All categories

3 years ago

Algebra2 |2-3(2w+1)=7w-3(7+w)

1 answer:

5 0

I believe your answer is -220w-22 2-3(2w+1)=7w-3(7+w) +7w -7w 2-3(9w+1)=-3(7+w) +w -w 2-3(10w+1)=-3(7) 2-3(10w+1)=-21 -1(10w+1=-21 -21 +21 -22(10w+1) -220w-22

You might be interested in

What is 100.34567 in a fraction and word form? Thank you! ❤

amid [387]

Wait sorry in fraction for it is 1000000/10

6 0

2 years ago

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)

4 0

3 years ago

Lacie wants to paint her bedroom walls. She gas to cover 1,165.5 square feet. About how many gallons of paint will she need? Gal

DanielleElmas [232]

Answer:

1. 4.66 gallons 2. 2.33 gallons 3. 1.55 gallons

Step-by-step explanation:

1. If her gallons cover is 250 square feet, the number of gallons of paint Lacie would need to cover 1,165.5 square feet of bedroom walls is

1,165.5/250 = 4.66 gallons

2. If her gallons cover is 500 square feet, the number of gallons of paint Lacie would need to cover 1,165.5 square feet of bedroom walls is

1,165.5/500 = 2.33 gallons

3. If her gallons cover is 750 square feet, the number of gallons of paint Lacie would need to cover 1,165.5 square feet of bedroom walls is

1,165.5/750 = 1.55 gallons

4 0

3 years ago

A radio telescope has a parabolic surface, as shown below.

krek1111 [17]

OK, so the graph is a parabola, with points x=0,y=0; x=6,y=-9; and x=12,y=0

Because the roots of the equation are 0 and 12, we know the formula is therefore of the form

y = ax(x - 12), for some a

So put in x = 6

-9 = 6a(-6)

9 = 36a

a = 1/4

So the parabola has a curve y = x(x-12) / 4, which can also be written y = 0.25x² - 3x

The gradient of this is dy/dx = 0.5x - 3

The key property of a parabolic dish is that it focuses radio waves travelling parallel to the y axis to a single point. So we should arrive at the same focal point no matter what point we chose to look at. So we can pick any point we like - e.g. the point x = 4, y = -8

Gradient of the parabolic mirror at x = 4 is -1

So the gradient of the normal to the mirror at x = 4 is therefore 1.

Radio waves initially travelling vertically downwards are reflected about the normal - which has a gradient of 1, so they're reflected so that they are travelling horizontally. So they arrive parallel to the y axis, and leave parallel to the x axis.

So the focal point is at y = -8, i.e. 1 metre above the back of the dish.

5 0

2 years ago

60ml of liquid is poured into a cuboidal tank with a length of 4.5cm, a width of 3.5cm and a height of

Burka [1]

Answer:

yo emanuael

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers