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3 years ago

Convert logx y = 1/2 to exponential form.

Mathematics

1 answer:

Lena [83]3 years ago

8 0

Answer:

Exponential form: y = x^½

Step-by-step explanation:

Given

$log_xy= \frac{1}{2}$

Required:

The exponential form

To convert to an exponential function, we have to take exponents of both sides using the base of the logarithm function.

This gives us

$x^{log_xy}= x^\frac{1}{2}$

Since the base of the exponential function and the logarithm is the same (x), they'll cancel out one another

This leaves us with

$y= x^\frac{1}{2}$

Hence, the exponential form of the expression

$log_xy= \frac{1}{2}$ is $y= x^\frac{1}{2}$

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Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your

Law Incorporation [45]

Answer:

According to the rule of 72, the doubling time for this interest rate is 8 years.

The exact doubling time of this amount is 8.04 years.

Step-by-step explanation:

Sometimes, the compound interest formula is quite complex to be solved, so the result can be estimated by the rule of 72.

By the rule of 72, we have that the doubling time D is given by:

$D = \frac{72}{Interest Rate}$

The interest rate is in %.

In our exercise, the interest rate is 9%. So, by the rule of 72:

$D = \frac{72}{9} = 8$ .

According to the rule of 72, the doubling time for this interest rate is 8 years.

Exact answer:

The exact answer is going to be found using the compound interest formula.

$A = P(1 + \frac{r}{n})^{nt}$

In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

So, for this exercise, we have:

We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.

is double the initial amount, double the principal.

$A = 2P$

$r = 0.09$

The interest is compounded anually, so $n = 1$

$A = P(1 + \frac{r}{n})^{nt}$

$2P = P(1 + \frac{0.09}{1})^{t}$

$2 = (1.09)^{t}$

Now, we apply the following log propriety:

$\log_{a} a^{n} = n$

So:

$\log_{1.09}(1.09)^{t} = \log_{1.09} 2$

$t = 8.04$

The exact doubling time of this amount is 8.04 years.

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3 years ago

Are 12:14 and 60:70 equivalent ratios? yes no

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Answer:

Yes, they are equalent

Step-by-step explanation:

12:14 = 6:7

60:70 =6:7

both can be simplified to 6:7

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3 years ago

I need help finding y. I keep getting answers that are bigger than they should be.

MakcuM [25]

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2 years ago

Jane’s cell phone plan is $40 each month plus $0.15 per minute for each minute over 200 minutes of call time. Janes cell phone b

san4es73 [151]

Answer:

The equation is $40+0.15m = 58.00$ whose solution is $m =120\:minutes.$

Step-by-step explanation:

Let us call $m$ the number of minutes the phone is used over 200 minutes, then we have

$\boxed{40+0.15m = 58.00}$ (this says monthly bill of $40 plus the cost of phone usage over 200 minutes must equal $58 )

This equation can be used to solve for $m$ u as follows:

$0.15m = 58-40$

$m = \dfrac{18}{0.15}$

$\boxed{m = 120\:minutes}$

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3 years ago

Select all the expressions that are equivalent to the polynomial below.

jekas [21]

The answer to this question is D. or C.

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2 years ago

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