What is the value of 1/2^-2x^-3y^5 for x=2 and y=-4?
1 answer:
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9514 1404 393
Answer:
- resultant force: 93.946∠-10.62° N
- line of action: 17.314x +92.337y = 809.433
Step-by-step explanation:
We can use the notation a∠b to represent the (x, y) components (a·cos(b), a·sin(b)), where angle b is measured CCW from the +x direction. If we label the forces a, b, c, d clockwise from A, then we have ...
a = 80∠0° = (80, 0)
b = 60∠90° = (0, 60)
c = 90∠45° = (63.640, 63.640)
d = 150∠-110° = (-51.303, -140.954)
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If we label point A the origin, then the clockwise torque on point A is the sum of products of the force x-component and its y location, and its y-component and the negative of its x location.
T = (0, 0)·(80, 0) +(3, 0)·(0, 60) +(3, -8)·(63.640, 63.640) +(0, -8)·(-51.303, -140.954)
T = 809.433 . . . . n·m, the CW torque on point A
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The sum of forces is ...
F = a +b +c +d = (92.337, -17.314) = 93.946∠-10.62° . . . N
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This force, applied to the point of application, must generate the same torque as the given forces. That is ...
F·(y, -x) = 809.433
Then the equation of the line of action is ...
17.314x +92.337y = 809.433 . . . . . x and y in meters measured from A
Any point (x, y) on this line will serve as a point of application of the force. Unfortunately, this line of action does not pass through the rectangular plate. The attachment shows the point (D) on the line of action that is closest to point A.
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<em>Additional comment</em>
The resultant force could be decomposed into two forces acting <em>on the rectangular plate</em>. One could be of much larger magnitude, operating at the corner opposite point A. This force would provide the necessary torque. Another would be acting on point A, providing no torque, but with components such that the resultant has the correct magnitude and direction.
Answer:
0.3101001000......
0.410100100010000....
Step-by-step explanation:
To find irrational number between any two numbers, we first need to understand what a rational and irrational number is.
Rational number is any number that can be expressed in fraction of form . Since q can be 1, all numbers that terminate are rational numbers. Example: 1, 12.34, 123.66663
Irrational number on the other hand can't be expressed as a fraction and do not terminate. Also, there is no pattern in numbers i.e. there is no repetition in numbers after the decimal point.
For example: 3.44444..... can be expressed as rational number 3.45.
But 3.414114111.... is an irrational number as there no pattern observed. Also,it does not terminate.
We can find infinite number of irrational numbers in between two rational numbers.
<u>Irrational numbers in between 0.3 and 0.7:</u>
0.3101001000......
0.410100100010000....
0.51010010001.......
0.6101001000....
There are many others. We can choose any two as answers.