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3 years ago

PLEASE HELP ME!!!!!!!

Mathematics

1 answer:

Anastasy [175]3 years ago

7 0

Answer:

:))

Step-by-step explanation:

Collect like terms, keeping the integer rules in mind

5. 5a + 9b - 3a + 2b + 4a

5a + 4a - 3a + 9b + 2b (REARRANGE, if you find it to help)

6a + 11b

6. 7m + 3n - 8m + 2n + 10m

7m + 10m - 8m + 3n + 2n

9m + 5n

10. 10m²n + 5mn + 9m²n - 2mn

10m²n + 9m²n + 5mn - 2mn

19m²n + 3mn

Try to do the rest on your own :)

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Two forces with magnitudes of 150 and 100 pounds act on an object at angles of 30° and 120°, respectively. Find the direction an

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<h2>Answer:</h2>

$Magnitude=180.27 \ lbf \\ \\ Direction=63.69 \ degrees$

<h2>Step-by-step explanation:</h2>

We have two forces as follows:

<u>First force:</u>

Magnitude: 150 pounds

Angle: 30°

<u>First force:</u>

Magnitude: 100 pounds

Angle: 120°

So the components can be found as follows:

$F_{1x}=150cos(30)=129.90 \ lbf\\F_{1y}=150sin(30) = 75 \ lbf \\ \\ F_{2x}=100cos(120)=-50 \ lbf\\F_{2y}=100sin(120) = 86.60 \ lbf$

So the components of the resultant force can be found by adding each component of the individual forces as follows:

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$Magnitude \rightarrow R=\sqrt{R_{x}^2+R_{y}^2}=\sqrt{79.90^2+161.6^2}=180.27 \ lbf \\ \\ Direction \rightarrow \theta=tan^{-1}(\frac{R_{y}}{R_{x}})=tan^{-1}(\frac{161.6}{79.90})=63.69 \ degrees$

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