By applying the concepts of differential and derivative, the differential for y = (1/x) · sin 2x and evaluated at x = π and dx = 0.25 is equal to 1/2π.
<h3>How to determine the differential of a one-variable function</h3>
Differentials represent the <em>instantaneous</em> change of a variable. As the given function has only one variable, the differential can be found by using <em>ordinary</em> derivatives. It follows:
dy = y'(x) · dx (1)
If we know that y = (1/x) · sin 2x, x = π and dx = 0.25, then the differential to be evaluated is:





By applying the concepts of differential and derivative, the differential for y = (1/x) · sin 2x and evaluated at x = π and dx = 0.25 is equal to 1/2π.
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Answer:
See explaination
Explanation:
We can describe Aspiration Effect as a phenomenon of providing an allowance for the release of air from the mold cavity during the metal pouring.
See the attached file for detailed solution of the given problem.
Answer and Explanation:
The coefficient of determination also called "goodness of fit" or R-squared(R²) is used in statistical measurements to understand the relationship between two variables such that changes in one variable affects the other. The level of relationship or the degree to which one affects the other is measured by 0 to 1 whereby 0 means no relationship at all and 1 means one totally affects the other while figures in between such 0.40 would mean one variable affects 40% of the other variable.
In making a decision as an engineer while using the coefficient of determination, one would try to understand the relationship between variables under consideration and make decisions based on figures obtained from calculating coefficient of determination. In other words when there is a 0 coefficient then there is no relationship between variables and an engineer would make his decisions with this in mind and vice versa.
Answer:
(a) T = W/2(1-tanθ) (b) 39.81°
Explanation:
(a) The equation for tension (T) can be derived by considering the summation of moment in the clockwise direction. Thus:
Summation of moment in clockwise direction is equivalent to zero. Therefore,
T*l*(sinθ) + W*(l/2)*cosθ - T*l*cosθ = 0
T*l*(cosθ - sinθ) = W*(l/2)*cosθ
T = W*cosθ/2(cosθ - sinθ)
Dividing both the numerator and denominator by cosθ, we have:
T = [W*cosθ/cosθ]/2[(cosθ - sinθ)/cosθ] = W/2(1-tanθ)
(b) If T = 3W, then:
3W = W/2(1-tanθ),
Further simplification and rearrangement lead to:
1 - tanθ = 1/6
tanθ = 1 - (1/6) = 5/6
θ = tan^(-1) 5/6 = 39.81°