Answer:
c
Step-by-step explanation:
Answer:
![x^{\frac{21}{4} }](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7B21%7D%7B4%7D%20%7D)
Step-by-step explanation:
Given expression is:
![(\sqrt[8]{x^7} )^{6}](https://tex.z-dn.net/?f=%28%5Csqrt%5B8%5D%7Bx%5E7%7D%20%29%5E%7B6%7D)
First we will use the rule:
![\sqrt[n]{x} = x^{\frac{1}{n} }](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7Bn%7D%20%7D)
So for the given expression:
![\sqrt[8]{x^{7}}=(x^{7} )^{\frac{1}{8} }](https://tex.z-dn.net/?f=%5Csqrt%5B8%5D%7Bx%5E%7B7%7D%7D%3D%28x%5E%7B7%7D%20%29%5E%7B%5Cfrac%7B1%7D%7B8%7D%20%7D)
We will use tha property of multiplication on powers:
![=x^{7*\frac{1}{8} }](https://tex.z-dn.net/?f=%3Dx%5E%7B7%2A%5Cfrac%7B1%7D%7B8%7D%20%7D)
![= x^{\frac{7}{8} }](https://tex.z-dn.net/?f=%3D%20x%5E%7B%5Cfrac%7B7%7D%7B8%7D%20%7D)
Applying the outer exponent now
![(x^{\frac{7}{8} })^6](https://tex.z-dn.net/?f=%28x%5E%7B%5Cfrac%7B7%7D%7B8%7D%20%7D%29%5E6)
![= x^{\frac{7}{8}*6 } \\= x^{\frac{42}{8} }\\= x^{\frac{21}{4} }](https://tex.z-dn.net/?f=%3D%20x%5E%7B%5Cfrac%7B7%7D%7B8%7D%2A6%20%7D%20%5C%5C%3D%20x%5E%7B%5Cfrac%7B42%7D%7B8%7D%20%7D%5C%5C%3D%20x%5E%7B%5Cfrac%7B21%7D%7B4%7D%20%7D)
For these questions it is asking you to convert different measurements.
For the first part,
You must convert 10 kilometres to meters
Or 500 meters to kilometres
For this example I will covert 500 meters to kilometres
1000 meters = 1 kilometer
So 500 meters is 0.5 kilometres or half a kilometer
So on the first day you ride 10 kilometres and increase by 0.5 kilometres a day that means you increase by 1 kilometer every two days
The question is asking how many days until you get to 15 kilometres well
15-10=5
5x2 =10 so the answer to the first part is 10 days
In the second part you have to convert again I am going to convert kilometres to meters this time
We know 1km = 1000m
So you times the kilometer by 1000 to get the meters
0.75 x 1000 = 750
So you start with 7500 and increase by 750 every day
The question asks you the total after 3 days so we must find out each day and add them up
1st day: 7500
2nd day: 7500+750=8250
3rd day: 8250+750=9000
Now we must add them together so
7500+8250+9000=24750
So the answer to this part is 24750 meters
The last part is asking you to compare the programs so let’s start with training program A
20-10=10
10x2= 20
So A is 20 days
Training program B:
We know from previous questions that on the third day you do 9000 meters so we must carry on from there
4th day: 9000+750=9750
5th day: 9750 +750=10500
6th day: 10500 + 750=11250
7th day: 11250 + 750 = 12000
As you can see there is a pattern here on the 3rd day we are on 9000 and on the 7th day we are on 12000 that means it has increased by 3000 in 4 days this is because 750 x 4 = 3000
This means we know 18000 is the 15th day
We will carry on from here
16th day: 18000+750=18750
17th day: 18760+750=19500
18th day: 19500+750=20250
Here we have gone over 200000 which is 20 km on the 18th day meaning training program B is quicker
Answer:
2
Step-by-step explanation:
Rise / Run
= 4/2
= 2