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vredina [299]
3 years ago
5

How do you find the Domain of a function

Mathematics
1 answer:
aksik [14]3 years ago
5 0
There are different way but I will give you 2 ways;
1. Learn the definition of the domain. The domain is defined as the set of input values for which the function produces an output value. In other words, the domain is the full set of x-values that can be plugged into a function to produce a y-value.
---
2. Learn how to find the domain of a variety of functions. The type of function will determine the best method for finding a domain. Here are the basics that you need to know about each type of function, which will be explained in the next section:
A polynomial function without radicals or variables in the denominator. For this type of function, the domain is all real numbers.
A function with a fraction with a variable in the denominator. To find the domain of this type of function, set the bottom equal to zero and exclude the x value you find when you solve the equation.
A function with a variable inside a radical sign. To find the domain of this type of function, just set the terms inside the radical sign to >0 and solve to find the values that would work for x.
A function using the natural log (ln). Just set the terms in the parentheses to >0 and solve.
A graph. Check out the graph to see which values work for x.
A relation. This will be a list of x and y coordinates. Your domain will simply be a list of x coordinates.
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A car rental agency rents 190 cars per day at a rate of 29 dollars per day. for each 1 dollar increase in the daily rate, 5 fewe
Leviafan [203]

The equation that we can create from this situation is:

i = (190 – 5 x) * (29 + x)

where i is the income and x is the increase in daily rate

Expanding the equation:

i = 5510 + 190x – 145x - 5x^2

i = -5x^2 + 45x + 5510

Taking the 1st derivative:

di/dx = -10x +45

Set to zero to get the maxima:

-10x + 45 = 0

x = 4.5

 

So the cars should be rented at:

29 + x = 33.5 dollars per day

 

The maximum income is:

i = (190 – 5*4.5) * (33.5)

i = 5,611.25 dollars

7 0
2 years ago
Invest $6,300 in two different accounts the first account paid 11% the second account paid 6% in interest at the end of the year
MAVERICK [17]

Answer: he invested $5300 at 11% and $1000 at 6%

Step-by-step explanation:

Let x represent the amount which he invested in the first account paying 11% interest.

Let y represent the amount which he invested in the second account paying 6% interest.

He Invest $6,300 in two different accounts the first account paid 11% the second account paid 6% in interest. This means that

x + y = 6300

The formula for determining simple interest is expressed as

I = PRT/100

Considering the first account paying 11% interest,

P = $x

T = 1 year

R = 11℅

I = (x × 11 × 1)/100 = 0.11x

Considering the second account paying 6% interest,

P = $y

T = 1 year

R = 6℅

I = (y × 6 × 1)/100 = 0.06y

At the end of the year, he had earned $643 in interest , it means that

0.11x + 0.06y = 643 - - - - - - - - - -1

Substituting x = 6300 - y into equation 1, it becomes

0.11(6300 - y) + 0.06y = 643

693 - 0.11y + 0.06y = 643

- 0.11y + 0.06y = 643 - 693

- 0.05y = - 50

y = - 50/ - 0.05

y = 1000

x = 6300 - y = 6300 - 1000

x = 5300

7 0
3 years ago
If you had 11 dollars and spent 7 what fraction of the money did you spend
tatyana61 [14]

Answer:

7/11

Step-by-step explanation:

3 0
2 years ago
A garden hose fills a 2-gallon bucket in 5 seconds.
natulia [17]
The filling rate is 2/5=0.4 gallons per second. So the appropriate equation is A.
5 0
3 years ago
Read 2 more answers
a college freshman started the year with $4000 in spending money and after three months,she has $2800 left.assume that she will
gulaghasi [49]
Let's find out how much she spent every month.

4000 (starting money) - 2800 (remaining money) = 1200 spent over 3 months

1200/3 = 400 per month was spent

So if she continues to spend 400 a month?

How many months are left? 12 (months of the year) - 3 (months she already spent) = 9

So 9 (remaining months) * 400 (amt per month) = 3600 she'll spend at the going rate over 9 months.

But she only has 2800 left.

2800 (remaining) - 3600 (estimated total of spending) = -800

So she will be 800$ in debt at the end of the year at the current rate.
3 0
3 years ago
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