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crimeas [40]
2 years ago
13

There is a elephant shaped weather vane at the top of a corn dryer tower that is 45 m high. If the weather vane weighs 190 N, wh

at is the Potential Energy that the wether vane has?
Mathematics
1 answer:
egoroff_w [7]2 years ago
4 0

Answer:

Potential Energy = 8550 Joules

Step-by-step explanation:

The potential energy of the body is the energy possessed by it due to its position therefore:

Potential energy = mgh

m = mass of the body measured in kg

g= acceleration due to gravity

h= height or distance measured in meters

But in the question asked we are not given mass but weight so

w= mg   measured in newtons

We have

w= 190 N

h= 45m

PE= mgh

PE  = w h= 190 * 45 =  8550 J

The unit of energy is Joule.

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Step-by-step explanation:

It has only 1 line of symmetry. The line is a vertical line that passes through the top vertex.

Answer: 1

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1 year ago
Solve y" + y = tet, y(0) = 0, y'(0) = 0 using Laplace transforms.
irina1246 [14]

Answer:

The solution of the diferential equation is:

y(t)=\frac{1}{2}cos(t)- \frac{1}{2}e^{t}+\frac{t}{2} e^{t}

Step-by-step explanation:

Given y" + y = te^{t}; y(0) = 0 ; y'(0) = 0

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ℒ[y" + y]=ℒ[te^{t}]

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So, the transformation is equal to:

s²·Y(s)+Y(s)=\frac{1}{(s-1)^{2}}

(s²+1)·Y(s)=\frac{1}{(s-1)^{2}}

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To be able to separate in terms, we use the partial fraction method:

\frac{1}{(s^{2}+1)(s-1)^{2}}=\frac{As+B}{s^{2}+1} +\frac{C}{s-1}+\frac{D}{(s-1)^2}

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With the previous equation we can make an equation system of 4 variables.

The system is given by:

A+C=0

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The solution of the system is:

A=1/2 ; B=0 ; C=-1/2 ; D=1/2

Therefore, Y(s) is equal to:

Y(s)=\frac{s}{2(s^{2} +1)} -\frac{1}{2(s-1)} +\frac{1}{2(s-1)^{2}}

By using the inverse of the Laplace transform:

ℒ⁻¹[Y(s)]=ℒ⁻¹[\frac{s}{2(s^{2} +1)}]-ℒ⁻¹[\frac{1}{2(s-1)}]+ℒ⁻¹[\frac{1}{2(s-1)^{2}}]

y(t)=\frac{1}{2}cos(t)- \frac{1}{2}e^{t}+\frac{t}{2} e^{t}

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