ANSWER
![3 {x}^{2} y \sqrt[4]{y}](https://tex.z-dn.net/?f=3%20%7Bx%7D%5E%7B2%7D%20y%20%5Csqrt%5B4%5D%7By%7D%20)
EXPLANATION
We want to simplify:
![\sqrt[4]{81 {x}^{8} {y}^{5} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B81%20%7Bx%7D%5E%7B8%7D%20%7By%7D%5E%7B5%7D%20%20%7D%20)
We can split the radical sign to obtain:
![\sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{5} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B81%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7B%20%7Bx%7D%5E%7B8%7D%20%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7B%20%7By%7D%5E%7B5%7D%20%7D%20)
Or
![\sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4} \times y}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B81%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7B%20%7Bx%7D%5E%7B8%7D%20%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7B%20%7By%7D%5E%7B4%7D%20%20%5Ctimes%20y%7D%20)
![\sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B81%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7B%20%7Bx%7D%5E%7B8%7D%20%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7B%20%7By%7D%5E%7B4%7D%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7By%7D%20)
![\sqrt[4]{ {3}^{4} } \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%20%7B3%7D%5E%7B4%7D%20%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7B%20%7Bx%7D%5E%7B8%7D%20%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7B%20%7By%7D%5E%7B4%7D%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7By%7D%20)
Recall that:
![\sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} }](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7B%20%7Ba%7D%5E%7Bm%7D%20%7D%20%20%3D%20%20%7Ba%7D%5E%7B%20%5Cfrac%7Bm%7D%7Bn%7D%20%7D%20%20)
![{3}^{4 \times \frac{1}{4} } \times {x}^{8 \times \frac{1}{4} } \times {y}^{4 \times \frac{1}{4} }\times \sqrt[4]{y}](https://tex.z-dn.net/?f=%7B3%7D%5E%7B4%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B4%7D%20%7D%20%20%5Ctimes%20%20%7Bx%7D%5E%7B8%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%7D%20%20%5Ctimes%20%20%7By%7D%5E%7B4%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B4%7D%20%7D%5Ctimes%20%20%5Csqrt%5B4%5D%7By%7D%20)
![3 {x}^{2} y \sqrt[4]{y}](https://tex.z-dn.net/?f=3%20%7Bx%7D%5E%7B2%7D%20y%20%5Csqrt%5B4%5D%7By%7D%20)
Answer:
The magnitude of the boat's velocity is 5.66 m/s
Step-by-step explanation:
Given;
Radius of curvature of the circular path, r = 40 m
speed of the boat, v = 0.8 t m/s
The magnitude of the boat's velocity when it has traveled 20 m is ?
a = dv / dt,
v = 0.8 t (differentiate with respect to t)
dv / dt = 0.8 = a
thus, a = 0.8 m/s²
If the boat starts from rest, initial velocity, u = 0
Apply kinematic equation, to solve for the boat velocity at 20 m
v² = u² + 2as
v² = 0 + 2 x 0.8 x 20
v² = 0 + 32
v² = 32
v = √32
v = 5.66 m/s
Therefore, the magnitude of the boat's velocity when it has traveled 20 m is 5.66 m/s
Answer: 7/8
Step-by-step explanation: Notice that 1/2 and 3/8 are unlike fractions. Our first when adding unlike fractions is to get a common denominator.
The common denominator of 2 and 8 will be the least common multiple of 2 and 8 which is 8.
To get an 8 in the denominator of 1/2, we multiply the numerator and the denominator by 4 which gives us 4/8.
Notice that 3/8 already has an 8 in the denominator so we leave it how it is.
Now we are adding like fractions.
To add like fractions, or fractions that have the same denominator, simply add the numerators and keep the original denominator.
So here, if we add the numerators we have 4 + 3 which gives us 7 and we put this over our original denominator which is 8 and we have our answer. Also, notice that 7/8 is in lowest terms so it's our final answer.
This means that 3/8 + 1/2 = 7/8
The scale factor was D. 4. We can figure this out by multiplying 3 by 4 to get 12 and 1 by 4 which is 4 to get the dimensions of the larger triangle.
I hope this helped! :-)
Answer:
3 1/4 + 2 1/3 = 67 / 12 = 57 1/2
Step-by-step explanation:
Conversion a mixed number to a improper fraction: 3 1/4 = 3 · 4 + 1
4
= 13
4
Conversion a mixed number to a improper fraction: 2 1/3 = 2 · 3 + 1
3
= 7
3
Add: 13
4
+ 7
3
= 13 · 3
4 · 3
+ 7 · 4
3 · 4
= 39
12
+ 28
12
= 39 + 28
12
= 67
12