Try the following word problem using GRASP strategy

Mathematics

1 answer:

andrew11 [14]3 years ago

3 0

Answer:

Step-by-step explanation:

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Find the exact value of sin2 theta given sin theta =5/13, 90°<theta <180°

Zepler [3.9K]

Now, we know that 90°< θ <180°, that simply means the angle θ is in the II quadrant, where sine is positive and cosine is negative.

$\bf sin(\theta )=\cfrac{\stackrel{opposite}{5}}{\stackrel{hypotenuse}{13}}\impliedby \textit{now let's find the \underline{adjacent side}}
\\\\\\
\textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}$

$\bf \pm\sqrt{13^2-5^2}=a\implies \pm\sqrt{144}=a\implies \pm 12 =a \implies \stackrel{II~quadrant}{-12=a}
\\\\\\
therefore \qquad cos(\theta )=\cfrac{\stackrel{adjacent}{-12}}{\stackrel{hypotenuse}{13}}
\\\\
-------------------------------\\\\
sin(2\theta )\implies 2sin(\theta )cos(\theta )\implies 2\left(\frac{5}{13} \right)\left( \frac{-12}{13} \right)\implies -\cfrac{120}{169}$

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4 years ago

Hong needs to memorize words on a vocabulary list for Russian class. He has 14 words to memorize, and he is one-half done. How m

GREYUIT [131]

Step-by-step explanation:

He has done one half = ½

Finding ½ of 14

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Hence, Hong has memorized 7 words

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3 years ago

Use the following function rule to find f(9).<br> f(x) = x + 8<br> f(9) =

Studentka2010 [4]

Answer:

Step-by-step explanation:

f(x) = x + 8

f(9) = 9 + 8

= 17

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2 years ago

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alexgriva [62]

Answer:

y = 4x

Step-by-step explanation:

When two lines are parallel, their slopes are equal. The slope in this equation is 4. Therefore, any line with slope 4 will suffice.

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3 years ago

a man sells an article at a gain of 15%. if it was sold for rupees 600 he would have gained 20%. find the selling price of the a

DanielleElmas [232]

First, you multiply 600 and .20 to find 20% of 600 rupees, which is 120 rupees. Second, you subtract the 20%, (120 rupees) from 600 rupees, which is 480 rupees. After that, you have the original selling price of 480 rupees that the man purchased the article for, but the question is stating that he gained 15% of the original sales price. So, you multiply 480 and .15 to find 15% of 480 rupees, which is 72. However, he GAINED more money than what he payed for the article so you add 72 rupees to 480 rupees to get 552 rupees. In conclusion, the man sells the article for 552 rupees.

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