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3 years ago

Area of a Circle

Mathematics

2 answers:

Shkiper50 [21]3 years ago

7 0

Answer:

i) Diameter = 38 meters

ii) Radius = 19 meters

iii) Area = 361 m²

Step-by-step explanation:

i) According to the formula given in the question, the formula for the circumference, C = πD

C = 120 meters

Diameter, D = 120/π

D = 38 meters

ii) The value of the radius

Radius, r = (Diameter, D)/2

r = 38/2

r = 19 meters

iii) What is the approximate area

From the question, the expression for the area is A = r²

Area, A = 19²

A = 361 meters

Cloud [144]3 years ago

4 0

Answer:

The diameter of the pond is 38 m.

The radius of the pond is 19 m.

The area of the pond is 361 m^2.

Step-by-step explanation:

We know that the circumference C of a circle is equal to

$C=\pi D$

In this case, C is equal to 120 m.

The diameter is then:

$D=C/\pi=120/3.14=38.21\approx 38$

Rounded to the nearest whole number, the diameter is D=38 metres.

The radius is equal to half the diameter, so the radius of this pond is R=19 metres.

$R=D/2=38/2=19$

The area can be calculated from the radius as:

$A=r^2=19^2=361$

The area is 361 m^2

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Read 2 more answers

Given y = log3(x + 4), what is the range?

lora16 [44]

Answer:

The range is all real numbers.

The domain is all reals numbers that are greater than -4.

Step-by-step explanation:

$y=\log_3(x+4)$ only exists when $x+4$ is positive.

You can take the log of a negative or 0 number.

So $x+4>0$ implies $x>-4$ . (I just subtract 4 on both sides.)

So the domain is x>-4. You should see this also when you graph the curve that the curve only exist to the right of -4.

Now the range. The range is where the curve exist for the y-values.

The equivalent exponent form of $y=\log_3(x+4)$ is $3^{y}=x+4$

We can solve this for x be subtract 4 on both sides:

$x=3^y-4$

Now here y can be anything; there are no restrictions on the exponent.

Also if you look at the graph of $y=\log_3(x+4)$ you should see every y getting hit by the curve (look down to up; use the y-axis as a guide).

Let's think about the inverse I found above a little more (I'm going to swap x and y).

$y=3^x-4$ .

If we look at the domain and range of this we can just swap it to get the domain and range of $y=\log_3(x+4)$ .

$y=3^x-4$ is an exponential function of 3^x that has been moved down 4 units.

The range since it has been moved down 4 units is $(-4,\infty)$ .

The domain of an exponential function is all real numbers. There are no restrictions on what you can plug in for x.

So swapping these to find the domain and range of $y=\log_3(x+4)$ :

Domain: $(-4,\infty)$

Range : $(-\infty,\infty)$

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3 years ago

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nata0808 [166]

Answer:

Hi there!

Your answer is:

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Step-by-step explanation:

The square root of 2.25 = 1.5

Check your work!

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Hope this helps!

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