What is 78% of 550? (Percent calculations)

Answers

Answer 1

Answer: To fine 78% of 550, all you have to do is multiply 550 by 0.78

$550*0.78=429$

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Solid figure with a pentagon for a base and triangular faces

Answers

It's a pentagonal pyramid.

it is a pentagonal pyramid.

Two ants are at a common point at time t=0, the first ant starts crawling along a straight line at the rate of 4 ft/min. Two minutes later, the second ant starts crawling in a direction perpendicular to that of the first, at a rate of 5 ft/min. How fast is the distance between them changing when the first insect has traveled 12 feet? Thank you!

Answers

I looked at this just before going to bed, and it ruined my night, worrying
about it. Then, this morning, when I actually set pencil to paper, it turned
out not to be such a vicious limbic twister.

You DO need to know how to take a chain derivative, though. I must say,
I'm surprised to see this much Calculus at the middle school level. Maybe
it's MY problem, but I just can't see a way to do it without this derivative,
so I'll just show you how I did it:

The ants begin together, and crawl out along the legs of a right triangle.

-- The first one moves at 4 ft/min, so after 't' minutes, he's 4t-ft from
the vertex. The question concerns what happens when this one has
covered 12-ft. That will happen in (12/4) = 3 minutes after he starts out.

-- The second one starts out 2-min later, and moves at 5-ft/min. So,
after 't' minutes, he's 5(t-2) ft from the vertex.

-- The distance between them is the hypotenuse of the right triangle.
The square of the distance is the sum of the squares of the legs:

D² = (4t)² + [ 5(t-2) ]²

We're actually going to need to know how far apart they are after 3 minutes,
so let's do that now.

   D² = (4 x 3)² + (5 x 1)² = (12)² + (5)² = 144 + 25 = 169

   D = √169 = 13-ft apart, after the first guy has covered 12 feet.
   We will need this shortly.

OK. Now, let's simplify the equation for the distance between them,
(as we get ready to differentiate it).

   D² = (4t)² + [ 5(t-2) ]²

   D² = 16t² + (25) (t² - 4t + 4)

   D² = 16t² + 25t² - 100t + 100

   D² = 41t² - 100t + 100

The question asks "How fast is the distance between them changing . . . ? ",
and we know that this is the derivative of 'D' with respect to 't' . It's easy to
take the derivative of the right side of the equation, but what about the derivative
of ' D² ' ?   That's the part that I'm not so sure about in middle school, so I'll just
give it to you:

   (Derivative of D²) is [ (2D) times (derivative of D) ] .

Now we can take the derivative of each side of the equation:

   (2D) x (derivative of D) = 82 t - 100 .

derivative of D = (82 t - 100) / (2D)

That's how fast the distance between them is changing at any time 't' .

After 3 minutes, we calculated 'D' earlier. It's 13-ft

   derivative of D = [ (82 x 3) - 100 ] / (2 x 13)

   = 146 /    26

   = 5.615 feet per second.

Are you confident ? Do you trust me?
I'm not confident at all, and I don't trust myself.
The best I can suggest is for you to go through this and look for my mistakes,
or better yet, sit down with your teacher and go through it for mistakes.
That'll help you think about it and understand it, even if my work is wrong.

Ok, so I'll be quantizing time here to get you the most accurate result I can give you.

What you have to know is that:

$D=\sqrt { { x }^( 2 )+{ y }^( 2 ) }$

Also:

t=time snapshot (in minutes)

x=distance first ant has travelled

y=distance second ant has travelled (perpendicular to the first ant)

D=distance between both ants

--------------------------------------

Now, when:

t=0, x=0, y=0, D=0

t=1, x=4, y=0, D=4

t=2, x=8, y=0, D=8

t=3, x=12, y=5, D=13

Now we quantize time and find the tangent line (slope) between two points on the distance vs time graph at t=3 and t=3.000001, knowing that distance is represented by feet and time is represented in minutes.

When t=3.000001, x=12.000004, y=5.000005 D=13.00000562...

Now we find the slope on the distance vs time graph between the points (3,13) and (3.000001, 13.00000562).

$m=\frac { 13.00000562-13 }{ 3.000001-3 } \n \n =\frac { 281 }{ 50 }$

So, at the point (3,13) on the distance vs time graph, the two ants are moving away from each other at approximately 5.62 feet per minute.

Notations you may require to understand problem in the attachment below.

Write this expression in words 8+16=24

Answers

The sum of eight and sixteen is equal to twenty-four

Is the proper way to word the expression

eight plus sixteen is equal to 24

Two intersecting lines have zero, an infinite number, two, or one of the same points in common?

Answers

If two lines intersect, then there are two possibilities

A) The lines intersect at exactly one point. This happens if the slopes of the two lines are different (the y intercepts may or may not be the same).

B) The lines intersect at infinitely many points. This happens when both slopes are the same and when both y intercepts are the same. In short, the two equations are identical. Often they may be written in different forms. For example, the equation y = 2x+1 and 2y = 4x+2 are the same equation. Divide everything in equation (2) by 2 and you'll get equation (1).

A large bin of mixed nuts contains peanuts, cashews, almonds, and walnuts. Sheila scoops out a bowl full of nuts and counts how many of each type she has: 17 peanuts, 9 cashews, 12 almonds, and 10 walnuts. Armando scoops out a bowl of 32 nuts. About how many should he expect to be cashews?

A.
5

B.
6

C.
9

D.
18

Answers

Assuming that the ratios stay the same, the answer is going to be 6 because the total number of nuts drawn originally was 48, and 9 were cashews. To maintain this ratio when 32 nuts were drawn, the number of cashews will be 6.

Peter sells 2/3 lb. of rice every 1/3 hour. How much rice does Peter sell in an hour? Please explain

Answers

For this you should set up a proportion.

2/3. 1/3
------ = --------
x. 3/3

Then cross multiply 3/3 x 2/3 and divide by 1/3

2/3 x 3/3 = 6/9

6/9 \ 1/3 = 6/9 x 3/1 = 18/1

Peter sells 18 bags of rice per hour.

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