During an experiment conducted on the effort E to lift a load W when using a simple the following values were recorded.

………………………………………………………………………………………………
|Effort E| 20 | 24.8|30 | 35 | 45 |
……………………………………………………………………………………………
|Load W |100 | 200 |300 | 400| 600|
|…………………………………………………………………………………………
If E and W are connected by the law of the form E= aw+b, determine.

(a).The value of a and b .
(b).the value of E when W = 280N.

To determine the values of a and b in the equation E = aw + b, we will use the given data points and solve a system of equations.

(a). To find the values of a and b, we need to select two data points, substitute the values into the equation, and create a system of equations to solve. Let's choose two points, (20, 100) and (30, 300).

Using the first point (20, 100):
E = aw + b
100 = 20a + b -- Equation 1

Using the second point (30, 300):
E = aw + b
300 = 30a + b -- Equation 2

Now we have a system of two equations with two variables (a and b). We can solve this system to find the values of a and b.

To eliminate b from the equations, we can subtract Equation 1 from Equation 2:
(30a + b) - (20a + b) = 300 - 100
10a = 200
a = 200/10
a = 20

Substituting the value of a back into Equation 1:
100 = 20a + b
100 = 20(20) + b
100 = 400 + b
b = 100 - 400
b = -300

So, the values of a and b in the equation E = aw + b are a = 20 and b = -300.

(b). To find the value of E when W = 280N, we can simply substitute the given value of W into the equation and solve for E.

E = aw + b
E = 20(280) - 300
E = 5600 - 300
E = 5300

Therefore, when W = 280N, the value of E is 5300.