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RUDIKE [14]
3 years ago
10

Write an equation to model this situation. Then use your equation to solve. Jack has saved $16.50 to spend on the fair ride tick

ets. Each ticket costs $0.75. How many tickets can jack afford?
Mathematics
1 answer:
Tomtit [17]3 years ago
3 0

Answer:

22.

Step-by-step explanation:

"Plug and chug" .75 multiplied by different numbers, up until you get to 16.5 as an answer. 22 is what you multiply it by, so that is correct.

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Forces of 9 lbs and 13 lbs act at a 38º angle to each other. Find the magnitude of the resultant force and the angle that the re
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Answer: R=20.84\ lb\quad 22.57^{\circ},15.43^{\circ}

Step-by-step explanation:

Given

Two forces of 9 and 13 lbs acts 38^{\circ} angle to each other

The resultant of the two forces is given by

\Rightarrow R=\sqrt{a^2+b^2+2ab\cos \theta}

Insert the values

\Rightarrow R=\sqrt{9^2+13^2+2(9)(13)\cos 38^{\circ}}\\\Rightarrow R=\sqrt{81+169+184.394}\\\Rightarrow R=\sqrt{434.394}\\\Rightarrow R=20.84\ lb

Resultant makes an angle of

\Rightarrow \alpha=\tan^{-1}\left( \dfrac{b\sin \theta}{a+b\cos \theta}\right)\\\\\text{Considering 9 lb force along the x-axis}\\\\\Rightarrow \alpha =\tan^{-1}\left( \dfrac{13\sin 38^{\circ}}{9+13\cos 38^{\circ}}\right)\\\\\Rightarrow \alpha =\tan^{-1}(\dfrac{8}{19.244})\\\\\Rightarrow \alpha=22.57^{\circ}

So, the resultant makes an angle of 22.57^{\circ} with 9 lb force

Angle made with 13 lb force is 38^{\circ}-22.57^{\circ}=15.43^{\circ}

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Check the picture below.

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