Mmmm! I love apple cider punch this time of year, and so do all my neighbors. My recipe calls for
two quarts of apple cider, three teaspoons of cinnamon, and one pint of lemon-lime soda. This will
make enough for eight people to share. In my neighborhood, however, there are 72 people. How much
do I need of each ingredient to make enough for my whole neighborhood to share?

Do you mean the 5th roots of 1? Or the 5th roots of 1^(1/5), i.e. the 5th roots of the 5th roots of 1?

I assume you mean the former. To begin with,

1 = exp(0°i ) = cos(0°) + i sin(0°)

Take the 5th root, i.e. (1/5)th power of both sides, so that by DeMoivre's theorem,

1^(1/5) = [ cos(0°) + i sin(0°) ]^(1/5)

1^(1/5) = cos((0° + 360°n)/5) + i sin((0° + 360°n)/5)

where n = 0, 1, 2, 3, or 4. Then 1^(1/5) has the 5 possible values,

• cos(0°/5) + i sin(0°/5) = 1

• cos(360°/5) + i sin(360°/5) = cos(72°) + i sin(72°)

• cos(720°/5) + i sin(720°/5) = cos(144°) + i sin(144°)

• cos(1080°/5) + i sin(1080°/5) = cos(216°) + i sin(216°)

• cos(1440°/5) + i sin(1440°/5) = cos(288°) + i sin(288°)

If you wish, or are required to, you can go on to write these in terms of radicals by expanding cos(5x) and sin(5x) (where x = 72° so that 5x = 360°). For example,

cos(5x) = cos⁵(x) - 10 cos³(x) sin²(x) + 5 cos(x) sin⁴(x)

cos(5x) = cos⁵(x) - 10 cos³(x) (1 - cos²(x)) + 5 cos(x) (1 - cos²(x))²

cos(5x) = 16 cos⁵(x) - 20 cos³(x) + 5 cos(x)

which follows from the expansion

(cos(x) + i sin(x))⁵ = cos(5x) + i sin(5x)

due to DeMoivre's theorem and equating the real parts. Then cos(5x) = 1, and you can try to solve for cos(x) :

1 = 16 cos⁵(x) - 20 cos³(x) + 5 cos(x)

Actually, it would be easier to find sin(x) first, since sin(5x) = 0. The expansion in terms of sin(x) will look quite similar to the one shown here.

Answer:

the answer is the 2nd option

domain = { -1, 0, 1 }

Answer:

Y=cd-ax/b

Step-by-step explanation:

You r to use change of subject of the dormula

Answer:

y= -9+√122, or -9 - √122

Step-by-step explanation:

You have to solve the equation for y to find each variable of the quadratic and applying the quadratic formula.

after solved, I got the answer as decimal,

y = 2.0453610.....

i simpler form : y = 2.05

Also, an answer can be y= -9+√122, or -9 - √122

Answer:

I believe it is c and d

Step-by-step explanation:

math stuff and math

Answer:

2

Step-by-step explanation:

1+1=2

Answer:

Its 2

Step-by-step explanation:

Thank you for the points

Answer:

y = 7.25x + 3.50

Answer: 15

Step-by-step explanation:

The average number of cars sold for entire 8 days is $33250.

In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

Given that, a new cars salesperson, sold an average of $28,000 per day for the first 5 days she worked.

So, number of cars sold for 5 days =28,000×5

= 140000

The next 3 days she worked, she sold an average of $42,000.

Number of cars sold for 3 days

= 42,000×3

= 126000

So, average of 8 days =(140000+126000)/8

= 266000/8

= 33250

Therefore, the average number of cars sold for entire 8 days is $33250.

To learn more about an average visit:

https://brainly.com/question/11195029.

#SPJ2

Answer:

g(h(10)) = 43

Step-by-step explanation:

Given: g(x) = 4x – 4 and h(x) = 2x – 8.

We are to find g(h(10))

First we need to get g(h(x))

g(h(x)) = g(2x-8)

Replace x in g(x) with 2x-8 as shown:

g(2x-8) = 4(2x-8)-4

g(2x-8)= 8x-32-5

g(2x-8) = 8x-37

Hence g(h(x)) = 8x-37

g(h(10)) = 8(10)-37

g(h(10)) = 80-37

g(h(10)) = 43

Hence g(h(10)) is 43

Answer:

y+1=6(x-4)

This is if you want it in point slope for,.

Step-by-step explanation:

Then, if you simplify it.

y+1=6x-24

y=6x-25

Now, it is in slope intercept form.

Answer:

[tex]\sqrt{65}[/tex]

Step-by-step explanation:

Please see work attached.

hit the heart button :)

Answer:  [tex]\sqrt{65}[/tex]

Step-by-step explanation:

distance formula is [tex]\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1} )^{2}}[/tex]

take the 2points in the given (-4,-5) as ([tex](x_{1},y_{1} )[/tex]) and (3,-1) as [tex](x_{2},y_{2})[/tex]

and just substitute to get [tex]\sqrt{65}[/tex]

Answer:

Derek; by 11600 m.

Step-by-step explanation:

Convert 1.5km into m.

1.5 is 1500m.

1500 * 12 = 18000 m

8 * 800 <= Lucy

6400 m  <= Lucy's distance

18000-6400=11600m

Based on the information, Derek went further by 11600m.

Lucy did 8 laps of an 800m. The total distance will be:

= 8 × 800m

= 6400m

Derek did 12 laps of a 1.5km track. The total distance will be:

= 12 × 1500m

= 18000m

Therefore, the difference will be:

= 18000m - 6400m

= 11600m

Learn more about multiplication on:

https://brainly.com/question/25545513

Answer:

-3/2

Rise over run!

Answer:

2. We can't see the figure so we can't answer this

4. they are both the symmetrical, so we can safely assume that they are both equal.

Answer:

0

Step-by-step explanation:

because we can't multiply anything by 0.

is like saying 0×0×0×0=0

Hope this helps :D

Answer:

10

Step-by-step explanation:

The sum of the measures of the exterior angles in a convex polygon is 360°. And each exterior angle measure 36 degrees so Number of side will be 10.

Answer:

It would take him 60 minutes to run 20 laps.

Step-by-step explanation:

We can solve using proportions.

[tex] \frac{9 \: laps}{27 \: minutes} = \frac{20 \: laps}{x} \\ \\ \frac{540}{9} = \frac{9x}{9} \\ \\ 60 = x[/tex]

It would take him 60 minutes.

I think it's a pattern, so x would be 3 and y would be 5 for the first one

x would be 20 for the second

and i dont even do word problems so...

Answer:

lol you didnt add a pic

Step-by-step explanation:

Answer:

x<5

Step-by-step explanation:

Answer:

x<5

Step-by-step explanation:

First, subtract 10 from both sides which will give you −5x>−25.

Then just divide both sides by -5 and you should get the same answer x<5

I hope this helps :)

Answer:

Yes! You would sub 10-3x for y and solve.

Don't forget to use the distributive property! Your answer should be 5.

Answer:

41+42=83 ... therefore these are the required integers.

Step-by-step explanation:

Answer:

112 cups

Step-by-step explanation:

multiply the gallons by 16 to get 112 cups

Answer:

112 U.S Cups

Step-by-step explanation:

Answer:

the numbers at the bottom go on the side and the ones on the top graph them on the bottom numbers

Step-by-step explanation:

Answer:

A) The 4 and (-4) are 0s.

B) 0 points after the second round

C) 4+(-4) is 0

The 4 and the (-4) are the zero pairs in the model

Andrew has 4 + (-4) = 0 points after the second round.

4 + (-4) = 0