find the width of radius r if the width w of the shaded region is 2cm and its area is 176cm^2, use 22/7 for pi (its a full circle)
Answers
The area of a shape is the amount of space it can occupy.
The value of r is 13
From the question (see attachment), we have:
[tex]\mathbf{A =176}[/tex] --- area of the shaded region
[tex]\mathbf{w = 2}[/tex] --- the width of the shaded region
The area of the complete circle would be:
[tex]\mathbf{A_1 =\pi (r + w)^2}[/tex]
The area of the small circle is:
[tex]\mathbf{A_2 =\pi r^2}[/tex]
So, the area of the shaded region is:
[tex]\mathbf{A = A_1 - A_2}[/tex]
Substitute known values
[tex]\mathbf{176 =\pi (r + w)^2 - \pi r^2 }[/tex]
Substitute 2 for w
[tex]\mathbf{176 =\pi (r + 2)^2 - \pi r^2 }[/tex]
Expand
[tex]\mathbf{176 =\pi (r^2 + 4r + 4) - \pi r^2 }[/tex]
Open brackets
[tex]\mathbf{176 =\pi r^2 + 4\pi r + 4\pi - \pi r^2 }[/tex]
Cancel out line terms
[tex]\mathbf{176 =4\pi r + 4\pi }[/tex]
Divide through by 4
[tex]\mathbf{44 =\pi r + \pi }[/tex]
Factor out pi
[tex]\mathbf{44 =\pi(r+ 1) }[/tex]
Divide through by pi
[tex]\mathbf{r + 1= \frac{44}{ \pi} }[/tex]
Substitute 22/7 for pi
[tex]\mathbf{r + 1= \frac{44}{ 22/7} }[/tex]
Using a calculator, we have
[tex]\mathbf{r + 1= 14}[/tex]
Solve for r
[tex]\mathbf{r= 14 -1}[/tex]
[tex]\mathbf{r= 13}[/tex]
Hence, the value of r is 13
Read more about areas of circles at:
https://brainly.com/question/23328170
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Answers
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Step-by-step explanation:
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Not sure about the answer but I hope this helped a bit
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Step-by-step explanation:
Here is how I got it!
First, you will have to borrow the 520,000 from the word problem.
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The 3 is the number of years, n is the nearest $ answer.
--
First, do [tex]0.19^3[/tex]
[tex]0.19*0.19*0.19=0.006859[/tex]
(Again, that's a crazy number!)
--
With 0.006859, multiply it with 520,000
[tex]520,000*0.006859=3566.68[/tex]
3566.68 is technically (in money) $3,566.68 (with .68 being sixty-eight cents).
--
Finally, it states to answer to the nearest $.
Just round up the .68 to 1 dollar which will just add one more dollar to 3,566
[tex]3,566.32[/tex] ⇒ [tex]3,567.00[/tex] (since .32 is below .50, you can't round it UP)
Add you $ symbol
With the result being: $3,567.00
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(1st picture): y=2x+3 and y=x+5
(2nd picture): y=4x+2 and y =3x+2
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See the graph given below the solution is the point (5,2).
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See the graph given below the solution is the point (7,3).
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See the graph given below the solution is the point (2,7).
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(6) systems of equations
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See the graph given below the solution is the point (3,5).
Therefore, the solutions to the system of equations are given below in the figure.
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Answer:6200
Step-by-step explanation:
:We round the number up to the nearest hundred if the last two digits in the number are 50 or above.
: We round the number down to the nearest hundred if the last two digits in the number are 49 or below.
: If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.
:In this case, Rule B applies and 6248 rounded to the nearest hundred is:
6200
Answer: the answer is 6,200 hope it helps!
Step-by-step explanation: