2 years ago

(Secx/sinx)-(sinx/cosx)

1 answer:

6 0

$\dfrac{\sec x}{\sin x}-\dfrac{\sinx }{\cos x}=\dfrac{\sec x\cos x}{\sin x\cos x}-\dfrac{\sin^2x}{\sin x\cos x}=\dfrac{1-\sin^2x}{\sin x\cos x}=\dfrac{\cos^2x}{\sin x\cos x}=\dfrac{\cos x}{\sin x}=\cot x$

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the length of a rectangle is five feet less than its width. If the area of the rectangle is 84 square feet, find its dimensions

KIM [24]

Let
x---------> the length of the rectangle
y--------> the width of the rectangle

we know that
A=84 ft²
[area of rectangle]=x*y-----> 84=x*y-----> equation 1
x=y-5------> equation 2
substitute 2 in 1
84=[y-5]*y-----> 84=y²-5y---------> y²-5y-84=0

using a graph tool-----> to resolve the second order equation
see the attached figure

the solution is
y=12
x=y-5-----> x=12-5-----> x=7

the answer is
the length of the rectangle is 7 ft
the width of the rectangle is 12 ft