Answer: 42 cm3
Step-by-step explanation:
<span>y=−1/3x+1
</span>x = -6, y = −1/3(-6) +1 = 3<span>
x = -3, y = </span>−1/3(-3) +1 = 2<span>
x = 0, y = 1
</span>x = 3, y = −1/3(3) +1 = 0
x = 6, y = −1/3(6) +1 = -1
<span>
Table
x y
-6 3
-3 2
0 1
3 0
6 -1
</span>
So for the 40-40-90 degree triangle, whenever the two legs are x values, then the hypotenuse is x value times the square root of 2.
--> a changed into a√2
√2 changed in √2 * √2
= 2
So the hypotenuse of the 40-40-90 degree triangle is 2.
Now for the 30-60-90 degree triangle, the smallest leg with the value of x is then changed to the value of x√3 if finding the longer leg.
-> a is changed to a√3
2 is changed into 2√3
So, y is 2√3 or approximately 3.46 units.
Answer:
![r = \sqrt[3]{\frac{3V}{4 \pi}}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B3V%7D%7B4%20%5Cpi%7D%7D)
Step-by-step explanation:
From the formula of volume of a sphere we have to isolate "r" on one side of the equation i.e. we have to make "r" the subject of the equation.
![V=\frac{4}{3} \pi r^{3}\\\\ \text{Multiplying both sides by 3/4 we get}\\\\\frac{3V}{4} = \pi r^{3}\\\\ \text{Dividing both sides by } \pi \\\\ \frac{3V}{4 \pi} = r^{3}\\\\\text{Takeing cube root of both sides}\\\\\sqrt[3]{\frac{3V}{4 \pi}} = r](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E%7B3%7D%5C%5C%5C%5C%20%5Ctext%7BMultiplying%20both%20sides%20by%203%2F4%20we%20get%7D%5C%5C%5C%5C%5Cfrac%7B3V%7D%7B4%7D%20%3D%20%5Cpi%20r%5E%7B3%7D%5C%5C%5C%5C%20%5Ctext%7BDividing%20both%20sides%20by%20%7D%20%5Cpi%20%5C%5C%5C%5C%20%5Cfrac%7B3V%7D%7B4%20%5Cpi%7D%20%3D%20r%5E%7B3%7D%5C%5C%5C%5C%5Ctext%7BTakeing%20cube%20root%20of%20both%20sides%7D%5C%5C%5C%5C%5Csqrt%5B3%5D%7B%5Cfrac%7B3V%7D%7B4%20%5Cpi%7D%7D%20%3D%20r)
Therefore:
