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Kazeer [188]
3 years ago
9

If r = 24.9 and s = 18.9, find S. Round to the nearest tenth. S = 37.2° S = 38.2° S = 39.2° S = 36.2°

Mathematics
1 answer:
snow_lady [41]3 years ago
6 0

\boxed{S=37.2^{\circ}}

<h2>Explanation:</h2>

Below has been attached a diagram with the meaning of this problem. So we have a right triangle whose <em>Opposite side (s) </em>measures 18.9 and whose <em>Adjacent side (r) </em>measures 24.9. So, these two sides are related in the following form:

tan(S)=\frac{Opposite \ side}{Adjacent \ side}=\frac{s}{r} \\ \\ tan(S)=\frac{18.9}{24.9} \\ \\ tan(S)=0.76 \\ \\ S=arctan(0.76) \\ \\ S=37.23^{\circ} \\ \\ Rounding \ off: \\ \\ \boxed{S=37.2^{\circ}}

<h2>Learn more:</h2>

Angles in triangles: brainly.com/question/4400594

#LearnWithBrainly

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The vendor has to sell 88 gingerbread houses to earn a profit of $665.60 and there is no chance that the vendor will earn $1500.

Given an equation showing profits of A Christmas vendor as

P=-0.1g^{2}+30g-1200.

We have to find the number of gingerbread houses that the vendor needs to sell in order to earn profit of $665.60 and $1500.

To find the number of gingerbread houses we have to put P=665.60 in the equation given which shows the profit earned by vendor.

665.60=-0.1g^{2}+30g-1200

0.1g^{2}-30g+1200+665.60=0

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Divide the above equation by 0.1.

g^{2}-300g+18656=0

Solving for g we get,

g=[300±\sqrt{(300)^{2}-4*1*18656 }]/2*1

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g=[300±\sqrt{15376}]/2

g=(300±124)/2

g=(300+124)/2       , g=(300-124)/2

g=424/2,  g=176/2

g=212,88

Because 212 is much greater than 88 so vendor prefers to choose selling of 88 gingerbread houses.

Put the value of P=1500 in equation P=-0.1g^{2}+30g-1200.

-0.1g^{2}+30g-1200=1500

0.1g^{2}-30g+1500+1200=0

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Dividing equation by 0.1.

g^{2}-300g+27000=0

Solving the equation for finding value of g.

g=[300±\sqrt{300^{2} -4*1*27000}]/2*1

=[300±\sqrt{90000-108000}] /2

=[300±\sqrt{-18000}]/2

Because \sqrt{-18000} comes out with an imaginary number so it cannot be solved for the number of gingerbread houses.

Hence the vendor has to sell 88 gingerbread houses to earn a profit of $665.60 and there is no chance that the vendor will earn $1500.

Learn more about equation at brainly.com/question/2972832

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