If you are in college, this question is likely done with calculus.
a = 12
k = 0.2
v(x) = 0 at the maximum after differentiation
V(x) = kx(a - x)
The easiest way to do this is to remove the brackets.
V(x) = akx - kx^2 Substitute the constants
V(x) = 12*0.2*x - 0.2x^2
V(x)/dx = 2.4 - 0.4x = 0 at the maximum
2.4 - 0.4x = 0
0.4x = 2.4
x = 2.4/0.4
x = 6
If you don't know any calculus yet, you can do this by completing the square.
Answer:
Graph a dot at the coordinates (0, 5) and (1, 0). Afterwards, connect the two dots!
Step-by-step explanation:
You just want a line that has a y-intercept of 5 and an x-intercept of 1. This is quite easy to make by just plotting the x-intercept at 1, thus (1, 0) and plotting the y-intercept at 5, thus (0, 5), and connecting the two dots and extending them to make a line.
Answer:
The value for 20th term is 10.
Step-by-step explanation:
First, you have to find the formula for the sequence.
Given that the formula of this sequence is an = -10n + 210. Next, you have to find 20th term :
(Correct me if I am wrong)
From the title of your worksheet, you have to convert improper fractions to proper fractions. So, you see those two numbers on the top and the bottom separated by a line? Those are fractions. For example, 12/4 is an improper fraction.(I can't use the exact 'line' that separates it as its not on my keyboard, so I'm just using '/'.) In 12/4, 12 is 'on top'. The number on top is the numerator. And the number on the bottom, 4, is the denominator. 12/4 is an improper fraction as the numerator is bigger than the denominator. So, you can divide 12 by 4, giving you 3. 3 is a whole number as 12 could be divided by 4 without remainder, so that's your answer if you wanted to convert it into a proper fraction. That's just an example, though. Another example for things that have remainder when divided; let's use 13/4 for this example. 13 can't be divided by 4 perfectly, so you use the closest number that can be divided by 4, which is 12. But what happens to the the number left after using 12? 13-12=1. That's where the fraction comes along. The denominator was 4 in 13/4 so the proper fractions that you get is 3(the whole number) and 1/4(the one left after using 12).
So, for that example, your answer's 3 1/4.(note that the whole number should be bigger than the fraction when you write it out.)
Sorry for this really long answer. I didn't want to just give you the answer without you understanding it.
Anyway, for your questions in your worksheet.
I'm starting from question 1 and not the example question in your worksheet.
1) 4 5/8
2) 10 3/10
3) 6 2/4
Or in simplest form if required: 6 1/2
4) 3 1/3
5) 5 3/8
6) 3 6/7
7) 10 9/10
8) 7 1/3
9) 7 4/5
10) 2 4/5
11) 4 1/2
12) 5 1/3
13) 9 2/8
Or in simplest form if required: 9 1/4
14) 5 2/3
15) 8 9/10
16) 8 3/4
17) 10 1/6
18) 1 2/6
19) 7 3/6
20) 10 7/10
( I put some spaces between the whole numbers and fractions so that it's not too complicating.)
I apologize if I made any mistakes ^^;;
Happy learning! :)
