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natta225 [31]
4 years ago
6

Write a complete sentence that states the type of transformation that was preformed and explains the transformation in detail. Q

uadrilateral EFGH is the image....

Mathematics
1 answer:
LUCKY_DIMON [66]4 years ago
6 0
The green figure is the original quadrilateral, ABCD.  The red is the image, EFGH.  You can see from the figure that they are both oriented (turned) the same way.  It appears that the transformation applied was a translation.  Each ordered pair has an <em>x</em>-coordinate that is 4 larger than the preimage and a <em>y</em>-coordinate that is 5 smaller than the preimage.  Therefore the transformation was a translation 4 units right and 5 units down.

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A large tank is filled to capacity with 300 gallons of pure water. Brine containing 5 pounds of salt per gallon is pumped into t
Gwar [14]

Answer:

(a) A = 1500(1 - e^{-0.01t})

(b) t = 0

Step-by-step explanation:

Given

V= 300gal --- Volume of tank

B = 5lb/gal --- Brine solution

R_1 = 3gal/min  --- Rate in, in gallon/min

R_2 = 6gal/min --- Rate out, in gallon/min

Required

Determine A(t)

First, calculate the rate in (R in) and (R out) in lb/min

R_{in} = B * R_1

R_{in} = 5lb/gal * 3gal/min

R_{in} = 15lb/min

R(out) is calculated by multiply the rate at which brine leaves the tank (lb/gal) * R2

So, we have:

R_{out} = \frac{A(t)}{300} lb/gal * 3gal/min

R_{out} = \frac{3*A(t)}{300} lb/min

R_{out} = \frac{A(t)}{100} lb/min

The change in the amount of brin e in the tank at time t is given as:

A'(t) = R_{in} - R_{out}

A'(t) = 15 - \frac{A(t)}{100}

Rewrite:

\frac{dA}{dt} = 15 - \frac{A}{100}

Multiply through by dt

dA = [15 - \frac{A}{100}]* dt

Make dt stand alone

\frac{dA}{15 - \frac{A}{100}} = dt

ln|15 - \frac{A}{100}| = -0.01t + ln\ c

Express as exponents

15 - \frac{A}{100} = ce^{-\frac{t}{100}}

Multiply through by 100

1500 - A = 100ce^{-\frac{t}{100}}

A = 1500 - 100ce^{-\frac{t}{100}}

A = 1500 - 100ce^{-0.01t}

Apply initial conditions

A(0) = 0

Substitute 0 for t in: A = 1500 - 100ce^{-0.01t}

0 = 1500 - 100ce^{-0.01*0}

0 = 1500 - 100ce^{0}

0 = 1500 - 100c

100c = 1500

c = 15

Substitute 15 for c in A = 1500 - 100ce^{-0.01t}

A = 1500 - 100*15e^{-0.01t}

A = 1500 - 1500e^{-0.01t}

Factorize:

A = 1500(1 - e^{-0.01t})

How long to empty the tank

Set A to 0

1500(1 - e^{-0.01t}) = 0

Divide through by 1500

1 - e^{-0.01t} = 0

Collect Like Terms

e^{-0.01t} = 1

Take ln of both sides

ln\ (e^{-0.01t}) = ln\ 1

-0.0t  = 0

t = 0

8 0
3 years ago
Write your equation for y=4 x=2
Elis [28]
It’s literally just y=5 x=2
3 0
3 years ago
a father is 27 years older than his son. ten years ago he was twice as old as his son. how old is the father​
BlackZzzverrR [31]

Answer:

thus the father is 64 years and son is 37years

Step-by-step explanation:

Let father be X and son be y

X=27+Y...........(I)

X-10=2(Y-10)

putting the value of X from eqn(I)

27+Y-10=2Y-20

Y+17=2Y-20

17+20=2Y-Y

37=y

X=27+Y

X=64

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sashaice [31]

Answer:

1ft and 3in or 1 1/4ft

Step-by-step explanation:

1ft

12 individed by 3=4in

3 times 4=12 so 1ft and 3in is 1 1/4ft

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Answer:-lecture-2-equation-price-line-20-12-2-1-slope-2-slope-2-2-ps-pr-q28284683 ... answers/60-30-20-10-0-4000-3000-2000-1500-1000-wavenumbers-cm-1-q28284756

Step-by-step explanation:

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