I need to do this assignment but I need help on how to draw it and answer the questions because I am confused on how to do these things. Thank you
Answers
1) The domain is [0,300]. The range is [0,250]
2) The slope for the initial climb is 3.57. The equation of the line is
3) The rate of change of the second hill is -1.4
4) The rate of change of the third hill is -2.1
5) The blue hill is steeper
6) It is not a function
Step-by-step explanation:
1)
The domain of a function is the set of values of x (the input) for which the function itself is defined.
Instead, the range of a function is the set of values of y (the output) that the function can take.
To find the domain, we have to look at the x-axis and see for which values of x the function is defined. By looking at the graph, we see that the function is defined between
x = 0 and x = 300
So, the domain is [0,300].
To find the range, we have to look at the y-axis and see for which values of y the function has an output. By looking at the graph, we see that the function has values of y between
y = 0 and x = 250
So, the range is [0,250].
2)
The slope of a function in a certain range is given by
where
is the change in the y-coordinate
is the change in the x-coordinate
For the initial climb (pink line), we have:
Therefore, the slope in this part is
We can now write the equation of the line in the form
y = mx + b
where b is the y-intercept: since it is zero, the line has simply the form
3)
Again, to calculate the slope of the hill, we use:
where
is the change in the y-coordinate
is the change in the x-coordinate
For the green hill, we have:
So the rate of change is
4)
As before, the rate of change of the hill is
For the blue hill, we have:
So the rate of change is
5)
To know which hill is steeper, we need to compare the magnitude of their rate of change.
In fact, both hills have rate of change negative - because we are going down along the slope. Therefore, we have to consider the magnitude of their slope.
For the green hill:
For the blue hill:
We see that the blue hill has a greater slope (in magnitude): therefore, the blue hill is steeper.
6)
A function is defined as a mapping (operation between two sets of variables) in which to one value of x (the input) corresponds one and only one value of y (the output).
This means that a function cannot have multiple values of y for the same x (the input).
By looking at the graph, we see that this function does not respect this criterium: in fact, we see that certain values of x give multiple values of the output, y (for instance, at x=300 the function has two values). So, this is not a function.
Related Questions
Please help me and answer that ??
Answers
Answer: A. 7/21 = 1/x
Step-by-step explanation: 7/21 = 1/3 so x would be 3.
need help with this problem?
Answers
A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, how many grains of wheat should be placed on square 24 ? Also find the total number of grains of wheat on the board at this time and their total weight in pounds. (Assume that each grain of wheat weighs 1/7000 pound.)
Answers
Answer:
1) 8,388,608 grains of wheat.
2) 16,777,215 grains of wheat.
3) 239,674.5 pounds.
Step-by-step explanation:
Question 1)
We know that on the first square, there is 1 grain of wheat.
On the second, 2 grains of wheat.
On the third, 4 grains of wheat.
And on the fourth, 8 grains of wheat.
Therefore, we have a geometrically increasing sequence. It looks like:
1, 2, 4, 8...
Therefore, to find the number of grains on the 24th square, we can write an explicit formula.
The standard form for the explicit formula for a geometric sequence is:
[tex]x_n=a(r)^{n-1}[/tex]
Where a is the initial amount, r is the common ratio, and n is the nth term (starting from 1).
We know that the initial term a is 1 because there’s one grain of wheat on the first square.
And the common ratio will be 2 because each square has double the amount of the previous square.
So, substitute 1 for a and 2 for r. This yields:
[tex]x_n=1(2)^{n-1}\\[/tex]
We can simplify this:
[tex]x_n=2^{n-1}[/tex]
So, to find the amount of wheat on the 24th square, we simply need to substitute 24 for n and evaluate. So:
[tex]x_{24}=2^{24-1}=2^{23}[/tex]
Evaluate. Use a calculator:
[tex]x_{24}=8,388,608[/tex]
Therefore, on the 24th square, there are 8,388,608 grains of wheat.
Question 2.1)
We want to find the total number of grains of wheat on the board at this time.
In other words, we want to find the sum of our geometric sequence when n is 24.
The formula for the sum of a geometric series is:
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
Where rⁿ is the value of the number of terms n, r is the common ratio, and a is the initial term.
We want to find the sum after 24 times. So, n is 24.
So, substitute 24 for n, 2 for r, and 1 for a. This yields:
[tex]S_{24}=\frac{(1)(2^{24}-1)}{2-1}[/tex]
Evaluate. Use a calculator:
[tex]S_{24}=16, 777, 215[/tex]
Therefore, the total sum of the number of grains of wheat at the board at the 24th square is 16,777,215.
Question 2.2)
And to find the weight, we will just have to multiply our total amount by 1/7000. So:
[tex]W=16777215(\frac{1}{70})[/tex]
Use a calculator:
[tex]W=239,674.5\text{ lbs}[/tex]
So, the total weight is 239,674.5 pounds.
Which is the better deal 8 ounces of shampoo for $0.99 or 12 ounces for $1.47?
Answers
Answer:
12 ounces for $1.47.
Step-by-step explanation:
:) ello
What is the value of x?
A) 42
B)48
C)138
D)158
Answers
Answer:
138 I think
Step-by-step explanation:
math go brrr
A teacher divides the students into three groups for project. Each group has the same number of students. Is the total number of students prime or composite? Explain period
Answers
It could be either.
1 + 1 + 1 = 3, which is prime
2 + 2 + 2 = 6, which is composite
How do I do this problem?
Answers
What is the additive inverse of the polynomial
9xy² + 6x²y -5x
Answers
Answer:
-9xy² - 6x²y + 5x
Step-by-step explanation:
The additive inverse of a polynomial is simply defined as the same polynomial but the difference is that the signs attached to each of the terms will change. This means that positive sign will change to negative while negative sign will change to positive.
Now, we are given the polynomial;
9xy² + 6x²y - 5x
Thus, from earlier description, additive inverse of this polynomial is;
-9xy² - 6x²y + 5x
The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial population P0 has doubled in 5 years. Suppose it is known that the population is 9,000 after 3 years.
Required:
a, What was the initial population P0?
b. How fast is the population growing at t = 10?
Answers
Step-by-step explanation:
Let the initial population of a community be P0 and the population after time t is P(t).
If the population of a community is known to increase at a rate proportional to the number of people present at time t, this is expressed as:
[tex]P(t) = P_0e^{kt}[/tex]
at t = 5 years, P(t) = 2P0
substitute:
[tex]2P_0 = P_0e^{5k}\\2 = e^{5k}\\ln2 = lne^{5k}\\ln2 = 5k\\k = \frac{ln2}{5}\\k = 0.1386[/tex]
If the population is 9,000 after 3 years
at t = 3, P(t) = 9000
a) Substitute into the formula to get P0
[tex]9000 = P_0e^{0.1386\times 3}\\9000 = P_0e^{0.4158}\\9000 = 1.5156P_0\\P_0 = \frac{9000}{1.5156}\\ P_0 = 5938.24[/tex]
Hence the initial population is approximately 5938.
b) In order to know how fast the population growing at t = 10, we will substitute t = 10 into the formula as shown:
[tex]P(10) = 5938.24e^{0.1386(10)}\\P(10) = 5938.24e^{1.386}\\P(10) = 5938.24(3.9988)\\P(10) = 23,745.97[/tex]
Hence the population of the community after 10 years is approximately 23,746
c is opposite___
AC
AC and BC
Answers
Answer:a=bc
Step-by-step explanation:
over evaluate function
Answer:
C. hope it helps :)
Step-by-step explanation:
What is the product of 5/11 and 3/4
Answers
Answer:
15/ 44
Step-by-step explanation:
just multiply across
5 x 3 = 15
11 x 4 = 44
= 15/44
Answer:
[tex]\frac{15}{44}[/tex]
I hope this helps!
The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate.
Principle $ 20,000 Rate 5.5% Compounded Daily Time 16 years
Required:
a. Find how much money there will be in the account after the given number of years. (Assume 360 days in a year.)
b. Find the interest earned.
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given that:
Principal = $20000
Interest rate = 5.5% = 0.055 compounded daily
Time = 16years =(360 * 16) = 5760
n = number of times interest is applied per period
Amount of money in account after 16 years :
A = p(1 + r/n)^nt
A = total amount
A = 20000(1 + 0.055/360)^(360*16)
A = 20000(1 + 0.0001527)^5760
A = 20000(1.0001527)^5760
A = 48193.1611
Interest on principal :
$48193.1611 - $20000
= $28193.1611
two times a number is four times that number minus a negative eighteen
Answers
Answer:
-9
Step-by-step explanation:
the number is x
2x = 4x - - 18
2x = 4x + 18
-2x = 18
x = -9
Answer:
-9
Step-by-step explanation:
Let's solve your equation step-by-step.
2x=4x−(−18)
Step 1: Simplify both sides of the equation.
2x=4x+18
Step 2: Subtract 4x from both sides.
2x−4x=4x+18−4x
−2x=18
Step 3: Divide both sides by -2.
−2x/−2
= 18 /−2 x
=−9
A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs
170 lb and each box of books weighs 60 lb. The maximum capacity of the elevator is 1300 lb. How many boxes
of books can the delivery person bring up at one time?
Answers
Answer:
18 at most.
Step-by-step explanation:
A recipe calls for 18 ounces of cream cheese with 15 ounces of sugar." How many ounces of cream cheese are there per ounce of sugar?
PLEASE HELP
Answers
Answer:
1.2
Step-by-step explanation:
Just divide
Answer:
1.2
Step-by-step explanation:
Divide 18 by 15 and get the answer.
Find the focus and directrix of the parabola with the given equation. y^2-4x=0
Answers
Answer:
directrix: x=-1
focus: (1,0)
Step-by-step explanation:
Perform the indicated operation
3/4 divided by 1/3
Answers
Answer:
2 1/4
Step-by-step explanation:
3/4 ÷ 1/3 = ?
(to divide fractions faster you flip the second fraction so:)
3/4 x 3/1 = 2 1/4
Help plz Easy math I know the answer isn’t A
Answers
Answer: B
Step-by-step explanation: It is greater or equal to -6 and less than or equal to 5.
Help me guys I suck at fractions :(
Answers
Answer:
its b are c i think
Step-by-step explanation:
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE i'll give you brainliest
When a piece of metal is subject to below zero temperatures, shrinking will normally take place. If the diameter of a steel rod shrinks from 0.02 meters to 0.015 meters, what is the percentage decrease in the diameter?
Answers
1.333...percent
Hope it helps
The sum of 48 and itself, its half and half of the half is added to 18.
Answers
Answer:
150
Step-by-step explanation:
This is a word problem which should be tackled accordingly.
The sum of 48 and itself
= 48+48
= 96
It's half and half of its half
= 48/2 and (48/2)/2
= 24+ 24/2
= 24+12
= 36
Is added to 18
= 96+36+18
= 150
From the description above the entire sum is 150.
Wilson paints 40% of a bookcase in 20 minutes. How much more time will it take to finish the bookcase
Answers
Answer:
50 mins
hope this helped :)
A bee flies at 10 feet per second directly to a flowerbed from its hive. The bee stays at the
flowerbed for 16 minutes, and then fies directly back to the hive at 8 feet
per second it is away from the hive for a total of 20 minutes
a. What equation can you use to find the distance of the flowerbed from the hive?
b. How far is the flowerbed from the hive?
a. Write the equation Leld be the distance of the flowerbed from the hive
(Type an equation Use integers of fractions for any numbers in the equation. Do not simplity)
Answers
Answer:
a. s = [tex]\frac{d}{t}[/tex]
b. 9600 ft
Step-by-step explanation:
In the given question, the motion of the bee involves speed (s), distance (d) and its time of flight (t).
a. The equation required to determine the distance of the flowerbed from the hive/ hive to flowerbed is;
speed = [tex]\frac{distance}{time}[/tex]
i.e s = [tex]\frac{d}{t}[/tex]
b. Given that: the bee flies back at 8 feet per second, and in 20 minutes (1200 seconds);
s = [tex]\frac{d}{t}[/tex]
⇒ d = s x t
= 8 ft/s x 1200 s
= 9600 ft
The flowerbed is 9600 feet from the hive.
Pleas help I am brainliesting and explain please
Answers
Answer:
-2.63 is bigger
Step-by-step explanation:
-2 5/7 is the same as -2.71428571428...
and when you compare a negative the smaller number is always greater than the bigger number because it is negative.
TRUE OR FALSE? The difference between two numbers is (-3). WHICH OF THE EXPRESSIONS COULD REPRESENT THE SUBTRACTION PROBLEM? (HINT: Solve each expression - if it equals (-3) it is TRUE - if it does NOT equal (-3) than it is FALSE) REMEMBER: Change subtraction problem into addition problem before solving. A) -4 - 1
Answers
Answer:
A) True
Step-by-step explanation:
[tex]-4,-1[/tex]
If we subtract the two numbers we get
[tex]-4-(-1)=-4+1=-3[/tex]
It can be seen that subtracting the two numbers changes the sign of one number by which we can algebraically subtract the numbers. Since, the addition of 1 shifts the number towards zero in the number line, the minus sign still remains.
So A)-4 -1 is true.
Mrs. Olen wants to join a gym. Francis Lewis Gym charges a new member fee of $150 plus $10 each month. Clintonville Gym charges a new member fee of $50 plus $35 each month.
Answers
Answer:Step-by-step explanation:
a. Let x = number of months
Amount charged by Francis Lewis Gym = 150 + 10x
Amount charged by Clintonville Gym = 50 + 35x
Set each expression equal to the other to generate an equation to use in finding the number of months for which the cost of membership will be the same at both months
150 + 10x = 50 + 35x
Collect like terms
150 - 50 = -10x + 35x
100 = 25x
Divide both sides by 25
100/25 = x
4 = x
Answer: 4 months
b. Substitute x = 2 into each if the expression of the amount charged by each gym. The one that gives the lowest amount should be the one Mrs. Open should should join.
Amount charged by Francis Lewis Gym = 150 + 10x
= 150 + 10(2)
= 150 + 20
= $170
Amount charged by Clintonville Gym = 50 + 35x
= 50 + 35(2)
= 50 + 70
= $120
She should join the Clintonville Gym if she plans to join a gym for 2 months.
Answer: Clintonville Gym
Which equation represents the situation below?
John owed the bank 7 dollars, but he made 12 dollars.
Answers
Answer:
12-7=5
Step-by-step explanation: if you u need a equation for how much he has there u go
The volume of air in a balloon is represented by the function v(n) = nr), where r is the radius of the balloon, in
inches. The radius increases with time, in seconds, by the function r(t) = 4,2. Which statements are true?
Answers
Answer:
When V is composed with r, the composite function is [tex]\frac{1}{48} \pi t^{6}[/tex]
When Vr6 shows that the volume is 9724. When the radius is increased to 6 inches.
Step-by-step explanation:
Volume is determined by [tex]cm^{3}[/tex] if the balloon is filled with air its volume will be increased and the composite function will represent the volume of the balloon. The radius of the balloon will rise in seconds. If t seconds are consumed to reach to a radius of 6 inches then the pie function is used to determine the volume.
What is the value of the expression -(-4)(-6)-3/5(10+15)
Answers
Answer:
-(-4)(-6)*3/5(10+15)
when there is a (-) in front of an expression in parentheses, change the sing of each term in the expression.
4*(-6)*3/5*(10+15)
Add the numbers (10+15)
4(-6)*3/5*25
multiplying an odd number of negative terms makes the product negative
-4*6*3/5*25
reduce the number with the greatest common factor 5
-4*6*3*5
calculate the product
solution
-360
Help please!!!!!! I can’t figure it out.
Answers
Answer:
A.) parallel
Step-by-step explanation:
they are on opposite sides, and will never touch.
Hope I helped!! :)
