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shutvik [7]
3 years ago
12

What will the new dimensions of the rectangle be after a dilation with a scale factor of 9/4​

Mathematics
1 answer:
elena-14-01-66 [18.8K]3 years ago
5 0

Answer:

The new dimensions of the rectangle, after a dilation will be 72 ft by 18 ft

Step-by-step explanation:

we know that

The new dimensions of the rectangle, after a dilation will be equal to the original dimensions multiplied by the scale factor

we have

The scale factor is 9/4

Original length =32 ft

Original width=8 ft

Find the new dimensions after dilation

New length=(9/4)32=72 ft

New width=(9/4)8=18 ft

therefore

The new dimensions of the rectangle, after a dilation will be 72 ft by 18 ft

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For the following amount at the given interest rate compounded​ continuously, find​ (a) the future value after 9 ​years, (b) the
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Answer:

(a) The future value after 9 ​years is $7142.49.

(b) The effective rate is r_E=4.759 \:{\%}.

(c) The time to reach ​$13,000 is 21.88 years.

Step-by-step explanation:

The definition of Continuous Compounding is

If a deposit of P dollars is invested at a rate of interest r compounded continuously for t years, the compound amount is

A=Pe^{rt}

(a) From the information given

P=4700

r=4.65\%=\frac{4.65}{100} =0.0465

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Applying the above formula we get that

A=4700e^{0.0465\cdot 9}\\A=7142.49

The future value after 9 ​years is $7142.49.

(b) The effective rate is given by

r_E=e^r-1

Therefore,

r_E=e^{0.0465}-1=0.04759\\r_E=4.759 \:{\%}

(c) To find the time to reach ​$13,000, we must solve the equation

13000=4700e^{0.0465\cdot t}

4700e^{0.0465t}=13000\\\\\frac{4700e^{0.0465t}}{4700}=\frac{13000}{4700}\\\\e^{0.0465t}=\frac{130}{47}\\\\\ln \left(e^{0.0465t}\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t\ln \left(e\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t=\ln \left(\frac{130}{47}\right)\\\\t=\frac{\ln \left(\frac{130}{47}\right)}{0.0465}\approx21.88

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3 years ago
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x = -0.93 (repeating 3)

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Answer:

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Step-by-step explanation:

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The final expression gives the required answer

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