terms:7x=-8-1

Calculate the sum or difference: 8x=-9

Divide both sides of the equation by the coefficient of variable: x=-9/7

Substitute into one of the equations:y=-2×(-9/7)-8

Write as a single fraction:y=2×9/7-8

Calculate the product or quotient:y=18/7 -8

Convert the expression into a fraction: y=18/7 -8/1

Expand the fraction to get the least common demominator:y=18/7-8x7/1x7

Calculate the product or quotient: y=18/7-56/7

Write the numerators over common denominator:y=18-56/7

Calculate the sum or difference: y=-38/7

Rewrite the fraction: y= -38/7

The solution of the system is:

x= -9/7

y= -38/7

5 0

2 years ago

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