Attached is a Venn diagram of your problem.
Knowing how many likes all three will help. You know that 10 students like all three.
Rock and Jazz only:
16 like rock and jazz while 10 like all three. To get how many like jazz only, subtract 10 from 16.
16-10 = 6
Rock and Classical only:
13 like rock and classical while 10 like all three. To get how many like jazz only, subtract 10 from 13.
13-10 = 3
Jazz and classical only:
12 like jazz and classical while 10 like all three. To get how many like jazz only, subtract 10 from 12.
12-10 = 2
Now with that data you fill up the 4 intersecting areas. To get the outer, just remember that all areas within a circle should add up to the first assumption.
27 rock
24 classical
28 Jazz
All numbers in the rock circle should add up to 27.
All numbers in the classical circle should add up to 24.
All numbers in the Jazz circle should add up to 28.
Rock:
3+10+6+x = 27
19+x=27
x = 27-19
x= 8
Classical:
3+10+2+x = 24
15 + x = 24
x = 24-15
x = 9
Jazz:
10+6+2+x = 28
18 + x = 28
x = 28 - 18
x = 10
In summary: 8 liked only Rock, 9 liked only Classical, 10 liked only Jazz.
Answer:
The given function is
f(x)=cos 3x-7 x²+ 4x
f'(x)=-3 sin 3 x-14 x+4
When you will draw the graph of the function , you will find that root of the function lie between (-1,0).
Consider initial root as,
![x_{0}=0](https://tex.z-dn.net/?f=x_%7B0%7D%3D0)
Using Newton method to find the roots of the equation
![x_{n+1}=x_{n}-\frac{f{x_n}}{f'{x_{n}}}\\\\x_{1}=x_{0} - \frac{cos 3x_{0}-7 x_{0}^2+ 4x_{0}}{-3 sin 3 x_{0}-14 x_{0}+4}\\\\x_{1}=-\frac{\cos 0^{\circ}-0+0}{-3 \times 0-0+4}\\\\x_{1}=\frac{-1}{4}\\\\x_{1}= -0.25\\\\x_{2}=x_{1} - \frac{cos 3x_{1}-7 x_{1}^2+ 4x_{1}}{-3 sin 3 x_{1}-14 x_{1}+4}\\\\x_{2}=-0.25 -\frac{cos (-0.75)-7\times (0.0625)- 1}{-3 sin (-0.75)+3.50+4}\\\\x_{2}= -0.176054](https://tex.z-dn.net/?f=x_%7Bn%2B1%7D%3Dx_%7Bn%7D-%5Cfrac%7Bf%7Bx_n%7D%7D%7Bf%27%7Bx_%7Bn%7D%7D%7D%5C%5C%5C%5Cx_%7B1%7D%3Dx_%7B0%7D%20-%20%5Cfrac%7Bcos%203x_%7B0%7D-7%20x_%7B0%7D%5E2%2B%204x_%7B0%7D%7D%7B-3%20sin%203%20x_%7B0%7D-14%20x_%7B0%7D%2B4%7D%5C%5C%5C%5Cx_%7B1%7D%3D-%5Cfrac%7B%5Ccos%200%5E%7B%5Ccirc%7D-0%2B0%7D%7B-3%20%5Ctimes%200-0%2B4%7D%5C%5C%5C%5Cx_%7B1%7D%3D%5Cfrac%7B-1%7D%7B4%7D%5C%5C%5C%5Cx_%7B1%7D%3D%20-0.25%5C%5C%5C%5Cx_%7B2%7D%3Dx_%7B1%7D%20-%20%5Cfrac%7Bcos%203x_%7B1%7D-7%20x_%7B1%7D%5E2%2B%204x_%7B1%7D%7D%7B-3%20sin%203%20x_%7B1%7D-14%20x_%7B1%7D%2B4%7D%5C%5C%5C%5Cx_%7B2%7D%3D-0.25%20-%5Cfrac%7Bcos%20%28-0.75%29-7%5Ctimes%20%280.0625%29-%201%7D%7B-3%20sin%20%28-0.75%29%2B3.50%2B4%7D%5C%5C%5C%5Cx_%7B2%7D%3D%20-0.176054)
![x_{3}=x_{2} - \frac{cos 3x_{2}-7 x_{2}^2+ 4x_{2}}{-3 sin 3 x_{2}-14 x_{2}+4}\\\\x_{3}=-0.176054 -\frac{cos (3\times -0.176054)-7\times (-0.176054)^2+4 \times -0.176054}{-3 sin (-0.176054)-14 \times (-0.176054)+4}\\\\x_{3}= -0.1689](https://tex.z-dn.net/?f=x_%7B3%7D%3Dx_%7B2%7D%20-%20%5Cfrac%7Bcos%203x_%7B2%7D-7%20x_%7B2%7D%5E2%2B%204x_%7B2%7D%7D%7B-3%20sin%203%20x_%7B2%7D-14%20x_%7B2%7D%2B4%7D%5C%5C%5C%5Cx_%7B3%7D%3D-0.176054%20-%5Cfrac%7Bcos%20%283%5Ctimes%20-0.176054%29-7%5Ctimes%20%28-0.176054%29%5E2%2B4%20%5Ctimes%20-0.176054%7D%7B-3%20sin%20%28-0.176054%29-14%20%5Ctimes%20%28-0.176054%29%2B4%7D%5C%5C%5C%5Cx_%7B3%7D%3D%20-0.1689)
So, root of the equation is
=0.1688878
=0.1689(approx)
Answer:
5(4+6)
5(6+4)
(45+6)-1
Step-by-step explanation:
Answer:
420 miles
Step-by-step explanation:
To start, let's find the distance between A and B when they both start moving. This is two hours after the car starts moving, and that is 2*60=120 miles. There are 620 miles total, so they are 500 miles apart when they both start moving. Notice that they are moving in opoposite directions, so every hour they will get 60+40=100 miles closer to each other, so it will take 500/100=5 hours to meet. To find the distance from city A, we need to find how far the car moved, which is just 2+5=7 hours times 60 mph or 420 miles away from city A.
Answer:
add 10 which gives yoy 5x=10 divode by 5 that givdz u 2