Answer:
The approximated length of arc x is 4 inches ⇒ C
Step-by-step explanation:
- The diameter of the outer circle is 28 inches
- There is a boundary with width 2 inches
That means the diameter of the inner circle is less than the diameter of the outer circle by 4 inches (2 in from each side)
- The diameter of the inner circle = 28 - 4 = 24 inches
The circumference of the inner circles formed from 20 congruent arcs of length x inches
- The circumference of the inner circle = 20 x
Now let us find x
The formula of the circumference of a circle is C = π d, where d is the diameter of the circle
∵ The diameter of the inner circle is 24 inches
∴ d = 24
∴ C = 24 π
∵ C = 20 x
- Equate 20 x by 24 π
∴ 20 x = 24 π
- Divide both sides by 20
∴ x = 3.769911184
- Round it to the nearest unit
∴ x ≅ 4
The approximated length of arc x is 4 inches
Answer: 22.5
Step-by-step explanation:
9514 1404 393
Answer:
a) 5 cm
b) 8 cm
c) 9 m
Step-by-step explanation:
It can be worthwhile to work the last attachment (a) first, since these are all variations of the same triangle.
The Pythagorean theorem tells you the sum of the squares of the legs is the square of the hypotenuse.
<u>Problem 6a</u>:
3² +4² = x² . . . . fill in the given numbers; all measures in cm
9 + 16 = x² . . . . simplify exponents
25 = x² . . . . . . . simplify sum
x = √25 = 5 . . . take the square root.
x = 5 cm . . . . . . apply units
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Note that this triangle is a 3-4-5 right triangle. That is a set of side lengths (ratios) that is useful to remember. In this problem set, you see it again immediately.
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<u>Problem 6b</u>:
Shortest-to-longest, the side ratios of the given triangle are ...
6 : x : 10
For some x', this is ...
3 : x' : 5 . . . . . . . . . . . . . matches a 3-4-5 triangle with x' = 4
The scale factor is 6/3 = 10/5 = 2, so we have ...
x = 2·x' = 2·4 = 8
x = 8 cm . . . . . with units
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<u>Problem 6c</u>:
The side ratios are ...
x : 12 : 15 which reduces to x' : 4 : 5
This matches a 3-4-5 triangle with x' = 3, and a scale factor of 12/4 = 15/5 = 3.
Then ...
x = 3·x' = 3·3 = 9
x = 9 m . . . . . with units
Answer:
-4
Step-by-step explanation:
Consider (-4, -2) and (-2, -10).
Change in x: 2
Change in y: -8
Slope = (change in y)/(change in x) = -4
The height of the rectangular prism is 5 cm
The rectangular prism has a base area of 16 cm².
<h3>Volume of rectangular prism;</h3>
Therefore,
V = 16h
where
h = height of the rectangular prism
Another box has a volume of 320 cm³ and holds 4 of the rectangular prism with no extra space.
Therefore,
4(16h) = 320
64h = 320
divide both sides by 64
64h / 64 = 320 / 64
h = 5
Therefore, the height of the rectangular prism is 5 cm
learn more on rectangular prism here: brainly.com/question/26187572
