6 cups is it greater than, equal to or less than 12 pints?

slader (a) Find parametric equations for the line through (4, 1, 8) that is perpendicular to the plane x − y + 4z = 2. (Use the

Pavel [41]

Answer:

(x(t), y(t), z(t)) = (4 + t, 1 - t, 8 + 4t)

xy - plane (x, y, z) = (2, -1, 0)

yz - plane (x, y, z) = (0, 5, -8)

xz - plane (x, y, z) = (5, 0, 12)

Step-by-step explanation:

The given point (x, y ,z) = (4, 1, 8)

The plane x -y + 4z = 2

Normal vector (n) = < 1, -1, 4 >

The equation of line through point (4, 1, 8) and the plane is:

(x(t), y(t), z(t)) = (4, 1, 8) + t(1, -1, 4)

(x(t), y(t), z(t)) = (4 + t, 1 - t, 8 + 4t)

Any point on the line P(x, y, z) = ( 4 + t, 1 - t, 8 + 4t)

xy-Pane ⇒ z = 0

8 + 4t = 0

4t = - 8

t = -8/4

t = -2

∴

(x, y, z) = (4 - 2, 1 - 2, 8 + 4(-2))

(x, y, z) = (2, -1, 0)

yz-plane ⇒ x = 0

4 + t = 0

t = -4

∴

(x, y, z) = (4 + (-4) , 1-(-4), 8 + 4(-4)

(x, y, z) = (0, 5, -8)

xz-plane ⇒ y = 0

1 - t = 0

-t = -1

t = 1

∴

(x, y, z) = ( 4 + 1, 1 - 1, 8 + 4(1) )

(x, y, z) = (5, 0, 12)

6 0

3 years ago

In one year, three awards (research, teaching, and service) are given to a class of 25 graduate students in a statistics departm

allochka39001 [22]

Answer:

13,800

Step-by-step explanation:

This is a permutation, not a combination, because order matters.

Here's why:

Arbitrarily, let's say that the three students chosen for the award are Abby, Bob, and Charlie. The order of which each award is given to the three of them matters, because otherwise they would be receiving different awards. For example, if Abby gets the research award, Bob gets the teaching award, and Charlie gets the service award, this would be notably different than if Abby got the teaching award, Bob got the service award, and Charlie got the research award.

Therefore, for the first award, we have 25 people to choose from. After we select that person, we have 24 people to choose from, since the problem stipulates that each student can receive at most one award. Then 23, and so on.

Since we're choosing three people to give awards to, there are:

$25\cdot 24\cdot 23=\boxed{13,800}$ permutations. Because order matters (refer to explanation above), this is our final answer.

3 0

3 years ago

NEED HELP ASAP!!!

lyudmila [28]

Answer:

5

that is your answer plz mark brainlyest

8 0

3 years ago

Read 2 more answers

Need Help!!!!! solving these problems

Tanzania [10]

I'll tell you how to do the first exercise, since they all apply the same logic. Only the numbers will be different from time to time, so if you understand how to do the first one, you'll be able to do as many other as you want.

All these expressions are in the form

$y=mx+q$

which means that they represent a line. To draw a line, it is sufficient to draw two of its point. Then you can connect them with a segment, and extend the segment beyond the endpoints.

So, we simply need to sample two points from each equation. A point is a couple of coordinate $(x,y)$ . The equation tells us in which relationship they have to be. So, you can arbitrarily choose two x values, and compute the corresponding y values. It is usually a good idea to use "easy", i.e. small, x values, to make computations easier.

So, for the first equation, let's choose the values x=0 and x=1, and see the corresponding y values. If we choose x=0, we have

$y = -3\cdot 0 + 4 = 4 \implies P_1 = (0,4)$

And if we choose x=1, we have

$y = -3\cdot 1 + 4 = 1 \implies P_2 = (1,1)$

Now, draw the two points on a coordinate plane and connect them, and you have your line.

5 0

3 years ago

If the volume of a box is 1,463,000 cubic millimeters, what is the volume of the box in cubic meters? (1 millimeter = 0.001 mete

Stells [14]

Answer:

The volume of the box would be 0.001463 cubic meters

Step-by-step explanation:

You first have to to do the conversion from cubic milimiters to cubic meters using the rule given. A cubic milimiter is only 1^3 = or 1*1*1. We transform then this rule so it applies for cubic measures.

1 millimeter = 0.001 meter

(1 millimeter)^3 = (0.001 millimeter)^3 (raise to the cubic power)

1 cubic milimiter = (0.001*0.001*0.001) cubic meters= 0.000000001 or 1 * 10^-9 in scientific notation.

Then we us a rule of three as follows

1 cubic millimiter / 1 * 10^-9 cubic meters =1,463,000¨cubic milimiters / x cubic meters

x = 1,463,000*1 * 10^-9= 0.001463 cubic meters

8 0

4 years ago