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butalik [34]
3 years ago
9

The potential energy, P, in a spring is represented using the formula P = 1/2kx2. Lupe uses an equivalent equation, which is sol

ved for k, to determine the answers to her homework. Which equation should she use?
k = 2Px2
k = 1/2Px2
k = 2p/x^2
k = p/2x^2
Mathematics
2 answers:
sukhopar [10]3 years ago
7 0

Answer:

k=\frac{2P}{x^2}


Step-by-step explanation:

The formula is P=\frac{1}{2}kx^2

<em>We need to solve for k, so we can perform the steps shown below:</em>

P=\frac{1}{2}kx^2\\P=\frac{kx^2}{2}\\2P=kx^2\\\frac{2P}{x^2}=k


Hence, the third answer choice is correct.

katovenus [111]3 years ago
3 0
We need to find a way to get k by itself so lets get it by itself.
For convenience I will switch the equal sign.
1/2kx^2 = p
Multiply both sides by 2
kx^2 = 2p
divide by x^2
k = 2p/x^2

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<em />

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Step-by-step explanation:

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Which number produces a rational number when multiplied by 0.5?
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7 0
3 years ago
A tunnel is built in form of a parabola. The width at the base of tunnel is 7 m. On
anastassius [24]

Given:

The width at the base of parabolic tunnel is 7 m.

The ceiling 3 m from each end of the base there are light fixtures.

The height to light fixtures is 4 m.

To find:

Whether it is possible a trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel.

Solution:

The width at the base of tunnel is 7 m.

Let the graph of the parabola intersect the x-axis at x=0 and x=7. It means x and (x-7) are the factors of the height function.

The function of height is:

h(x)=ax(x-7)             ...(i)

Where, a is a constant.

The ceiling 3 m from each end of the base there are light fixtures and the height to light fixtures is 4 m. It means the graph of height function passes through the point (3,4).

Putting x=3 and h(x)=4 in (i), we get

4=a(3)((3)-7)

4=a(3)(-4)

\dfrac{4}{(3)(-4)}=a

-\dfrac{1}{3}=a

Putting a=-\dfrac{1}{3}, we get

h(x)=-\dfrac{1}{3}x(x-7)              ...(ii)

The center of the parabola is the midpoint of 0 and 7, i.e., 3.

The width of the truck is 4 m. If is passes through the center then the truck must m 2 m on the left side of the center and 2 m on the right side of the center.

2 m on the left side of the center is x=1.5.

A trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is possible if h(1.5) is greater than 2.8.

Putting x=1.5 in (ii), we get

h(1.5)=-\dfrac{1}{3}(1.5)(1.5-7)

h(1.5)=-(0.5)(-5.5)

h(1.5)=2.75

It is clear that h(1.5)<2.8, therefore the trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is not possible.

4 0
3 years ago
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