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Nuetrik [128]
3 years ago
8

Frank has devised a formula for his catering business that calculates the number of meatballs he needs to prepare. The formula i

s m=ra+2c, where c= number of children;m = meatballs; a = number of adults. How many meatballs are required for a party of 25 adults and 5 children?
Mathematics
1 answer:
Aleonysh [2.5K]3 years ago
4 0
<span>m = 4a + 2c

a = 25; c = 5

Replace a with 25. Replace c with 5.
Then evaluate the expression.

m = 4 * 25 + 2 * 5

m = 100 + 10

m = 110

Answer: 110 meatballs are needed.</span>
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If you're using the app, try seeing this answer through your browser:  brainly.com/question/2862279

_______________


Simplify the trigonometric expression.

Call the expression E:

\mathsf{E=\dfrac{sin\,\theta}{\sqrt{1-sin^2\,\theta}}\qquad\qquad(but~~1-sin^2\,\theta=cos^2\,\theta)}\\\\\\&#10;\mathsf{E=\dfrac{sin\,\theta}{\sqrt{cos^2\,\theta}}}\\\\\\&#10;\mathsf{E=\dfrac{sin\,\theta}{\left|cos\,\theta\right|}}}


\mathsf{E}=\left\{\!\begin{array}{rl}\mathsf{\dfrac{sin\,\theta}{cos\,\theta}\,,}&\mathsf{\quad if~~cos\,\theta>0}\\\\\mathsf{\dfrac{sin\,\theta}{-\,cos\,\theta}\,,}&\mathsf{\quad if~~cos\,\theta


So basically E is equivalent to \pm\,\mathsf{tan\,\theta}, where the sign depends on which quadrant \theta lies. Shortly,

\mathsf{\dfrac{sin\,\theta}{\sqrt{1-sin^2\,\theta}}}=\left\{\!&#10;\begin{array}{rl}&#10;\mathsf{tan\,\theta,}&\mathsf{\quad if~\theta~lies~either~in~the~1^{st}~or~the~4^{th}~quadrant}\\\\&#10;\mathsf{-\,tan\,\theta,}&\mathsf{\quad if~\theta~lies~either~in~the~2^{nd}~or~the~3^{rd}~quadrant}&#10;\end{array}


I hope this helps. =)


Tags:  <em>simplify trigonometric trig expression sine cosine tangent sin cos tan absolute value modulus trigonometry</em>

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