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3 years ago

Use the Pythagorean theorem

Mathematics

2 answers:

Nookie1986 [14]3 years ago

7 0

Answer:

Step-by-step explanation:

hypotenuse^2=side^2+side^2

Stels [109]3 years ago

4 0

Answer:

the pythgorean theorem is

a^2 +b^2=c^2

Step-by-step explanation:

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in 2012, the population of a city was 63,000. by 2017, the population was reduced to approximately 54,100. identify any equation

Akimi4 [234]

Answer:

$f(x) = 63000(0.97)^x$

Step-by-step explanation:

Given

$f(0) = 63000$ ---x = 0, in 2012

$f(5) = 54100$ -- x = 5, in 2017

Required

Select all possible equations

Because there is a reduction in the population, as time increases; the rate must be less than 1.

An exponential function is represented as:

$f(x) = ab^x$

Where

$b = rate$

rate > 1 in options (a) and (b) i.e. 1.03

This implies that (a) and (b) cannot be true

For option (c), we have:

$f(x) = 63000(0.97)^x$

Set x = 0

$f(0) = 63000(0.97)^0 = 63000*1=63000\\$

Set x = 5

$f(5) = 63000(0.97)^5 = 63000*0.8587=54098.1 \approx 54100$

This is true because the calculated values of f(0) and f(5) correspond to the given values

For option (d), we have:

$f(x) = 52477(0.97)^x$

Set x = 0

$f(0) = 52477(0.97)^0 - 52477* 1 = 52477$

This is false because the calculated value of f(0) does not correspond to the given value

For option (e), we have:

$f(x) = 63000(0.97)^\frac{1}{5x}$

Set x = 0

$f(0) = 63000(0.97)^\frac{1}{5*0} = 63000(0.97)^\frac{1}{0} =$ undefined

This is false because the f(x) is not undefined at x = 0

For option (f), we have:

$f(x) = 52477(0.97)^{5x$

Set x = 0

$f(0) = 52477(0.97)^{5*0} = 52477(0.97)^0 =52477*1= 52477$

This is false because the calculated value of f(0) does not correspond to the given value

From the computations above, only (c) $f(x) = 63000(0.97)^x$ is true

4 0

3 years ago

in circle O the radius is 4ft and the measure of minor arc ab is 120 degrees find the length of minor arc ab to the nearest inte

KIM [24]

Answer:

$8\:\text{ft}$

Step-by-step explanation:

The length of the arc is proportional to the degree measure it in encompasses. Since there are 360 degrees in a circle and the arc is 120 degrees, the arc's length will be $\frac{120}{360}=\frac{1}{3}$ of the circle's length (circumference).

The circumference of a circle is given by $2\pi r$ , where $r$ is the radius of the circle. Therefore, the circumference of the circle is $2\pi(4)=8\pi$ . As we found earlier, the length of the arc is $\frac{1}{3}$ of this circumference. Therefore, the arc's length is $8\pi\cdot \frac{1}{3}=\frac{8\pi}{3}$ .