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Y_Kistochka [10]
2 years ago
11

Given the function () = $

Mathematics
1 answer:
elena-s [515]2 years ago
6 0

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

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kolbaska11 [484]

The Random Variable that should be considered continuous is "The time it takes for a randomly chosen athlete to run 200 meters" , the correct option is (c) .

In the question ,

four random variables are given , we have to select the random variable that is continuous .

A Continuous Random Variable is a random variable X , which can take any value in its domain or in an interval or the union of intervals on the real line is called Continuous random variable .

For Example : weight of middle aged people lying between 40 Kg and 150 Kg .

From the given options ,

the option (c) , the time taken for a randomly chosen athlete to run 200 meters is a interval of time ,

So ,it is can be called as Continuous Random Variable .

Therefore , the option that represents Continuous Random Variable is option(c) .

The given question is incomplete , the complete question is

Which of the following random variables should be considered continuous ? Select one:

(a) The number of cars owned by a randomly chosen adult male

(b) The number of orders received by a mail-order company in a randomly chosen week

(c) The time it takes for a randomly chosen athlete to run 200 meters  

(d) The numbers of brothers a randomly chosen person has .

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3 0
1 year ago
assuming a trucker changes his tires every for 40,000 miles and that he starts with a brand new set of tires how many sets of ti
sdas [7]
80,000 tires will be used
8 0
3 years ago
Lim (x+1) (3x^2-9)<br> X2
mafiozo [28]

Answer:

\lim_{x \to 2} (x+1)(3x^2-9) = 9

Step-by-step explanation:

Step 1: Write out limit

\lim_{x \to 2} (x+1)(3x^2-9)

Step 2: Evaluate

(2 + 1)(3(2)² - 9)

3(3(4) - 9)

3(12 - 9)

3(3)

9

5 0
3 years ago
Hi can anyone help me with this please
Nostrana [21]

Answer:35in.

Step-by-step explanation:

I reccomend splitting it into sections when given problems like this.

The smaller two rectangles would be 5in * 2in which is 10in then just add them together.

For the bigger one, you'd do 5-2 in order to get the missing inches which will be 3+2 once added 5in*3in is 15in.

Finally, add 15+10+10 (15=The middle rectangle and 10=the sides)

8 0
3 years ago
Read 2 more answers
Make, Dan, Ed, and summer played together on a baseball team. Mike’s batting average was 0.349, dan’s was 0.2, Ed’s was 0.35, an
Harrizon [31]

the highest batting average is of Ed's and that is 0.350 .

<u>Step-by-step explanation:</u>

Here we have , Make, Dan, Ed, and summer played together on a baseball team. Mike’s batting average was 0.349, dan’s was 0.2, Ed’s was 0.35, and sy’swas 0.299. We need to find Who had the highest batting average . Let's find out :

According to question we have following parameters as :

Mike = 0.349\\Dan's=0.200\\Ed's=0.350\\Sy'swas=0.299

Arranging these data from decreasing to increasing order we get :

⇒ 0.200

⇒ (Dan's)0.200

Therefore ,  the highest batting average is of Ed's and that is 0.350 .

6 0
3 years ago
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