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RoseWind [281]
3 years ago
14

Which of the following exponential functions goes thru points (1,6) and (2,12)

Mathematics
1 answer:
Alexandra [31]3 years ago
7 0

Answer:

Noting that e^b = 6/a

Step-by-step explanation:

Use the general expo function y = ae^(bx).

Subbing 6 for y and 1 for x, we get  6 = ae^(b), or   e^b = 6/a.

Subbing 12 for y and 2 for x, we get   12 = ae^(2b), or 12/a = (e^b)²

Now let's find the value of the coefficient a.  Noting that e^b = 6/a, rewrite

12/a = (e^b)² as 12/a = (6/a)².

Dividing both sides by 6/a, we get 2 = 6/a, or a = 3.

Again Noting that e^b = 6/a, e^b = 6/3, or e^b = 2.

Taking the natural log of both sides, we get b = ln 2.

Then our y = ae^(bx) becomes:

                y = 3e^(ln 2·x), or   y = 3·2^x

Note:  next time, please share the answer choices.  Thank you.

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22,200/120=185

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2 years ago
Beef hope me I need you to answer the question. What is n * 54 - 688-20 =???³
blsea [12.9K]

Answer:n= 1/3d - 2/3m

Step-by-step explanation:

d=2m+3n

Step 1: Flip the equation.

2m+3n=d

Step 2: Add -2m to both sides.

2m+3n+−2m=d+−2m

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1jaiz4 and 1 more users found this answer helpful

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maxtext75

Helping Hand

15 answers

26 people helped

Answer:

n = d - 2m

        3*

Step-by-step explanation:

First we want to get n alone on one side, so we should subtract 2m from both side;

d = 2m + 3n

3n = d - 2m

Now to get n by itself, we need to divide by 3 from both sides;

3n = d - 2m

n = d - 2m

        3*

*Pretend there is a fraction bar between d - 2m and 3

Step-by-step explanation:

7 0
2 years ago
Pls help with 29..tank you
trapecia [35]

Answer:

See below

Step-by-step explanation:

Let the  2 roots be  A and A^2.

Then A^3 = c/a and A + A^2 = -b/a.

Using the identity a^3 b^3 = (a + b)^3 - 3ab^2 - 3a^2b:-

A^3 + (A^2)^3 =  ( A + A^2)^3 - 3 A.A^4 - 3 A^2. A^2

= (A + A^2)^3 - 3A*3( A + A^2)

Substituting:-

c/a + c^2/a^2 = (-b/a)^3 - 3 (c/a)(-b/a)

Multiply through by a^3:-

a^2c + ac^2 = -b^3 + 3abc

Factoring:-

ac(a + c) = 3abc - b^3

This is not the formula required in the question but let's see if the formula in the question reduces to this. If it does we have completed the proof.

a(c - b)^3 = a(c^3 - 3c^2b + 3cb^2 - b^3) = ac^3 - 3ac^2b + 3acb^2 - ab^3

c(a - b)^3 = c(a^3 - 3a^2b + 3ab^2 - b^3) = ca^3 - 3a^2bc + 3acb^2 - cb^3.

These are equal so we have

ca^3 - 3a^2bc + 3acb^2 - cb^3 = ac^3 - 3abc^2 + 3acb^2 - ab^3

The 3acb^2 cancel out so we have:-

a^3c - ac^3 =  3a^2bc - 3abc^2 + b^3c - ab^3

ac(a^2 - c^2) = 3abc( a - c) + b^3(c - a)

ac(a + c)(a -c) = 3abc(a - c) - b^3 (a - c)

Divide through by (a - c):-

ac(a + c) = 3abc - b^3 , which is the result we got earlier.

This completes the proof.

 

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