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4 years ago

Find an equation for a line that is normal to the graph of y=xe^x and goes through the origin

1 answer:

3 0

Y = xe^x
dy/dx(e^x x)=>use the product rule, d/dx(u v) = v*(du)/(dx)+u*(dv)/(dx), where u = e^x and v = x:
= e^x (d/dx(x))+x (d/dx(e^x))
y' = e^x x+ e^x
y'(0) = 1 => slope of the tangent
slope of the normal = -1
y - 0 = -1(x - 0)
y = -x => normal at origin

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What is the domain for the function sqrt(x+2)-2x

Oduvanchick [21]

$D:x+2\geq0\\
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3 years ago

Change 3/8 to a decimal using long divison

sveta [45]

Answer:

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Step-by-step explanation:

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3 years ago

Need help with this please.

sp2606 [1]

Answer:

$y = -\frac{3}{2} x + 4$

Step-by-step explanation:

First, let us find the gradient of AB:

Gradient of AB = $\frac{-1-3}{-1-5}$

= $\frac{2}{3}$

We also need to know that The product of gradients which are perpendicular to each other is -1. Using this idea, we can find the gradient of the perpendicular bisector:

(Gradient of perpendicular bisector)( $\frac{2}{3}$ ) = -1

Gradient of perpendicular bisector = $-\frac{3}{2}$

Now, we need to know at which coordinates the perpendicular bisector intersects AB. A perpendicular bisector bisects a line to two equal parts. Hence the coordinates of the intersection point is the midpoint of AB. Thus,

Coordinates of intersection = ( $\frac{-1 + 5}{2}$ , $\frac{-1 + 3}{2}$ )

= ( 2, 1 )

Now, we can construct our equation. The equation of a line can be formed using the formula $(y - y_{1}) = m(x - x_{1})$ where $m$ is the gradient and the line passes through $(x_{1} , y_{1} )$ . Hence by substituting the values, we get:

$(y - 1) = -\frac{3}{2} (x - 2)$

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$y = -\frac{3}{2} x + 4$

4 0

3 years ago

Simplify each sum or difference. State any restrictions on the variables.

maria [59]

Simplification of the equation $\frac{x}{3x+9}- \frac{8}{x^{2} +3x}$ is equal to (x² -24)/ 3x(x+3), restriction on the variables are x ≠0 , x≠ -3.

As given in the question,

Given equation $\frac{x}{3x+9}- \frac{8}{x^{2} +3x}$

Simplify the given equation,

x/ 3(x+3) - 8/x(x+3)

= (x² - 24) / 3x(x+3)

Restriction on the variables for the above equation is,

x≠ 0 , x≠ -3

Therefore, simplification of the equation $\frac{x}{3x+9}- \frac{8}{x^{2} +3x}$ is equal to (x² -24)/ 3x(x+3), restriction on the variables are x ≠0 , x≠ -3.

Learn more about variables here

brainly.com/question/17344045

#SPJ4

8 0

1 year ago

Find the zeros of the following polynomial p(x) = 3x³ + 9x² - 12x

alexira [117]

Answer:

x = - 4, x = 0, x = 1

Step-by-step explanation:

To find the zeros equate p(x) to zero, that is

3x³ + 9x² - 12x = 0 ← divide through by 3

x³ + 3x² - 4x = 0 ← factor out x from each term

x(x² + 3x - 4) = 0

x(x + 4)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x = 0

x + 4 = 0 ⇒ x = - 4

x - 1 = 0 ⇒ x = 1

8 0

3 years ago