a man uses a 11 foot bar to lift a 108 pound tire. he places a rock 2 feet the tire to act as the fulcrum. how much force must h
e exert to lift tire
1 answer:
The problem uses the concept of Lever and Fulcrum.
The tire is placed on one end of the bar and the man applies force on the other end. Rock is placed 2 feet from the tire. The total length of the bar is 11 feet. This means, the distance between man and the rock is 9 feet as shown in the mage below.
According to principle of Level and Fulcrum, the product of force and distance from the level must be same on both sides.
So, product of force applied by man and 9 must be equal to the product of 2 and weight of tire.
We can set up the equation as:
9x = 2(108)
Dividing both sides by 9, we get the values of x to be:
x = 24 pounds
Therefore, the man must exert 24 pounds of force to lift the 108 pound tire.
The tire is placed on one end of the bar and the man applies force on the other end. Rock is placed 2 feet from the tire. The total length of the bar is 11 feet. This means, the distance between man and the rock is 9 feet as shown in the mage below.
According to principle of Level and Fulcrum, the product of force and distance from the level must be same on both sides.
So, product of force applied by man and 9 must be equal to the product of 2 and weight of tire.
We can set up the equation as:
9x = 2(108)
Dividing both sides by 9, we get the values of x to be:
x = 24 pounds
Therefore, the man must exert 24 pounds of force to lift the 108 pound tire.
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4x + 2y = 8 (1)
8x + 4y = -4y (2)
A) Two lines are parallel if they have the same gradient
- putting both equations into the gradient- intercept form ( y = mx + c where m is the gradient)
(1) 4x + 2y = 8
2y = 8 - 4x
y = -2x + 4
(2) 8x + 4y = -4y
<span> </span>8x = -4y - 4y
y =
y = -x
<span>Thus the gradient of the two equations are different and as such the two lines are not parallel
</span>
B) When two lines are perpendicular, the product of their gradient is -1
p = (-2) * (-1)
p = 2
<span> ∴ the two lines are not perpendicular either.</span>
Thus these lines are SKEWED LINES
8x + 4y = -4y (2)
A) Two lines are parallel if they have the same gradient
- putting both equations into the gradient- intercept form ( y = mx + c where m is the gradient)
(1) 4x + 2y = 8
2y = 8 - 4x
y = -2x + 4
(2) 8x + 4y = -4y
<span> </span>8x = -4y - 4y
y =
y = -x
<span>Thus the gradient of the two equations are different and as such the two lines are not parallel
</span>
B) When two lines are perpendicular, the product of their gradient is -1
p = (-2) * (-1)
p = 2
<span> ∴ the two lines are not perpendicular either.</span>
Thus these lines are SKEWED LINES
Answer:
0.70275
Step-by-step explanation:
Data provided in the question:
4e²ˣ⁻¹ -1 = 5
now solving for 'x'
⇒ 4e²ˣ⁻¹ = 5 + 1
or
⇒ 4e²ˣ⁻¹ = 6
or
⇒
or
⇒
now,
taking natural log both sides, we get
⇒ 2x - 1 =
also,
we know
⇒
thus,
⇒ 2x - 1 = ln(3) - ln(2)
or
⇒ 2x - 1 = 1.0986 - 0.6931
or
⇒ 2x - 1 = 0.4055
or
⇒ 2x = 0.4055 + 1
or
⇒ 2x = 1.4055
or
⇒ x = 0.70275