The work done (in foot-pounds) in stretching the spring from its natural length to 0.7 feet beyond its natural length is 1.23 foot-pound
<h3>Data obtained from the question</h3>
From the question given above, the following data were obtained:
- Force (F) = 3 pounds
- Extension (e) = 0.6 feet
- Work done (Wd) =?
<h3>How to determine the spring constant</h3>
- Force (F) = 3 pounds
- Extension (e) = 0.6 feet
- Spring constant (K) =?
F = Ke
Divide both sides by e
K = F/ e
K = 3 / 0.6
K = 5 pound/foot
Thus, the spring constant of the spring is 5 pound/foot
<h3>How to determine the work done</h3>
- Spring constant (K) = 5 pound/foot
- Extention (e) = 0.7 feet
- Work done (Wd) =?
Wd = ½Ke²
Wd = ½ × 5 × 0.7²
Wd = 2.5 × 0.49
Wd = 1.23 foot-pound
Therefore, the work done in stretching the spring 0.7 feet is 1.23 foot-pound
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Answer:
yes
Step-by-step explanation:
the explanation is that a rhombus is a parallelogram in which all sides are equal. Their diagonals bisect each other at right angles.
Answer:
k = 9
length of chord = 2/3
Step-by-step explanation:
Equation of parabola: 
<u />
<u>Part 1</u>
If the curve passes through point
, this means that when
, 
Substitute these values into the equation and solve for
:


Apply the exponent rule
:



<u>Part 2</u>
- The chord of a parabola is a line segment whose endpoints are points on the parabola.
We are told that one end of the chord is at
and that the chord is horizontal. Therefore, the y-coordinate of the other end of the chord will also be 1. Substitute y = 1 into the equation for the parabola and solve for x:





Therefore, the endpoints of the horizontal chord are: (0, 1) and (2/3, 1)
To calculate the length of the chord, find the difference between the x-coordinates:

**Please see attached diagram for drawn graph. Chord is in red**
The temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C
From Newton's law of cooling, we have that

Where





From the question,


∴ 

Therefore, the equation
becomes

Also, from the question
After 1 hour, the temperature of the ice-cream base has decreased to 58°C.
That is,
At time
, 
Then, we can write that

Then, we get

Now, solve for 
First collect like terms


Then,


Now, take the natural log of both sides


This is the value of the constant 
Now, for the temperature of the ice cream 2 hours after it was placed in the freezer, that is, at 
From

Then






Hence, the temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C
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