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solong [7]
3 years ago
9

a rectangle is 6 units "wide" and x -8 use long it has the same area of a triangle with a height of 7 units and a base of x minu

s 3 years what is the area of the rectangle

Mathematics
1 answer:
Mashcka [7]3 years ago
3 0

Answer:

  42 square units

Step-by-step explanation:

The area of the rectangle is the product of its length and width:

  area = 6(x -8)

The area of the triangle is half the product of its base and height:

  area = (1/2)(x-3)·7

These two areas are equal, so we have ...

  6(x -8) = (1/2)(x -3)(7)

  6x -48 = 3.5x -10.5 . . . . eliminate parentheses

  2.5x = 37.5 . . . . . . . . . . . add 48 -3.5x

  x = 15 . . . . . . . . . . . . . . . divide by 2.5

The area of the rectangle is ...

  area = 6(15 -8) = 42 . . . . square units.

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Write each expression as an algebraic​ (nontrigonometric) expression in​ u, u > 0.
max2010maxim [7]

Answer:

\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0

Step-by-step explanation:

We want to write the trignometric expression:

\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0

As an algebraic equation.

First, we can focus on the inner expression. Let θ equal the expression:

\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)

Take the secant of both sides:

\displaystyle \sec(\theta)=\frac{u}{10}

Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:

\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}

By substitutition:

\displaystyle= \sin(2\theta)

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=2\sin(\theta)\cos(\theta)

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\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)

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