Michael runs 3.5 miles in 30 minutes. If he continues at this rate for 2 hours, determine his rate of change.

Drag the point A to the location indicated in each scenario to complete each statement.

Art [367]

The graph from which the position of the point A can determined following

the multiplication with a scalar is attached.

Responses:

If A is in quadrant I and is multiplied by a negative scalar, c, then c·A is in quadrant III

If A is in quadrant II and is multiplied by a positive scalar, c, then c·A is in quadrant II

If A is in quadrant II and is multiplied by a negative scalar, c, then c·A is in quadrant IV

If A is in quadrant III and is multiplied by a negative scalar, c, then c·A is in quadrant I

<h3>Methods by which the above responses are obtained</h3>

Background information;

The question relates to the coordinate system with the abscissa represent the real number and the ordinate representing the imaginary number.

Solution:

If A is in quadrant I; A = a + b·i

When multiplied by a negative scalar, c, we get;

c·A = c·a + c·b·i

Therefore;

c·a is negative

c·b is negative

c·A = c·a + c·b·i is in the quadrant III (third quadrant)

If A is quadrant II, we have;

A = -a + b·i

When multiplied by a positive scalar c, we have;

c·A = c·(-a) + c·b·i = -c·a + c·b·i

-c·a is negative

c·b·i is positive

Therefore;

c·A = -c·a + c·b·i is in quadrant II

Multiplying A by negative scalar if A is in quadrant II, we have;

c·A = -c·a + c·b·i

-c·a is positive

c·b·i is negative

Therefore;

c·A = -c·a + c·b·i is in quadrant IV

If A is in quadrant III, we have;

A = a + b·i

a is negative

b is negative

Multiplying A with a negative scalar c gives;

c·A = c·a + c·b·i

c·a is positive

c·b is positive

Therefore;

c·A = c·a + c·b·i is in quadrant I

Learn more about real and imaginary numbers here;

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4 0

2 years ago

a machinest can produce 114 parts in 6 minutes.at this rate,how many parts can the machinist produce in 15 minutes

JulsSmile [24]

The first thing we need to do is find the rate of parts for 15 minutes.

So, we divide 114 parts per 6 minutes and get 19 parts per minute

Then we multiply this rate per minute by 15 minutes

The answer is 285

Attached Work Below:

$Part1\\114\div6=19\\\\Part 2\\19\times15=285$

7 0

2 years ago

Read 2 more answers

Georgie put $500 in her savings account, earning interest at a rate of 4% each year. She did not make any more deposits or withd

zysi [14]

Answer:

a) $520

b) $580

c) Interest amount is same each year

Step-by-step explanation:

Given - Georgie put $500 in her savings account, earning interest at a rate of 4% each year. She did not make any more deposits or withdrawals.

To find - a) How much money was in the account after one year?

b) How much money was in the account after 4 years?

c) Was the amount of money earned in interest the same or different each year?

Proof -

Here given that,

Principal amount = $500

rate of interest = 4% = 4/100 = 0.04

Now,

a)

Amount = P [ 1 + RT ]

= 500 [ 1 + 0.04(1)]

= 500 [ 1 + 0.04] = 520

⇒Amount = $520

b)

Amount = P [ 1 + RT ]

= 500 [ 1 + 0.04(4)]

= 500 [ 1 + 0.16] = 580

⇒Amount = $580

c)

In 2nd year,

Amount = P [ 1 + RT ]

= 500 [ 1 + 0.04(2)]

= 500 [ 1 + 0.08] = 540

⇒Amount = $540

Now,

Interest in 1st year = 520 - 500 = 20

Interest in 2nd year = 540 - 520 = 20

So,

The interest amount is same each year

3 0

3 years ago

Katalin drove 300 miles on her vacation. She drove an average of 1.9 times faster on the second 150 miles of her trip than she d

viktelen [127]

300=x+1.9x
I got this by dividing the problem into two parts x[the speed of the first half] plus 1.9x [the speed of the second half increased by 1.9] both of those together should give you 300.
I went further and solved this...If you placed 103.5 into this problem for x you should get 300.15!

8 0

3 years ago

On Earth, 1kg=9.8N=2.2lbs. On the moon, 1kg=1.6N=0.37lbs

Trava [24]

A.50*9.8
B.50*1.6
C.45.359237
D.45.3*1.6

8 0

3 years ago