Answer:
r = 8
Step-by-step explanation:
Given that M is directly proportional to r² then the equation relating them is
M = kr² ← k is the constant of proportionality
To find k use the condition when r = 2 , M = 14
k =
=
= ![\frac{7}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B2%7D)
M = r² ← equation of proportion
When M = 224, then
224 =
r² ← multiply both sides by 2
7r² = 448 ( divide both sides by 7 )
r² = 64 ( take the square root of both sides )
r =
= 8
have wonderful day
<h2>
Basic Trigonometric Ratios</h2>
These are the three basic trigonometric ratios:
- The sine ratio:
![\sin(\theta)=\dfrac{opposite}{hypotenuse}](https://tex.z-dn.net/?f=%5Csin%28%5Ctheta%29%3D%5Cdfrac%7Bopposite%7D%7Bhypotenuse%7D)
- The cosine ratio:
![\cos(\theta)=\dfrac{adjacent}{hypotenuse}](https://tex.z-dn.net/?f=%5Ccos%28%5Ctheta%29%3D%5Cdfrac%7Badjacent%7D%7Bhypotenuse%7D)
- The rangent ratio:
![\tan(\theta)=\dfrac{opposite}{adjacent}](https://tex.z-dn.net/?f=%5Ctan%28%5Ctheta%29%3D%5Cdfrac%7Bopposite%7D%7Badjacent%7D)
Here, 'opposite' or adjacent are referring to the legs in relation to one of the interior angles of the triangle, θ.
We can use these ratios to help us solve for side lengths or angles, depending on what information is given to us and what information we must solve for.
<h2>Solving the Question</h2>
We're given:
- The indicated angle (θ) measures 70°
- The adjacent side measures 5.7 units
- We must solve for the other leg, which is the 'opposite' side
Because this question involves the adjacent and the opposite, we can use the tangent ratio to find the answer.
![\tan(\theta)=\dfrac{opposite}{adjacent}](https://tex.z-dn.net/?f=%5Ctan%28%5Ctheta%29%3D%5Cdfrac%7Bopposite%7D%7Badjacent%7D)
⇒ Plug in the given information:
![\tan(70^\circ)=\dfrac{opposite}{5.7}](https://tex.z-dn.net/?f=%5Ctan%2870%5E%5Ccirc%29%3D%5Cdfrac%7Bopposite%7D%7B5.7%7D)
⇒ Multiply both sides by 5.7 to isolate 'opposite:
![5.7\tan(70^\circ)=opposite\\opposite = 15.66062\dots](https://tex.z-dn.net/?f=5.7%5Ctan%2870%5E%5Ccirc%29%3Dopposite%5C%5Copposite%20%3D%2015.66062%5Cdots)
⇒ Round to the nearest tenth:
![opposite=15.7](https://tex.z-dn.net/?f=opposite%3D15.7)
<h2>Answer</h2>
The length of the other leg is 15.7 units.
NO!
1 yd=3 ft
36*3=108
108+2=110
114>110, therefore no
First you have to do what's in the parenthesis. So 18-15 is 3.
9÷3+4
There are no exponents so you skip that step.
There is no multiplication so you skip that step.
Now, divide 9 by 3. The answer is 3.
Now add 3+4.
The final answer is 7.