Answer:
Part 1) The exact value of the arc length is \frac{25}{6}\pi \ in
Part 2) The approximate value of the arc length is 13.1\ in
Step-by-step explanation:
ind the circumference of the circle
The circumference of a circle is equal to
C=2\pi r
we have
r=5\ in
substitute
C=2\pi (5)
C=10\pi\ in
step 2
Find the exact value of the arc length by a central angle of 150 degrees
Remember that the circumference of a circle subtends a central angle of 360 degrees
by proportion
\frac{10\pi}{360} =\frac{x}{150}\\ \\x=10\pi *150/360\\ \\x=\frac{25}{6}\pi \ in
Find the approximate value of the arc length
To find the approximate value, assume
\pi =3.14
substitute
\frac{25}{6}(3.14)=13.1\ in
Correct answer is B bc it extends the range of her times, creating variation.
Step-by-step explanation for Surface Area:
So, to find the surface area, you use the formula: <u />
I'll explain what each part means and why they are like that. (btw, it would help you more if you looked at a rectangular prism I added while you read the explanation :) )
First of all, you do <em>lw</em> because that is the base of the right rectangular pyramid (since you're finding the surface area, you need to find the area of all the surfaces on the pyramid)
You add because now you're trying to find the triangular side with the length. You multiply the length, because that's how wide the "triangle" is. You do the square root because of the pythagorean theorem (since you're using the hypotenuse times the length to find that side). The width is divided by two, because as you can see in my attachments, that's how far away the height is from the length (if you look at the base, see where the height line drops in comparison to the length). (look at my second screenshot)
You add for the same reason, except dealing with the width. You're finding the side with the width. You multiply the width by the hypotenuse of the right triangle (look at the third screenshot i attached). The length is divided by two because that's the distance between the bottom of the height line to the w.
I do believe that this should explain the meaning behind each piece of the formula (I'm not sure this is what you asked for lol but it does make understanding it a little easier, I think). To get the answer, you just substitute each variable with those values. So...
A ≈ 183.3
As for the Volume:
. I'm not 100% on why it's divided by three, but with any volume, you're always going to end up with an answer that is in cubed units. So that explains the three variables in the numerator. I'd like to think the three just has to do with the <em>three</em> variables, but I don't know. Give me the points if you'd like? I don't think this is a proper explanation though.
Good luck!
Answer:
Step-by-step explanation:
The given number,
38,332,521,
For writing the number as the product of a single digit and an exponent of 10,
We need to move decimal left side 7 times,
Thus, the exponent of 10 in the resultant number is 7,
Also, after shifting the decimal left side 7 times the resultant number is 3.8332521,
i.e.
X + 45 = 76
Isolate the x, what you do to one side, you do to the other, because there is a equal sign
x + 45 (-45) = 76 (-45)
x = 76 - 45
x = 31
31 is your answer
hope this helps