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wariber [46]
3 years ago
7

1. The rectangle shown is dilated by a scale factor of 2.

Mathematics
1 answer:
Alexus [3.1K]3 years ago
8 0
1. Since the one SHOWN is to be dilated by a factor of 2, our new dimensions are 2x by 2y. We multiply each side length by two to get our new dilated image.

SIDE LENGTHS

AB= 30cm
BD= 16cm

I have a picture of the new dilated image below.

You are welcome! Have a nice day.

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The rate of change of the number of squirrels S(t) that live on the Lehman College campus is directly proportional to 30 − S(t),
pishuonlain [190]

Answer:

S(3)=22

Step-by-step explanation:

The rate of change of the number of squirrels S(t) that live on the Lehman College campus is directly proportional to 30 − S(t).

\dfrac{dS}{dt}=k(30-S(t))\\ \dfrac{dS}{dt}+kS(t)=30k\\$The integrating factor: e^{\int k dt}=e^{kt}\\$Multiply all through by the integrating factor\\ \dfrac{dS}{dt}e^{kt}+kS(t)e^{kt}=30ke^{kt}

(Se^{kt})'=30ke^{kt} dt\\$Integrate both sides\\ Se^{kt}=\dfrac{30ke^{kt}}{k}+C$ (C a constant of integration)\\Se^{kt}=30e^{kt}+C\\$Divide both sides by e^{kt}\\S(t)=30+Ce^{-kt}

When t=0, S(t)=15

15=30+Ce^{-k*0}\\C=15-30\\C=-15

When t = 2, S(t)=20

20=30-15e^{-2k}\\20-30=-15e^{-2k}\\-10=-15e^{-2k}\\e^{-2k}=\dfrac23\\$Take the natural log of both sides$\\-2k=\ln \dfrac23\\k=-\dfrac{\ln(2/3)}{2}

Therefore:

S(t)=30-15e^{\frac{\ln(2/3)}{2}t}\\$When t=3$\\S(t)=30-15e^{\frac{\ln(2/3)}{2} \times 3}\\S(3)=21.8 \approx 22

8 0
3 years ago
A student estimated a mass for by 325g, but upon carefully mesuring it, found the actual mass to be 342g. What is the percent er
vlada-n [284]

Answer:

5.2307 %

Step-by-step explanation:

(acutal mass- estimated mass) / ( estimated mass)

7 0
3 years ago
The top and bottom margins of a poster are each 6.5 cm and the side margins are each 4.5 cm. The area of printed material on the
ycow [4]

Answer:

384cm^2,

Step-by-step explanation:

The top and bottom margins of a poster are each 6 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 384 cm^2,

8 0
3 years ago
Find the rule and the graph of the function whose graph can be obtained by performing the translation 3 units left and 2 units d
ahrayia [7]

Answer: Option b.

Step-by-step explanation:

 1. You have the following parent function given in the problem above:

f(x)=x³ (This is the simplest form. We need to translate it 3 units left and 2 units down)

2. If you take the parent function and make y=f(x+3), then you have:

y=f(x+3)=(x+3)^{3} (The function is shifted 3 units left on the x-axis).

3. Then you if you make y=f(x+3)-2, as following, you obtain:

y=f(x+3)-2=(x+3)^{3}-2  (The function is shifted 2 units down on the y-axis).

4. Therefore, that is how you obtain the final function.

The answer is the graph shown in the option b.

5 0
3 years ago
How do you write -0.5555555 etc as a fraction?
lutik1710 [3]
-5/10 as a fraction!
5 0
3 years ago
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