An airplane travels at a rate of 7 miles per minute for 120 minute. Find the distance traveling using d=rt

elena-s [515]

The inverse of the function f(x) = 1/3x^2 - 3x + 5 is f-1(x) = 9/2 + √[3(x + 7/4)], the sum of the arithmetic series is 1078 and the common ratio of the sequence is 2

<h3>The inverse of the function?</h3>

The function is given as:

f(x) = 1/3x^2 - 3x + 5

Next, we rewrite the function as in vertex form

Using a graphing calculator, the vertex form of the function f(x) = 1/3x^2 - 3x + 5 is

f(x) = 1/3(x - 9/2)^2 - 7/4

Express f(x) as y

y = 1/3(x - 9/2)^2 - 7/4

Swap x and y

x = 1/3(y - 9/2)^2 - 7/4

Add 7/4 to both sides

1/3(y - 9/2)^2 = x + 7/4

Multiply through by 3

(y - 9/2)^2 = 3(x + 7/4)

Take the square root of both sides

y - 9/2 = √[3(x + 7/4)]

Add 9/2 to both sides

y = 9/2 + √[3(x + 7/4)]

Rewrite as an inverse function

f-1(x) = 9/2 + √[3(x + 7/4)]

<h3>Sum of arithmetic series</h3>

Here, we have:

5 + 18 + 31 + 44 + ... 161

Calculate the number of terms using:

L = a + (n -1)d

So, we have:

161 = 5 + (n - 1) * 13

This gives

(n - 1) * 13 = 156

Divide by 13

n - 1 = 12

Add 1

n = 13

The sum is then calculated as:

Sn = n/2 * [a + L]

This gives

Sn =13/2 * (5 + 161)

Evaluate

Sn = 1078

Hence, the sum of the arithmetic series is 1078

<h3>The common ratio of the sequence</h3>

Here, we have:

T11 = 32 * T6

The nth term of a geometric sequence is

Tn = ar^(n-1)

This gives

ar^10 = 32 * ar^5

Divide by ar^5

r^5 = 32

Take the fifth root

r = 2

Hence, the common ratio of the sequence is 2

Read more about sequence at:

brainly.com/question/7882626

#SPJ1

6 0

1 year ago

How do u write a expression

zhuklara [117]

Answer:

<h2><u>it depends on what expression u want </u></h2>

Step-by-step explanation:

An example of a mathematical expression with a variable is 2x + 3. All variables must have a coefficient, a number that is multiplied by the variable. In the expression 2x + 3, the coefficient of x is the number 2, and it means 2 times x plus 3.

3 0

2 years ago

Read 2 more answers

Help please !!!!! Super hard

Keith_Richards [23]

The image is really unclear but I will assume that the number of teams given = 66
and the formula is
$n = \frac{ {t }^{2} - t }{2}$
plug in the number of teams
$66 = \frac{ {t}^{2} - t }{2}$
multiply both sides by two
$132 = {t}^{2} - t$
subtract 132 from both sides and factor
t = 12

4 0

2 years ago

Leonard and Liam each own a collection of vintage cars. Leonard has 7 cars more than Liam has. Three times the number of cars Le

dimulka [17.4K]

Answer: The answer is (22, 15).

Step-by-step explanation: Given that 'x' represents the number of cars Leonard has and 'y' represents the number of cars Liam has.

Then, according to the given information, we have

$x-y=7,\\\\3x+2y=96.$

Multiplying the first equation by 2 and adding to the second equation, we have

$2x+3x=14+96\\\\\Rightarrow 5x=110\\\\\Rightarrow x=22.$

So,

$y=x-7=22-7=15.$

Therefore, Leonard has 22 cars and Liam has 15 cars.

Thus, (22, 15) is the solution to the given system.

5 0

2 years ago

Read 2 more answers

The data shown in the table below can be

kvv77 [185]

Answer:

6: 12

7: 14

8: 16

Step-by-step explanation:

You do the last (y) term given [18] minus the first (y) term [10] given divided by how many terms it takes to get from the last (y) term given minus the first (y) term given [4]. So the equation looks like this:

(18 - 10)/4= 8/4 = 2

4 0

2 years ago