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3 years ago

Rotate the given triangle 90°

Mathematics

2 answers:

Ad libitum [116K]3 years ago

6 0

Answer:

Step-by-step explanation:

kati45 [8]3 years ago

4 0

9514 1404 393

Answer:

$\left[\begin{array}{ccc}0&-1&-2\\0&-3&5\end{array}\right]$

Step-by-step explanation:

The rotation matrix for 90° CCW is ...

$\left[\begin{array}{cc}0&-1\\1&0\end{array}\right]$

Then the rotated coordinates are ...

$\left[\begin{array}{ccc}0&-1\\1&0\end{array}\right]\cdot\left[\begin{array}{ccc}0&-3&5\\0&1&2\end{array}\right]=\left[\begin{array}{ccc}0&-1&-2\\0&-3&5\end{array}\right]$

_____

The transformation of each ordered pair is ...

(x, y) ⇒ (-y, x)

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A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of

belka [17]

Let s(t) be the amount of salt in the tank at time t. Then s(0) = 50 lb.

Salt flows into the tank at a rate of

(2 gal/min) (6 lb/gal) = 12 lb/min

and flows out at a rate of

(2 gal/min) (s(t)/300 lb/gal) = s(t)/150 lb/min

so that the net rate at which salt is exchanged through the tank is

ds(t)/dt = 12 - s(t)/150 … (lb/min)

Solve for s(t). The DE is separable, so we have

ds/dt = 12 - s/150

150 ds/dt = 1800 - s

150/(1800 - s) ds = dt

Integrate both sides to get

-150 ln|1800 - s| = t + C

Solve for s :

ln|1800 - s| = -t/150 + C

1800 - s = exp(-t/150 + C )

1800 - s = C exp(-t/150)

s = 1800 - C exp(-t/150)

Now given that s(0) = 50, we solve for C :

50 = 1800 - C exp(-0/150)

50 = 1800 - C

C = 1750

Then the amount of salt in the tank at any time t ≥ 0 is

s(t) = 1800 - 1750 exp(-t/150)

To find the time it takes for the tank to hold 100 lb of salt, solve for t in

100 = 1800 - 1750 exp(-t/150)

1700 = 1750 exp(-t/150)

34/35 = exp(-t/150)

ln(34/35) = -t/150

t = -150 ln(34/35) ≈ 4.348

So it would take approximately 4.348 minutes.

By the way, we didn't have to solve for s(t), we could have instead stopped with

-150 ln|1800 - s| = t + C

Solve for C - this C is not the same as the one we found using the other method. s(0) = 50, so

-150 ln|1800 - 50| = 0 + C

C = -150 ln|1750|

==> t = 150 ln(1750) - 150 ln|1800 - s|

Then s(t) = 100 lb when

t = 150 ln(1750) - 150 ln(1700)

t = 150 ln(1750/1700)

t = 150 ln(35/34)

t ≈ 4.348

5 0

3 years ago

The coldest temperature recorded in Alaska was –80°F. This was 10°F warmer than the coldest temperature recorded in Siberia. Whi

Klio2033 [76]

The equation that can be used to find the coldest temperature recorded in Siberia is y + 10 = -80

Let the coldest temperature in Alaska be x

The coldest temperature recorded in Alaska was –80°F

x = –80°F

Let the coldest temperature in Siberia be y

The coldest temperature recorded in Alaska was 10°F warmer than the coldest temperature recorded in Siberia

This can be interpreted as:

Coldest temperature in Alaska = Coldest temperature in Siberia + 10

x = y + 10................(*)

Since x = -80

Substitute x = -80 into equation (*)

-80 = y + 10

This can be re-written as:

y + 10 = -80

The equation that can be used to find the coldest temperature recorded in Siberia is y + 10 = -80

Learn more here: brainly.com/question/2159099

7 0

2 years ago

The diameter of a basketball is 9.50 inches. What is the volume of the ball, rounded to the nearest hundredth?

Goryan [66]

Answer:

Step-by-step explanation:

4/3*pi*r^3

8 0

3 years ago

How do you do this question?

Maslowich

Answer:

11.736

Step-by-step explanation:

You take 82.80 divided by 12 = 6.9 then take 9 divided by 6.9 = 1.304 repeating then times by three =3.912 then times by 9 = 35.208 then divide by 3 = 11.736

7 0

3 years ago

2log(x+11) = (1/2)^x

Lina20 [59]

X = -1

Hope this helps!

7 0

3 years ago

Read 2 more answers