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2 years ago

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Out of the 1,480 students in Gila Monster High School, 896 are girls. A total of 373 of the students made the honor roll. The nu

mber of girls who appeared on the honor roll was 5 less than twice the number of boys.
How many girls are in the honor roll

How many boys are in the honor roll

1 answer:

Alborosie2 years ago

5 0

Answer:

There are 126 boys on the honor roll and 247 girls on the honor roll.

Step-by-step explanation:

Out of the 1,480 students in Gila Monster High School, a total of 373 of the students made the honor roll.

Let the number of girls that made the honor roll be g.

Let the number of boys that made the honor roll be b.

This means that:

b + g = 373_________________(1)

The number of girls who appeared on the honor roll was 5 less than twice the number of boys.

This means that:

g = 2b - 5___________________(2)

Let us insert (2) in (1):

b + (2b - 5) = 373

=> b + 2b - 5 = 373

3b = 373 + 5

3b = 378

=> b = 378 / 3 = 126

From (1):

b + g = 373

=> 126 + g = 373

g = 373 - 126

g = 247 girls

Therefore, there are 126 boys on the honor roll and 247 girls on the honor roll.

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Next , we find the magnitude of derivative of the position vector

$|| \boldsymbol{r}'(t)}||=\sqrt{(-2\sin \left(2t\right))^2+(2\cos \left(2t\right))^2} \\|| \boldsymbol{r}'(t)}||=\sqrt{2^2\sin ^2\left(2t\right)+2^2\cos ^2\left(2t\right)}\\|| \boldsymbol{r}'(t)}||=\sqrt{4\left(\sin ^2\left(2t\right)+\cos ^2\left(2t\right)\right)}\\|| \boldsymbol{r}'(t)}||=\sqrt{4}\sqrt{\sin ^2\left(2t\right)+\cos ^2\left(2t\right)}\\\\\mathrm{Use\:the\:following\:identity}:\quad \cos ^2\left(x\right)+\sin ^2\left(x\right)=1\\\\|| \boldsymbol{r}'(t)}||=2\sqrt{1}=2$

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