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2 years ago

Find an equation of a line that is parallel to 2x+3y=6 and passes through the point (4, 4)

Mathematics

2 answers:

wariber [46]2 years ago

7 0

Answer:

Answer:

Step-by-step explanation:

Slope of a line 2x+3y=6 is -2/3

So line passing through (0,4) has same slope because both are parallel

From slope intercept form we have

Y-y1 =m(x-1)

Y-4= -2/3(x-0)

3Y-12 = -2x

3Y+2x = 12

Which is required equation of a line.

Step-by-step explanation:

Colt1911 [192]2 years ago

6 0

Answer:

y = -2/3x + 20/3

Step-by-step explanation:

2x + 3y = 6

3y = -2x + 6

y = -2/3x + 2

y = -2/3x + b

4 = -2/3(4) + b

4 = -8/3 + b

20/3 = b

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Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 8exyz, (0, 0, 8

Dima020 [189]

Let $f(x,y,z)=x+y+z-8e^{xyz}$ . The tangent plane to the surface at (0, 0, 8) is

$\nabla f(0,0,8)\cdot(x,y,z-8)=0$

The gradient is

$\nabla f(x,y,z)=\left(1-8yze^{xyz},1-8xze^{xyz},1-8xye^{xyz}\right)$

so the tangent plane's equation is

$(1,1,1)\cdot(x,y,z-8)=0\implies x+y+(z-8)=0\implies x+y+z=8$

The normal vector to the plane at (0, 0, 8) is the same as the gradient of the surface at this point, (1, 1, 1). We can get all points along the line containing this vector by scaling the vector by $t$ , then ensure it passes through (0, 0, 8) by translating the line so that it does. Then the line has parametric equation

$(1,1,1)t+(0,0,8)=(t,t,t+8)$

or $x(t)=t$ , $y(t)=t$ , and $z(t)=t+8$ .

(See the attached plot; the given surface is orange, (0, 0, 8) is the black point, the tangent plane is blue, and the red line is the normal at this point)

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2 years ago

On a scale drawing 7 inches represents 10 miles. How much inches would represents 60 miles

Sergeeva-Olga [200]

Answer:

3.802e+6 miles

Step-by-step explanation:

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2 years ago

What is the value of the expression 5x2 + 2x when x = 5?

masha68 [24]

Answer:

135

Step-by-step explanation:

Given:

$x = 5$

To determine a numerical value for the expression, simply substitute the value of "x" into the expression and simplify the expression, if necessary, to determine a specific number for the expression provided.