Three times a number, x, increased by four is equal to five times the number, x. Which equation can be used to solve for x?
2 answers:
Answer:
X = 2
Step-by-step explanation:
From the question we can gather some pretty important information. For starters, "three <u>times</u> a number x" would give us 3x. Secondly, "<u>increased</u> by 4" would give us +4. Lastly, "<u>equal</u> to five <u>times</u> x" would be = 5x. If we put this all together we have the following Algebraic Equation.
Now we can start solving the equation.
So we can see that the value of x in this equation is 2.
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Answer:
138.06 lb N86.1°E
Step-by-step explanation:
There are several ways you can work this. One of the most straightforward is to resolve each vector into its north and east components, add those, and then covert the result back to magnitude and direction.
A diagram can help immensely.
We note that S78°E is the same as E12°S. Since we're used to seeing the coordinate system with the +x axis aligned with east, it can be convenient to think of the first force as 100 lb at -12°.
The angle of the second force is N53°E, which can be expressed as E37°N. Then in x-y coordinates, this force is 50 lb at +37°.
The components of the sum are the sum of the components:
R = F1 +F2 = (100cos(-12°) +50cos(37°), 100sin(-12°) +50sin(37°))
= (137.747, 9.300)
The the magnitude of the resultant is computed using the Pythagorean theorem:
||R|| = √(137.747² +9.300²) ≈ 138.06
and the angle is computed using the arctangent function. Here, our diagram tells us the angle is in the first quadrant, so is positive (relative to +x, or East).
∠R = arctan(9.300/137.747) ≈ 3.9°
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We want to express the answer in terms similar to the way the given forces are expressed, so we want the angle relative to north. The resultant is then described by ...
R = 138.06 lb at N86.1°E
