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2 years ago

Suppose that we wish to expand (x + y + z)17. what is the coefficient of x 2 y5z10

1 answer:

6 0

We use the trinomial theorem to answer this question. Suppose we have a trinomial (a + b + c)ⁿ, we can determine any term to be:

[n!/(n-m)!(m-k)!k!] a^(n-m) b^(m-k) c^k

In this problem, the variables are: x=a, y=b and z=c. We already know the exponents of the variables. So, we equate this with the form of the trinomial theorem.

n - m = 2
m - k = 5
k = 10

Since we know k, we can determine m. Once we know m, we can determine n. Then, we can finally solve for the coefficient.

m - 10 = 5
m = 15

n - 15 = 2
n = 17

Therefore, the coefficient is equal to:

Coefficient = n!/(n-m)!(m-k)!k! = 17!/(17-5)!(15-10)!10! = 408,408

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A botanist predicts that the height of a certain tree will increase by 2% every year. If the height of the tree is now 50 feet,

Neporo4naja [7]

To answer this kinda question, we gotta tackle it year by year.
By the end of the first year, the tree would grow by 2% = 102% of its original height.
Year 1: 102% x 50 = 51 feet
Year 2: 103% x 51 = 52.02 feet

Hope I helped!! xx

4 0

2 years ago

18. Manufacturers often package products in a way that uses the least amount of material One measure of the efficiency of a pack

Lemur [1.5K]

Answer:

a. $E=\frac{2h+2r}{rh}$

E of first can = $E=\frac{2h+2r}{rh}$

E of second can = $E=\frac{h+2r}{rh}$

c. Yes

Step-by-step explanation:

The efficiency ratio is:

E = Surface Area / Volume

We can write:

$E=\frac{S}{V}$

Where

S is surface area of cylinder

V is volume of cylinder

The formulas are:

S = $2\pi rh+2\pi r^2$

V = $\pi r ^2 h$

So, the <u>efficiency ratio (E) </u>is:

$E=\frac{2\pi rh+2\pi r^2}{\pi r^2 h}\\E=\frac{\pi r(2h+2r)}{\pi r(rh)}\\E=\frac{2h+2r}{rh}$

The first can has radius "r" and height "h", so the efficiency ratio is:

$E=\frac{S}{V}\\E=\frac{2\pi rh+2\pi r^2}{\pi r^2 h}\\E=\frac{\pi r(2h+2r)}{\pi r(rh)}\\E=\frac{2h+2r}{rh}$

The second can has same height, "h", and twice radius, "2r", so the efficiency ratio becomes:

$E=\frac{S}{V}\\E=\frac{2\pi (2r)h+2\pi (2r)^2}{\pi (2r)^2 h}\\E=\frac{4\pi rh +8\pi r^2}{4\pi r^2h}\\E=\frac{4\pi r(h+2r)}{4\pi r(rh)}\\E=\frac{h+2r}{rh}$

We now need to say if the company made a good decision or not.

If you look at both the Efficiency ratios above, you will see that the difference is in the numerator.

The first can has "2h"

The second can has "h"

The "2h" makes the numerator for the first can BIGGER than the "h" of the second can, so the Efficiency ratio of first can is thus, BIGGER.

We need smaller ratio.

So, 2nd can has indeed smaller ratio, so the company made a good decision.

6 0

2 years ago

HELP! A daycare purchases two type of snacks, granola bars and fruit rolls. One week, they purchase 10 packs of granola bars and

ch4aika [34]

10x+6y=152
5x+3y=76
7x+12y=200
-20x-12y=-304
-13x=-104
x=8
40+3y=76
3y=36
y=12
There are 8 granola bars in a pack and 12 fruit rolls in a pack

5 0

2 years ago

Read 2 more answers

Given AC ≅ FE and CB ≅ ED which statement is correct?

Kisachek [45]

Answer:

D is the correct answer.

Step-by-step explanation:

3 0

1 year ago

Read 2 more answers

Robby had 4 4/9 bags of pet food.All of the bags held the same amount of food when they were full.Of Robby's 4 4/9 bags of pet f

Tpy6a [65]

Answer: 1.8 bags

Step-by-step explanation:

From the question, given that robby have 4 4/9 bags of pet food, 2/5 were dog food

2/5 of 4 4/9 = dog foods

Convert 4 4/9 to proper fraction= 40/9

2/5 of 40/9 means 2/5 × 40/9

= 16/9

= 1.78 or 1.8

I hope this helps, please mark as brainliest answer.

4 0

1 year ago