Find an equation for the tangent line of y = e 2 x that is parallel to the linear equation y = 7 x + 13 . Provide your answer in slope–intercept form of a linear equation, y = m x + b , where m is the slope and b is the y - intercept. Express m and b as exact numbers.

Step-by-step explanation:

We are asked to find equation of tangent line of function that is parallel to the linear equation .

First of all, we will find the derivative of given function applying chain rule as:

Since derivative represents slope or rate of change, so we will equate derivative to slope of line   and solve for x as:

Now, we will substitute in equation to find value of y as:

Applying log property , we will get:

Now, we will substitute , and in point slope form as:

Therefore, the equation of the tangent line would be .

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation:

his first public project he is asked to create a small scale drawing. the garden is a right triangle with base 25m and height 30m. are you trying to solve for the last side/hypotenuse? the irrational form of the answer would be 5\sqrt{61}