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3 years ago

HW_Intro to functions

Mathematics

1 answer:

AveGali [126]3 years ago

3 0

Answer: Functions and Their Notation

A function maps a set of inputs onto a set of permissible outputs. Each input corresponds with one and only one output

Step-by-step explanation:

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Write your answer in a + bi form. A=___ B=___

Dmitry_Shevchenko [17]

Answer:

Step-by-step explanation:

$\frac{-3+7i}{-6-7i} \times \frac{-6+7i}{-6+7i} =\frac{18-21i-42i-49i^2}{(-6)^2-(7i)^2} \\=\frac{18-63i -49(-1)}{36-49i^2} \\=\frac{18+49-63 i}{36-49(-1)} \\=\frac{67-63i}{36+49} \\=\frac{67-63i}{85} \\=\frac{67}{85} +(\frac{-63}{85} )i\\$

$a=\frac{67}{85} \\b=\frac{-63}{85}$

3 0

2 years ago

Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n ≥ 1?

Dimas [21]

Option C: –10, –7.5, –5, –2.5, … is the sequence.

Explanation:

The given recursive formula is $f(n+1)=f(n)+2.5$ for $n\geq 1$

We need to determine the sequence.

The sequence can be determined by substituting n = 1, 2, 3, 4,....

And $f(1)=-10$

2nd term of the sequence:

Substituting n = 1 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(1+1)=f(1)+2.5$

Simplifying, we have,

$f(2)=-10+2.5=-7.5$

Thus, the 2nd term of the sequence is -7.5

3rd term of the sequence:

Substituting n = 2 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(2+1)=f(2)+2.5$

Simplifying, we have,

$f(3)=-7.5+2.5=-5$

Thus, the 3rd term of the sequence is -5

4th term of the sequence:

Substituting n = 3 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(3+1)=f(3)+2.5$

Simplifying, we have,

$f(4)=-5+2.5=-2.5$

Thus, the 4th term of the sequence is -2.5

Therefore, the sequence is –10, –7.5, –5, –2.5, …

Hence, Option C is the correct answer.

3 0

3 years ago

Read 2 more answers

Let F(s) 1.1s + 0.03s2 represent the stopping distance (in feet) of a car travelling at s miles per hour. Calculate F(60) and es

Alinara [238K]

Answer:

F(60) = 3666 feet

Estimated Increase in Stopping Distance: 123.1 feet

Actual Increase in Stopping Distance: 122.1 feet

The cost of producing 3000 bagels is $1036.5

The Estimated cost of the 3001st bagel is $1036.736.

The actual cost of the 3001 st bagel is $1036.737.

Step-by-step explanation:

F(s) = 1.1s + s²

F(60) = 1.1(60) + (60)²

= 66 + 3600

F(60) = 3666 feet

To find the estimate increase in stopping distance, differentiate the function to get F'(s) and then find F'(61)

F'(s) = $\frac{dF(s)}{ds}$ = 1.1 + 2s

F'(61) = 1.1 + 2(61)

F'(61) = 123.1 feet

If speed is increased from 60 to 61, we can find the actual increase by finding F(61) and then subtracting F(60) from it.

F(61) = 1.1(61) + (61)²

F(61) = 3788.1 feet

Increase = 3788.1 - 3666

Increase = 122.1 feet

F(60) = 3666 feet

Estimated Increase in Stopping Distance: 123.1 feet

Actual Increase in Stopping Distance: 122.1 feet

C(x) = 300 + 0.25x - 0.5 ( $\frac{x}{1000}$ )³

C(3000) = 300 + 0.25(3000) - 0.5 (3000/1000)³

= 300 + 750 - 13.5

C(3000) = $1036.5

The cost of producing 3000 bagels is $1036.5

To estimate the cost of the 3001st bagel, we need to differentiate the function and then find the increase in price at the 3001st bagel. The answer then needs to be added to C(3000). So,

C'(x) = 0.25 - 0.5*3 (x/1000)²/1000

C'(3001) = 0.25 - 0.5*3 (3001/1000)²/1000

C'(3001) = 0.236

C(3001) = C(3000) + C'(3001)

= 1036.5 + 0.236

C(3001) = $1036.736

The Estimated cost of the 3001st bagel is $1036.736.

C(3001) = 300 + 0.25(3001) - 0.5(3001/1000)³

= 300 + 750.25 - 13.5135

C(3001) = $1036.737

The actual cost of the 3001 st bagel is $1036.737.

5 0

3 years ago

If g stands for a whole number, find the first three possible values of g2 + 3.

Sati [7]

So the first three possible values of g^2 + 3 are:

3, 4, 7

The first option is the correct one.

<h3>Which ones are the first three possible values?</h3>

The set of the whole numbers is {0, 1, 2, 3...}

Then the first possible value is when g = 0.

0^2 + 3 = 3

The second possible value is when g = 1

1^2 + 3 = 4

The third possible value is when g = 2.

2^2 + 3 = 7

So the first three possible values of g^2 + 3 are:

3, 4, 7

The first option is the correct one.

If you want to learn more about whole numbers:

brainly.com/question/5243429

#SPJ1

5 0

2 years ago

Read 2 more answers

What is the answer ?? Need help plis

bagirrra123 [75]

Take a closer picture

8 0

3 years ago

Read 2 more answers