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3 years ago

Given 9, 12, 15, 18, 21, 24 ... Write an algebraic representation for this sequence.

Mathematics

2 answers:

makvit [3.9K]3 years ago

6 0

Answer:

tn=9+3(n-1)

Step-by-step explanation:

Formula: tn=t1+d(n-1)

AKA: term n=term 1 plus common difference times n minus 1

For this sequence: tn=tn; t1=9; common difference=3; n-1=n-1

Plug in the answer: tn=9+3(n-1)

harkovskaia [24]3 years ago

3 0

Answer:

y=X+3

Step-by-step explanation:

brainly pls

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2+9n=72 how do you find what n equals?

Greeley [361]

Answer:

the correct answer is 7.78

6 0

3 years ago

A) Findi

Romashka [77]

Answer:

Part A)

$\displaystyle \frac{dy}{dx}=-\frac{2xy+y^2}{x^2+2xy}$

Part B)

$\displaystyle y=-\frac{5}{8}x+\frac{9}{4}$

Step-by-step explanation:

We have the equation:

$\displaystyle x^2y+y^2x=6$

Part A)

We want to find the derivative of our function, dy/dx.

So, we will take the derivative of both sides with respect to x:

$\displaystyle \frac{d}{dx}\Big[x^2y+y^2x\Big]=\frac{d}{dx}\big[6\big]$

The derivative of a constant is 0. We can expand the left:

$\displaystyle \frac{d}{dx}\Big[x^2y\Big]+\frac{d}{dx}\Big[y^2x\Big]=0$

Differentiate using the product rule:

$\displaystyle \Big(\frac{d}{dx}\big[x^2\big]y+x^2\frac{d}{dx}\big[y\big]\Big)+\Big(\frac{d}{dx}\big[y^2\big]x+y^2\frac{d}{dx}\big[x\big]\Big)=0$

Implicitly differentiate:

$\displaystyle (2xy+x^2\frac{dy}{dx})+(2y\frac{dy}{dx}x+y^2)=0$

Rearrange:

$\displaystyle \Big(x^2\frac{dy}{dx}+2xy\frac{dy}{dx}\Big)+(2xy+y^2)=0$

Isolate the dy/dx:

$\displaystyle \frac{dy}{dx}(x^2+2xy)=-(2xy+y^2)$

Hence, our derivative is:

$\displaystyle \frac{dy}{dx}=-\frac{2xy+y^2}{x^2+2xy}$

Part B)

We want to find the equation of the tangent line at (2, 1).

So, let's find the slope of the tangent line using the derivative. Substitute:

$\displaystyle \frac{dy}{dx}_{(2,1)}=-\frac{2(2)(1)+(1)^2}{(2)^2+2(2)(1)}$

Evaluate:

$\displaystyle \frac{dy}{dx}_{(2,1)}=-\frac{4+1}{4+4}=-\frac{5}{8}$

Then by the point-slope form:

$y-y_1=m(x-x_1)$

Yields:

$\displaystyle y-1=-\frac{5}{8}(x-2)$

Distribute:

$\displaystyle y-1=-\frac{5}{8}x+\frac{5}{4}$

Hence, our equation is:

$\displaystyle y=-\frac{5}{8}x+\frac{9}{4}$

5 0

2 years ago

Ernie deposits $9,800 into a pension fund. The fund pays a simple interest rate of 7%. What will the balance be after four years

telo118 [61]

Answer:

$12,845.80

Step-by-step explanation:

take the first number and go +7%. repeat four times

hope this helps :-)

6 0

2 years ago

A positive real number is 1 less than another. When 2 times the larger is added to the square of the smaller, the result is 8. F

Igoryamba

Answer:

Let your two numbers be n and n-1. Then: 2n+n²-2n+1=51 n²=50 n=5√2 n-1=5√2-1

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3 0

7 months ago

Find the value of r ,so that the line passing through the points 6,2 and 10,r given and has a slope of 2

bonufazy [111]

Answer:

Step-by-step explanation:

Slope (m) of two points is expressed as :

m = (y2 - y1) / (x2 - x1)

Given m = 2

the equation becomes;

2 = (r - 2) / (10 - 6)

2 = (r - 2) / 4

cross multiplying becomes ;

2 * 4 = r - 2

8 = r - 2

r = 10

7 0

2 years ago