All categories

3 years ago

15 points

2 answers:

6 0

In this exercise is given that a triangle has a vertex R at the coordinate (-4,1) and it is says that this point was rotated 90 degrees counterclockwise from the origin. It is asked to find the rotation which is equivalent to 90 degree counterclockwise rotation.

First of all a 90 degree counterclockwise rotation is define by the rule
(x,y)--(-y,x), which means that every time a 90 degree counterclockwise rotation occurs the given point has to be changed according to the previous mention rule.

In the other hand, a 90 degree clockwise rotation is define by the rule (x,y)--(y,-x). A 360 degree counterclockwise rotation is define by (x,y)--(x,y), and a 270 degree clockwise rotation is represented by the rule (x,y)--(-y,x).

By the previous said, the rotation which is equivalent to a 90 degree counterclockwise rotation is a 270 degree clockwise rotation.

melisa1 [442]3 years ago

5 0

Clockwise 270 degrees is the answer

You might be interested in

Kryptonite is a material found on the planet Krypton and has various effects, most importantly on Superman. The most common type

Rashid [163]

Answer:

The maximum amount of red kryptonite present is 33.27 g after 4.93 hours.

Step-by-step explanation:

dy/dt = y(1/t - k)

separating the variables, we have

dy/y = (1/t - k)dt

dy/y = dt/t - kdt

integrating both sides, we have

∫dy/y = ∫dt/t - ∫kdt

㏑y = ㏑t - kt + C

㏑y - ㏑t = -kt + C

㏑(y/t) = -kt + C

taking exponents of both sides, we have

$\frac{y}{t} = e^{-kt + C} \\\frac{y}{t} = e^{-kt}e^{C} \\\frac{y}{t} = Ae^{-kt} (A = e^{C})\\y = Ate^{-kt}$

when t = 1 hour, y = 15 grams. So,

$y = Ate^{-kt}\\15 = A(1)e^{-kX1}\\15 = Ae^{-k}$ (1)

when t = 3 hours, y = 30 grams. So,

$y = Ate^{-kt}\\30 = A(3)e^{-kX3}\\30 = 3Ae^{-3k}$ (2)

dividing (2) by (1), we have

$\frac{30}{15} = \frac{3Ae^{-3k}}{Ae^{-k}} \\2 = 3e^{-2k}\\\frac{2}{3} = e^{-2k}$

taking natural logarithm of both sides, we have

-2k = ㏑(2/3)

-2k = -0.4055

k = -0.4055/-2

k = 0.203

From (1)

$A = 15e^{k} \\A = 15e^{0.203} \\A = 15 X 1.225\\A = 18.36$

Substituting A and k into y, we have

$y = 18.36te^{-0.203t}$

The maximum value of y is obtained when dy/dt = 0

dy/dt = y(1/t - k) = 0

y(1/t - k) = 0

Since y ≠ 0, (1/t - k) = 0.

So, 1/t = k

t = 1/k

So, the maximum value of y is obtained when t = 1/k = 1/0.203 = 4.93 hours

$y = 18.36(1/0.203)e^{-0.203t}\\y = \frac{18.36}{0.203}e^{-0.203X1/0.203}\\y = 90.44e^{-1}\\y = 90.44 X 0.3679\\y = 33.27 g$

<u>So the maximum amount of red kryptonite present is 33.27 g after 4.93 hours.</u>

3 0

3 years ago

Please I really need help <br> This is my last point <br> Show workings please

KiRa [710]

Step-by-step explanation:

By rotating a figure,

The length of its sides remain the same.

Therefore line AB = line A'B'.

=> 5x - 14 = 4x + 4

=> x = 18

Hence, line AB = 5(18) - 14 = 76.

7 0

3 years ago

Read 2 more answers

The expendlvre on good of a ram is Rs 8000 . If the number of degree of sector food is 40°. Find his total expenditure.

anzhelika [568]

The total expenditure is Rs 72,000.

<h3>What is the total expenditure?</h3>

The total expenditure can be determined using this equation:

(total amount spent on a good x total value of circle) / degree of the sector of good

(8000 x 360) / 40 = Rs 72,000

To learn more about division, please check: brainly.com/question/194007

#SPJ1

7 0

1 year ago

recall that two angles are supplementary if the sum of their measure is 180. find the measures of two supplementary angles if on

aleksklad [387]

Answer:

I don't know if it's correct

but I tried

Step-by-step explanation:

let the angle be x

20+4x+x=180

20+5x=180

5x=160

x=32

5 0

2 years ago

If a triangle is 4 feet on one side, 6 feet on another side, what is the measurement of the third side?

tino4ka555 [31]

It depends on what type of Triangle or what the volume or area is. This question is missing information.

7 0

3 years ago