Factor completely 5x2 − 5x − 100.

1 answer:

4 0

First, factor out 5:
5 (x² -x -20)
We need two numbers that add to -1 and multiply to -20. -5 and 4 satisfy this.
5(x-5)(x+4)

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Fiona invested $1000 at 7% compounded continuously. At the same time, Maria invested $1100 at 7% compounded daily. How long will

Natali [406]

9514 1404 393

Answer:

14,201 years

Step-by-step explanation:

The two compound interest formulas are ...

A = P·e^(rt) . . . . . continuous compounding at rate r for t years

A = P·(1 +r/365)^(365t) . . . . . daily compounding at rate r for t years

We went the amounts to be equal:

1000·e^(0.07t) = 1100·(1+0.07/365)^(365t)

Dividing by 1000(1 +0.07/365)^(365t), we have ...

((e^0.07)/(1+0.07/365)^365)^t = 1.1

The base of the exponential on the left is ...

( e^0.07)/(1+0.07/365)^365 ≈ 1.00000671149321522

Taking logs, we have ...

t×ln(1.00000671149321522) = ln(1.1)

t = ln(1.1)/ln(1.00000671149321522) ≈ 0.09531018/(6.7114704·10^-6)

t ≈ 14,201.09 . . . . . years

It will take about 14,201 years for the investments to be equal.

_____

<em>Additional comment</em>

The investment value at that time will be about $5.269·10^434. (That's a larger number than <em>anything</em> countable in the known universe, including energy quanta.)

These calculations are beyond the ability of many calculators, so might need to be carefully rewritten if the calculator only keeps 10 significant digits, or only manages exponents less than 100.

This shows that daily compounding is very close in effect to continuous compounding. It would take almost 150 years to make a difference of 0.1% in value.

4 0

3 years ago

Which transformation would create an image and a pre image that are similar figures?

Crank

Answer:

Dilation

Step-by-step explanation:

A dilation changes the size of a figure by enlarging the figure of making the figure smaller. The sides will be proportional and the angles will be congruent making the figures similar.

4 0

2 years ago

Which expressions are equivalent to –

olga_2 [115]

Answer:

The answer to your question is 10¹/⁴

Step-by-step explanation:

Expression

$\frac{10}{10^{3/4}}$