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2 years ago

A)clara believes the sequence 3,9,27,81,243 is arithmetic. Do you agree with clara?Explain your reasoning.

1 answer:

3 0

This is NOT an arithmetic sequence because there is no common difference. It is a geometric sequence because there is a common ratio. Meaning that each term is a constant ratio or multiple of the previous term. The recursive rule for this geometric sequence is:

a(n)=3*a(n-1), a(1)=3

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A town has a population of 5000 and grows at 4% every year. What will be the population after 7 years, to the nearest whole numb

Rudiy27

I think this is.. ↓

grows 4% at every year

after 7 years ↓↓

4 × 7 = 28

A town has a population of 5000

28% of 5000 = 1400

5000 + 1400 = 6400

after 7 years, town has 6400 population = after 7 year grows 28%

7 0

2 years ago

Read 2 more answers

In this problem we consider an equation in differential form Mdx+Ndy=0. (4x+2y)dx+(2x+8y)dy=0 Find My= 2 Nx= 2 If the problem is

zheka24 [161]

Answer:

$f(x,y)=2x^2+4y^2+2xy=C_1\\\\Where\\\\y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )$

Step-by-step explanation:

Let:

$M(x,y)=4x+2y\\\\and\\\\N(x,y)=2x+8y$

This is and exact equation, because:

$\frac{\partial M(x,y)}{\partial y} =2=\frac{\partial N}{\partial x}$

So, define f(x,y) such that:

$\frac{\partial f(x,y)}{\partial x} =M(x,y)\\\\and\\\\\frac{\partial f(x,y)}{\partial y} =N(x,y)$

The solution will be given by:

$f(x,y)=C_1$

Where C1 is an arbitrary constant

Integrate $\frac{\partial f(x,y)}{\partial x}$ with respect to x in order to find f(x,y):

$f(x,y)=\int\ {4x+2y} \, dx =2x^2+2xy+g(y)$

Where g(y) is an arbitrary function of y.

Differentiate f(x,y) with respect to y in order to find g(y):

$\frac{\partial f(x,y)}{\partial y} =2x+\frac{d g(y)}{dy}$

Substitute into $\frac{\partial f(x,y)}{\partial y} =N(x,y)$

$2x+\frac{dg(y)}{dy} =2x+8y\\\\Solve\hspace{3}for\hspace{3}\frac{dg(y)}{dy}\\\\\frac{dg(y)}{dy}=8y$

Integrate $\frac{dg(y)}{dy}$ with respect to y:

$g(y)=\int\ {8y} \, dy =4y^2$

Substitute g(y) into f(x,y):

$f(x,y)=2x^2+4y^2+2xy$

The solution is f(x,y)=C1

$f(x,y)=2x^2+4y^2+2xy=C_1$

Solving y using quadratic formula:

$y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )$

4 0

3 years ago

What is the general form of the equation for the given circle?

Tom [10]

Hhhhhhhhahahahahahahahahahahaahabahahah 4.7

4 0

2 years ago

You use 8 cups of flour to make 24 muffins at that rate how much flour will it take to make 30 muffins

Anettt [7]

10 cups of flour total. (8x30)/24

8 0

2 years ago

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What is XY=7a YZ=5a Xz=6a+24 In geometry

Cloud [144]

In light of the fact that point y is the point at which segment xz is divided, the value of the variable an is equal to 4.

<h3>How can I determine what the value of the variable an is?</h3>

Due to the fact that point y divides segment xz into two distinct halves, the following equation may be used to get segment xz's total length:

xz = xy + yz.

The following are the parameters for the test:

xy = 7a. yz = 5a. xz = 6a + 24.

As a result, we need to substitute into the equation and then solve for a.

xz = xy + yz

6a + 24 = 7a + 5a

12a = 6a + 24

6a = 24

a = 24/6

a = 4.