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3 years ago

13

Which statement BEST explains why the slope of each line segment formed by the hypotenuse of each triangle is the same?

1 answer:

Shkiper50 [21]3 years ago

6 0

Answer:

A

Step-by-step explanation:

Two triangles can be similar if their leg lengths are in proportion with each other, regardless of size. Since the triangles are the same in different sizes, they are similar. The hypotenuse of the triangles isn't the same, but the angles are the same, so the hypotenuse will still follow the same line.

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3 years ago

The mosquito population is a function of rainfall, and can be approximated by the formula N(x)=−x3+45x2+1000 where x is the numb

KiRa [710]

Answer:

Therefore the population will be maximum when x=30 inches.

Step-by-step explanation:

Given that, the mosquito population is a function of rainfall and can be approximated by the formula

$N(x)= -x^3+45x^2+1000$

where x is the number of inches of rainfall.

$N(x)= -x^3+45x^2+1000$

Differentiating with respect to x

$N'(x)= -3x^2+90x$

Again differentiating with respect to x

$N''(x)=-6x+90$

Now we set N'(x)=0

$-3x^2+90x=0$

$\Rightarrow -3x(x-30)=0$

$\Rightarrow x=0,30$

$N''(0)=-6.0+90=90>0$

$N''(30)=-6.30+90=-90$

Since at x=30, N''(x)<0, So at x=30, N(x) has maximum value.

Therefore the population will be maximum when x=30 inches.

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