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Law Incorporation [45]
3 years ago
13

Finding an Equation of a tangent Line in Exercise, find an equation of the tangent line to the graph of the function at the give

n point.
g(x) = e^x3 , (-1,1/e)
Mathematics
1 answer:
frutty [35]3 years ago
3 0

Answer:

y=\dfrac{3x}{e}+\dfrac{4}{e}

this is the equation of the tangent at point (-1,1/e)

Step-by-step explanation:

to find the tangent line we need to find the derivative of the function g(x).

g(x) =e^{x^3}

  • we know that \frac{d}{dx}(e^{f(x)})=e^{f(x)}f'(x)

g'(x) =e^{x^{3}}(3 x^{2})

g'(x) =3 x^{2} e^{x^{3}}

this the equation of the slope of the curve at any point x and it also the slope of the tangent at any point x. hence, g'(x) can be denoted as 'm'

to find the slope at (-1,1/e) we'll use the x-coordinate of the point i.e. x = -1

m =3 (-1)^{2} e^{(-1)^{3}}\\m =3e^{-1}\\m=\dfrac{3}{e}

using the equation of line:

(y-y_1)=m(x-x_1)

we'll find the equation of the tangent line.

here (x1,y1) =(-1,1/e), and m = 3/e

(y-\dfrac{1}{e})=\dfrac{3}{e}(x+1)\\y=\dfrac{3x}{e}+\dfrac{3}{e}+\dfrac{1}{e}\\

y=\dfrac{3x}{e}+\dfrac{4}{e}

this is the equation of the tangent at point (-1,1/e)

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List the angles in triangle QRS from smallest to largest.
schepotkina [342]

Answer:

angle R

Step-by-step explanation:

To solve this we will use cosine rule

Cosine rule

cos(A) = \frac{b^{2}+c^{2}-a^{2}}{2bc}

suppose,

q = 6.25

s = 11.04

r = 13.19

angleQ = cos^{-1}(\frac{13.19^{2}+11.04^{2}-6.52^{2}}{2(13.19)(11.04)})

            = 30.58

angleR = cos^{-1}(\frac{6.52^{2}+11.04^{2}-13.19^{2}}{2(6.52)(11.04)})

            = 93.82

angleS =  cos^{-1}(\frac{6.52^{2}+13.19^{2}-11.04^{2}}{2(6.52)(13.19)})

            = 56.63

4 0
3 years ago
I’m really stuck<br> Can. Someone help?
const2013 [10]

Answer:

-2\leq x < 8

Step-by-step explanation:

Notice that the leftmost endpoint, 2, has a closed circle, which means that it is included in the inequality. Also, the rightmost endpoint, 8, has an open circle, which means that is NOT included in the inequality.

Because the inequality only includes what is between the two numbers, you write the inequality as -2\leq x < 8 to show that -2 is included and 8 is not included.

8 0
1 year ago
Which sequence of transformations maps triangle PQR onto its image triangle P'Q'R'
erica [24]

Answer:

Reflect, Translate, Dilate

Step-by-step explanation:

1. Reflect across the y-axis

2. Translate the triangle (x + 1, y + 1)

3. Dilate PQR by: \frac{3}{2}

8 0
3 years ago
I will give brainliest
mars1129 [50]

Answer:

5^2 or 25

Step-by-step explanation:

5^6/5^4 = 5^2

4 0
3 years ago
Read 2 more answers
three distinct vertices of a cube are to be randomly chosen what is the probability that they will be the vertices of an equilat
jasenka [17]

The triangle formed by the vertices would be equilateral if the sides of the triangle coincide with the diagonals of the square face that defines the cube. See the attached sketch if that description is unclear.

Count the number of equilateral triangles that are possible. Such a triangle will always use up 3 vertices of the cube, and separate 1 vertex from the remaining 4. This means there are as many equilateral triangles as there are corners in the cube: 8.

Count the total number of triangles that can be made. From the 8 available vertices, we only need 3. If we fix 3 vertices, it doesn't matter in which order we connect them to make a triangle, so we count the number of combinations of 8 vertices taking 3 at a time, which is

\dbinom 83 = \dfrac{8!}{3!(8-3)!} = 56

Then the probability of forming an equilateral triangle is 8/56 = 1/7.

3 0
2 years ago
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