$f(x)=\frac{1}{\sqrt{x} }\\f'(x)=-\frac{1}{2} x^{-\frac{3}{2}}\\\\f'(4)=-\frac{1}{2} 4^{-\frac{3}{2} }=-\frac{1}{2} \frac{1}{4^\frac{3}{2} } \\=-\frac{1}{2} *\frac{1}{8}=-\frac{1}{16} \\when x=4\\y=f(x)=\frac{1}{\sqrt{4} } =\frac{1}{2} \\\\eq.~ of ~tangent ~line~is\\y=-\frac{1}{2} -\frac{1}{16} (x-4)$

3 0

3 years ago

Choose a variable to represent one of the unknowns. Express the remaining unknowns in terms of the variable you chose in step 1.

jok3333 [9.3K]

Let's just choose "x" as our variable for the length of a side of the triangle.

Two sides of a triangle are equal in length and double the length of the shortest side.

A triangle has 3 sides. Make the smallest side x then the two equal sides that are double the smallest side are both equal to 2x

The perimeter of the triangle is 35 inches. Perimeter is the sum of all sides.

x + 2x + 2x = 35

5x = 35

x = 7

So the smallest side is 7, and the other two sides are 14.

6 0

2 years ago