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3 years ago

Write the equation in slope-intercept form of the line that has a slope of 2 and contains

Mathematics

1 answer:

mina [271]3 years ago

8 0

Equation in slope-intercept form is y = 2x - 6

Step-by-step explanation:

Step 1: Given slope of the line, m = 2. Form an equation y = mx + b

⇒ y = 2x + b ---- (1)

Step 2: The line passes through the point (4,2). So it will satisfy the equation. Find b by substituting x = 4 and y = 2.

⇒ 2 = 2 × 4 + b = 8 + b

⇒ b = -6

Step 3: Form the slope-intercept equation.

⇒ y = 2x - 6

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Complete the missing value in the solution to the equa<br> 6x + 1 = y + 2x<br> 3,<br> Blank 1:

nadya68 [22]

Answer:

y = 4x +1

Step-by-step explanation:

6x + 1 = y + 2x

First you need to solve for y, so then you need to

1. Combine like terms

So since there isn't anything to combine we can more on.

2. Make Y by itself

You need to subtract the 2x from both side to get the answer

y = 4x +1

4 0

2 years ago

If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (2, 4, 0) in the direction

valentina_108 [34]

Answer:

a) $\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$ .

b) $Du_{f}(2,4,0) = -\frac{8}{\sqrt{11}}$

Step-by-step explanation:

Given a function $f(x,y,z)$ , this function has the following gradient:

$\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}$ .

(a) find the gradient of f

We have that $f(x,y,z) = x\sin{yz}$ . So

$f_{x}(x,y,z) = \sin{yz}$

$f_{y}(x,y,z) = xz\cos{yz}$

$f_{z}(x,y,z) = xy \cos{yz}$ .

$\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}$ .

$\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$

(b) find the directional derivative of f at (2, 4, 0) in the direction of v = i + 3j − k.

The directional derivate is the scalar product between the gradient at (2,4,0) and the unit vector of v.

We have that:

$\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$

$\nabla f(2,4,0) = \sin{0}\mathbf{i} + 0\cos{0}\mathbf{j} + 8 \cos{0}\mathbf{k}$ .

$\nabla f(2,4,0) = 0i+0j+8k=(0,0,8)$

The vector is $v = i + 3j - k = (1,3,-1)$

To use v as an unitary vector, we divide each component of v by the norm of v.

$|v| = \sqrt{1^{2} + 3^{2} + (-1)^{2}} = \sqrt{11}$

$v_{u} = (\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}})$

Now, we can calculate the scalar product that is the directional derivative.

$Du_{f}(2,4,0) = (0,0,8).(\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}}) = -\frac{8}{\sqrt{11}}$

6 0

3 years ago

What is the exact circumference of a circle with a diameter 15 inches

stepan [7]

47. 12388980384689 would be the exact circumference of a circle witha diameter of 15 inches :)

3 0

3 years ago

At Garcia's Bike Rentals, it costs $13 to rent a bike for 3 hours. How many dollars does it cost per hour of bike use?

Naily [24]

Answer:

$4.33

Step-by-step explanation:

3 hours -> $13

1 hour -> $13/3 = $4.33

5 0

3 years ago

Which of the following best describe when you need to borrow during subtracting

Allisa [31]

Need the choices cant really answer your question

4 0

3 years ago