Find the surface area of the prism below. Please see the attachment and a. 108cm ^2 is incorrect. Thanks!

Mathematics

1 answer:

creativ13 [48]2 years ago

5 0

Answer: OPTION B

Step-by-step explanation:

To solve this problem you must add the areas of each rectangle that form the prism;

The area of a rectangle can be calculated with the formula:

$SA=length*width$

There are three pairs of equal rectangles, then you can find the surface area of 3 rectangles and multiply each one by 2, then you obtain that the surface area of the prism is:

$SA_{prism}=2(6cm*2cm)+2(3cm*6cm)+2(3cm*2cm)=72cm^{2}$

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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

fiasKO [112]

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

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