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3 years ago

Write a rule for the nth term of the sequence 37, 32, 27, 22, . . . .

Mathematics

1 answer:

Radda [10]3 years ago

5 0

Answer:

a(n) = 37 - 5(n -1)

Step-by-step explanation:

Notice that each new term is obtained by subtracting 5 from the previous term. Thus, this is an arithmetic sequence with common difference -5 and first term 37.

The explicit formula for the nth term is a(n) = a(1) - 5(n - 1) = 37 - 5(n -1)

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A) Find a particular solution to y" + 2y = e^3 + x^3. b) Find the general solution.

Reptile [31]

Answer:

a.P.I= $\frac{e^{3x}}{11}+\frac{1}{2}(x^3-3x)$

b.G.S= $C_1Cos \sqrt2 x+C_2 Sin\sqrt2 x+\frac{1}{11}e^{3x}+\frac{1}{2}(x^3-3x}$

Step-by-step explanation:

We are given that a linear differential equation

$y''+2y=e^{3x}+x^3$

We have to find the particular solution

P.I= $\frac{e^{3x}}{D^2+2}+\frac{x^3}{D^2+2}$

P.I= $\frac{e^{3x}}{3^2+2}+\frac{1}{2} x^3(1+\frac{D^2}{2})^{-2}$

P.I= $\frac{e^{3x}}{11}+\frac{1-2\frac{D^2}{4}+3\frac{D^4}{16}+...}{2}x^3$

P.I= $\frac{e^{3x}}{11}+\frac{x^3-2\frac{\cdot3\cdot 2x}{4}}{2}+0}$ (higher order terms can be neglected

P.I= $\frac{e^{3x}}{11}+\frac{1}{2}(x^3-3x)$

b.Characteristics equation

$D^2+2=0$

$D=\pm\sqrt2 i$

C.F= $C_1cos \sqrt2x+C_2 sin\sqrt2 x$

G.S=C.F+P.I

G.S= $C_1Cos \sqrt2 x+C_2 Sin\sqrt2 x+\frac{1}{11}e^{3x}+\frac{1}{2}(x^3-3x)$

3 0

3 years ago

find the equation of a line through the coordinate (3,6) and parallel to the line represented by y=5/3 x-1

maw [93]

Slope-intercept form:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0 or (0,y))

For lines to be parallel, their slopes have to be the SAME.

The given line's slope is 5/3, so the parallel line's slope is also 5/3

y = 5/3x + b

To find "b", plug in the point (3,6) into the equation

y = 5/3x + b

6 = 5/3(3) + b

6 = 5 + b

1 = b

y = 5/3x + 1

5 0

3 years ago

Does anyone know how to solve this?

Olegator [25]

m=70/2=35

n=(360-70*2)/2=110

6 0

2 years ago

Read 2 more answers

Express the rate 50 yards per minute in feet per second

FrozenT [24]

   (50 yards/minute) x (3 feet/yard) x (1 minute / 60 seconds)

   = (50 · 3 · 1 / 60) (yard-feet-minute) / (minute-yard-second)

   =    2.5 feet/second .

3 0

2 years ago

Read 2 more answers

The spinner shown is spun once. Find the probability of each event. Write each answer as a fraction, percent, and decimal. Ma

poizon [28]

Complete question :

The spinner shown is spun once. Determine the probability of each event. Express each answer as a fraction, a decimal, and a percent. P(C)

Answer:

1 / 8; 0.125 ; 12.5%

Step-by-step explanation:

From the spinner :

The number of partitions or faces on the spinner is 8 ;

The number of occurences of c on the spinner is 1

The probability of obtaining c written as P(c) :

Probability = required outcome = number of c on spinner / total possible outcomes, total number of faces in spinner = 8

P(c) = 1 / 8

As decimal :

1/8 = 0.125

As a percentage :

0.125 * 100% = 12.5%

7 0

2 years ago