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3 years ago

Consider a sequence given by the formula f(n) = 1 / 3 ^ n−1 starting with n = 1. Generate the first 5 terms of the

Mathematics

1 answer:

denpristay [2]3 years ago

5 0

Answer:

Step-by-step explanation:

According to the formula we need to start from n = 1. So the first 5 terms of the sequence, will have the following values of n: 1,2,3,4,5

Now, we need to replace the values of n into the formula to get all the terms.

f(1) = 1/3 ^ 1-1 = 1/3^0 = 1.

This is because any number elevated to zero is always the unit, in this case, 1.

f(2) = 1/3 ^2-1 = 1/3 ^1 = 1/3

This, because any number elevated to 1, is always the same initial number.

f(3) = 1/3 ^3-1 = 1/3 ^2 = 1/9.

Because when the exponent is elevating a fraction number, the power goes to both numbers (numerator and denominator)

f(4) = 1/3 ^4-1 = 1/3 ^3 = 1/27.

f(5) = 1/3 ^5-1 = 1/3 ^4 = 1/81.

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a college student would like to invest the prices of sandwiches offered near the campus a sample of 50 shops that's so sandwiche

fredd [130]

Answer:

the answer is A

Step-by-step explanation:

because the graph is skewed to the left

3 0

3 years ago

Find the Area of the figure below, composed of an isoceles trapezoid and one

MAVERICK [17]

Answer:

the total area is 15.6 square units

Step-by-step explanation:

hello,

you can find the total area dividing the shape into two known shapes

total area= area of the trapezoid +area of the semicircle

then

step one

find the area of the isosceles trapezoid using

$A=\frac{a+b}{2}*h$

where

a is the smaller base

b is the bigger base

h is theheight

A is the area

let

a=2

b=5

h=4

put the values into the equation

$A=\frac{a+b}{2}*h\\A=\frac{5+2}{2}*4\\A=3.5*4\\A=14$

Step two

find the area of the semicircle

the area of a circle is given by

$A_{c}=\pi \frac{d^{2}}{4}\\$

but, we need the area of half circle, we need divide this by 2

$A_{semic}=\frac{ \pi \frac{d^{2}}{4}}{2}\\A_{semic}= \pi \frac{d^{2}}{8}$

now the diameter of the semicircle is 2, put this value into the equation

$A_{semic}= \pi \frac{2^{2}}{8}\\\\A_{semic}= \pi \frac{1}{2}\\ A_{semic}=\frac{\pi }{2}\\$

find the total area

total area= area of the trapezoid +area of the semicircle

$total\ area= 14+\frac{\pi }{2} \\total\ area=15.6$

so, the total area is 15.6 square units

Have a good day.

5 0

4 years ago

Which graph represents the polynomial function g(x)=x3+x2−17x+15?

IrinaVladis [17]

The graph which represents the polynomial function g(x) is:

the 2nd graph in the second line

Step-by-step explanation:

g(x) = x³ + x² - 17x + 15 is a cubic function because the greatest power

of x is 3

All graphs represent cubic functions

So to find which graph which represents g(x) we will do these steps

1. Put x = 0 to find the y-intercept

2. If there are more than one graph have the same y-intercept we will

find the maximum and the minimum points of the cure

3. If you still don't know which graph find the x-intercepts

Now let us find the graph which represents g(x)

∵ g(x) = x³ + x² - 17x + 15

∵ x = 0

∴ g(0) = (0)³ + (0)² - 17(0) + 15

∴ g(0) = 15

∵ g(0) is the y-intercept

∴ The graph intersect the y-axis at point (0 , 15)

There is only one graph intersects y-axis at point (0 , 15)

The attached figure is the graph of g(x)

The graph which represents the polynomial function g(x) is:

the 2nd graph in the second line

Learn more:

you can learn more about functions in brainly.com/question/10541435

brainly.com/question/10879401

#LearnwithBrainly

8 0

3 years ago

Read 2 more answers

Two consecutive odd integers are such that one-third the smaller is greater than one-seventh of the larger one by 6. Find the nu

vaieri [72.5K]

Answer:

the number is 33 and 35 respectively

Step-by-step explanation:

The computation is shown below:

Let us assume X and X + 2 are the two consecutive odd integers

Now the equation is

(X ÷ 3) = ((X + 2) ÷ 7) + 6

(X ÷ 3) = (X + 2 + 6 × 7) ÷ 7

(X ÷ 3) = (X + 2 + 42) ÷ 7

(X ÷ 3) = (X + 44) ÷ 7

Now do the cross multiplication

7X = 3(X + 44)

7X = 3X + 132

4X = 132

X = 33

And, X + 2 = 33 + 2 = 35

hence, the number is 33 and 35 respectively

5 0

3 years ago

H(x) =2x+3 James brought a plant that was 3 inches tall. Each week the plant grew 2 inches. The function h(x) = 2x + 3 describes

telo118 [61]

Answer:

<h2>For 6 weeks, the height will be 15 inches</h2>

Step-by-step explanation:

Step one:

given data

the initial height of plant= 3inches

growth in inches per week =2inches per wee

Step two:

for x number of weeks, the height is expressed as

$h(x) = 2x + 3$

With the given growth function, we can estimate the height of the plant after any number of weeks, say x=6, that is 6 weeks, the height will be

substitute x=6 in the growth function

$h(x) = 2(6)+ 3\\\\h(x) = 12 + 3\\\\h(x) = 15 inches$

8 0

3 years ago