A). Pi m
Explanation:
Arc length formula:
Arc length = (Ø/360°) * 2*Pi*r
Ø = given angle (degrees)
r = radius
Plug given numbers in:
(45°/360°)* 2* Pi * 4
This will give you the answer of Pi
The value of 'x' is 24.2 and the value of 'y' is 46.5.
To solve this, we do the following steps.
<u>Step 1:</u> Divide 'y' into 2 parts, 'a' and 'b'. 'a' would be the lower leg of the 45°-45°-90° triangle, while 'b' is the lower leg of the 30°-60°-90° triangle.<em>
</em><u>Step 2:</u> Given the hypotenuse (34) of the 30°-60°-90° triangle, solve for 'b' using the cosine of 30°.
cos30° = b/34 [adjacent over hypotenuse]
b = 34cos30° [cross-multiply]
b = 29.4
<u>Step 3:</u> Solve for the 90° leg (the side opposite the 30° angle) using the Pythagorean Theorem. We will name this leg "h" (cuz height).
l² + l² = hyp²
29.4² + h² = 34²
h² = 1156 - 864.36
√h² = √291.64
h = 17.1
<u>Step 4:</u> Solve for 'x' by using the 45°-45°-90° triangle ratio (1:1:√2). √2 would be the hypotenuse of the 45°-45°-90° triangle, while 1 would be both congruent legs.
Side 'h' is one of the legs; side 'a' is the other. Since these legs are congruent, 'a' also measures 17.1. Now all we need to do is solve for 'x', which is our hypotenuse. To do this, we simply multiply the measure of side 'h' or 'a' by √2.
x = 17.1 × √2
x = 24.2
<u>Step 5:</u> Now that we got the value of 'x', solve for 'y' by adding the measures of sides 'a' and 'b' together.<em>
</em><u /> y = a + b
y = 17.1 + 29.4
y = 46.5
And there you have it! <em>Hope this helps.</em>
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</em>
Answer:
Carla ran 0.1 miles per minute.
Step-by-step explanation:
To solve this, we need to use the distance formula.
The formula is d=rt, where d is the distance traveled, r is the rate in which the distance is traveled, and t is the amount of time it took to go that distance. So lets plug it all in.
d=rt
3=(r)(30)
Now, we need to do the inverse of multiplying 30 to both sides, which would be the same as dividing by 30 on both sides.
3/30=(r)(30/30)
0.1=r
The rate is 0.1. Carla ran 0.1 miles per minute.