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Wittaler [7]
3 years ago
8

The resultant of two forces acting at a point at right angles to each other is 32 pounds. If the horizontal force is 19 pounds,

what is the other force to the nearest pound?
A. 26 lb.
B. 30 lb.
C. 37 lb.
D. 50 lb.
Mathematics
2 answers:
svetoff [14.1K]3 years ago
7 0
The answer is C. Hope this helps you
Assoli18 [71]3 years ago
3 0

Answer:

<h2>A. 26 lb.</h2>

Step-by-step explanation:

The resultant force of a system is defined as

F_{R}=\sqrt{F_{x}^{2}+F_{y}^{2}}

Where

F_{R}=32

F_{x}=19

Replacing these values, we have

32=\sqrt{(19)^{2}+F_{y}^{2}}\\32^{2}=361+ F_{y}^{2}\\ F_{y}^{2}=1024-361\\ F_{y}=\sqrt{663} \approx 26lb

Therefore, the right answer is A. 26 lb.

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In this question ,it is given that

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find an equation in the form y=ax^2+bx+c for the parabola passing through the points. (2,28),(4,116),(-3,88)
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<h3>Answer:</h3>

y = 8x² -4x +4

<h3>Explanation:</h3>

I find it quick and easy to let a graphing calculator do quadratic regression on the given points. It gives the coefficients of the equation directly. (See attached.)

_____

If you want to do this "by hand," you can substitute each of the x and y value pairs into the equation to get three linear equations in a, b, and c. These are generally easy to solve, as the "c" variable can be eliminated right away.

<em>For x = 2</em>

... 28 = a·2² +b·2 +c = 4a +2b +c

<em>For x = 4</em>

... 116 = a·4² +4b +c = 16a +4b +c

<em>For x = -3</em>

... 88 = a·(-3)² +b·(-3) +c = 9a -3b +c

Subtracting the first and third equations from the second, we have ...

... (16a +4b +c) -(4a +2b +c) = (116) -(28) ⇒ 12a +2b = 88

... (16a +4b +c) -(9a -3b +c) = (116) -(88) ⇒ 7a +7b = 28

Dividing the first of these reduced equations by 2, and the second by 7, we have ...

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We choose the first of the original equations to find c:

... c = 28 -4a -2b = 28 -4·8 -2(-4)

... = 28 -32 +8 = 4

With (a, b, c) = (8, -4, 4), the equation of the parabola is ...

... y = 8x² -4x +4

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