Answer:
The total mechanical energy is 0.712 J.
Step-by-step explanation:
A blue 573 g mobile is moving on a metal rail. If on the mobile, the spring exerts a force to the right of modulus 0.85 N and in the indicated position the kinetic energy of the mobile-spring system is 0.47 J and its elastic potential energy is 0.242 J. Determine the mechanical energy of the system mobile-spring in the position shown as indicated in the figure.
The total mechanical energy is given by the sum of the kinetic energy and the potential energy.
Kinetic energy = 0.47 J
Potential energy = 0.242 J
The total mechanical energy is
T = 0.47 + 0.242 = 0.712 J
Answer:
Step-by-step explanation:
Let's identify what we are looking for in terms of variables. Sandwiches are s and coffee is c. Casey buys 3 sandwiches, which is represented then by 3s, and 5 cups of coffee, which is represented by 5c. Those all put together on one bill comes to 26. So Casey's equation for his purchases is 3s + 5c = 26. Eric buys 4 sandwiches, 4s, and 2 cups of coffee, 2c, and his total purchase was 23. Eric's equation for his purchases then is 4s + 2c = 23. In order to solve for c, the cost of a cup of coffee, we need to multiply both of those bolded equations by some factor to eliminate the s's. The coefficients on the s terms are 4 and 3. 4 and 3 both go into 12 evenly, so we will multiply the first bolded equation by 4 and the second one by -3 so the s terms cancel out. 4[3s + 5c = 26] means that 12s + 20c = 104. Multiplying the second bolded equation by -3: -3[4s + 2c = 23] means that -12s - 6c = -69. The s terms cancel because 12s - 12s = 0s. We are left with a system of equations that just contain one unknown now, which is c, what we are looking to solve for. 20c = 104 and -6c = -69. Adding those together by the method of elimination (which is what we've been doing all this time), 14c = 35. That means that c = 2.5 and a cup of coffee is $2.50. There you go!
A = 1/2 x bh
A = 1/2 x 5 x 12
A = 6 x 5
A = 30m
Answer:
a rectangle is twice as long as it is wide . if both its dimensions are increased 4 m , its area is increaed by 88 m squared make a sketch and find its original dimensions of the original rectangle
Step-by-step explanation:
Let l = the original length of the original rectangle
Let w = the original width of the original rectangle
From the description of the problem, we can construct the following two equations
l=2*w (Equation #1)
(l+4)*(w+4)=l*w+88 (Equation #2)
Substitute equation #1 into equation #2
(2w+4)*(w+4)=(2w*w)+88
2w^2+4w+8w+16=2w^2+88
collect like terms on the same side of the equation
2w^2+2w^2 +12w+16-88=0
4w^2+12w-72=0
Since 4 is afactor of each term, divide both sides of the equation by 4
w^2+3w-18=0
The quadratic equation can be factored into (w+6)*(w-3)=0
Therefore w=-6 or w=3
w=-6 can be rejected because the length of a rectangle can't be negative so
w=3 and from equation #1 l=2*w=2*3=6
I hope that this helps. The difficult part of the problem probably was to construct equation #1 and to factor the equation after performing all of the arithmetic operations.
Given :
- The length of a rectangle is 4m more than the width.
- The area of the rectangle is 45m²
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To Find :
- The length and width of the rectangle.
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Solution :
We know that,
So,
Let's assume the length of the rectangle as x and the width will be (x – 4).
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Now, Substituting the given values in the formula :
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Since, The length can't be negative, so the length will be 9 which is positive.
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