None of the options are entirely correct. The domain of the function is [tex]\( t \geq 0 \)[/tex] , and it does not directly represent the time to complete the hill or reach maximum height.The domain is representing all real numbers. The function doesn't directly indicate completion time or maximum height.
Let's analyze the given function [tex]\( h(t) = -3t^2 + 15t + 18 \)[/tex] to determine the domain and its meaning:
1. **Domain of the function**:
The domain of a quadratic function is all real numbers unless there are restrictions. In this case, there are no restrictions mentioned in the problem, so the domain is all real numbers. However, in the context of the roller coaster ride, the time ( t ) cannot be negative because it doesn't make sense for time to be negative in this scenario. Therefore, the practical domain is [tex]\( t \geq 0 \).[/tex]
2. **Time to reach maximum height**:
The time to reach the maximum height of the roller coaster can be found using the vertex formula: [tex]\( t = -\frac{b}{2a} \)[/tex] , where [tex]\( a = -3 \) and \( b = 15 \)[/tex] (coefficients from the quadratic function). Substituting these values into the formula:
[tex]\[ t = -\frac{15}{2(-3)} = -\frac{15}{-6} = \frac{15}{6} = \frac{5}{2} \][/tex]
Since time cannot be negative in this context, the time to reach the maximum height is [tex]\( t = \frac{5}{2} = 2.5 \)[/tex] seconds.
Now, let's analyze the given options:
- **Option 1: The domain of the function is [0, 6], and it represents the car's time to reach maximum height.**
- The domain given is correct [tex](\( t \geq 0 \)),[/tex] but it incorrectly states that it represents the time to reach maximum height. The correct time to reach maximum height is [tex]\( t = 2.5 \)[/tex] seconds, not 6 seconds.
[tex]\( t \geq 0 \),[/tex]
- **Option 2: The domain of the function is [-1, 6], and it represents the car's time to reach maximum height.**
- This option gives an incorrect domain. The domain is [tex]\( t \geq 0 \), not \( t \geq -1 \).[/tex]
- **Option 3: The domain of the function is [0, 6], and it represents the car's time to complete the hill.**
- This option correctly identifies the domain as [tex]\( t \geq 0 \).[/tex] However, it incorrectly states that it represents the time to complete the hill. The function does not directly represent the time to complete the hill; it represents the height of the car at any given time.
- **Option 4: The domain of the function is [-1, 6], and it represents the car's time to complete the hill.**
- This option gives an incorrect domain. The domain is [tex]\( t \geq 0 \),[/tex] not [tex]\( t \geq -1 \).[/tex]
Therefore, none of the options are entirely correct. The domain of the function is [tex]\( t \geq 0 \)[/tex] , and it does not directly represent the time to complete the hill or reach maximum height.
The vertex of a quadratic function is located at (1, 4), and the y-intercept of the function is (0, 1). What is the value of a if the function is written in the form y = a(x – h)2 + k?
a=____
Answer:
-3
Step-by-step explanation:
right on edge
Really need help! Been trying to solve for a while.
1. Solve the system by using a table. 3y=4x+7 , -4x-4y=28. These are the possible solutions:(–4, –3),(–3, –4), (4, 3),(3, 4).
2.Solve by graphing. -3x-y=-10, 4x-4y=8. possible solutions:(-1,3), (3-1), (1,3), (3,1)
Look at the rational expression below. x^2-4/2-x Which value of x makes the expression undefined?
Answer:
given rational function is undefined for x = 2
Step-by-step explanation:
The given rational function is
[tex]\frac{x^2-4}{2-x}[/tex]
The rational function is undefined if the denominator is zero.
Hence, the given rational function is undefined if
[tex]2-x=0[/tex]
Solve the equation for x
[tex]x=2[/tex]
Therefore, the given rational function is undefined for x = 2
Write an equation of the line that passes through the points (-2,-2) and (0,5)
Nancy randomly scattered one handful of seeds in her garden. The garden is circular and has a radius of 5 feet. Somewhere in the garden is a 2 feet by 2 feet square patch that has especially good soil for the seeds. If it is equally likely for a seed to land anywhere in the garden, what is the probability that a seed will land in the 2 feet by 2 feet square?
For model 5, the tip of the blade travels 0.18 mile per revolution. What is the approximate speed, in revolutions per minute,for model 5?
need the answer tooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
The approximate speed of model 5's 148-foot blade travels at 0.18 miles per revolution converted to feet is approximately 385.8 revolutions per hour.
To find the number of revolutions per minute for Model 5 with a blade length of 148 feet and a tip speed of 0.18 miles per revolution,
use the following calculation:
First, convert the tip speed from miles to feet:
0.18 miles × 5280 feet per mile = 950.4 feet per revolution
Now, divide this by the length of the blade in feet:
950.4 feet per revolution / 148 feet = 6.43 revolutions per minute
Finally, multiply this by 60 minutes per hour to get the number of revolutions per hour:
6.43 revolutions per minute × 60 minutes per hour = 385.8 revolutions per hour
Therefore, the required speed of model 5 has a blade that makes approximately 385.8 revolutions per hour.
Learn more about speed here
brainly.com/question/14311270
#SPJ3
Charlie used these steps to solve the equation 6x+5=1+2(3x+2)6x+5=1+23x+2. Which choice describes the meaning of his result, 5=5
Answer:
All values of x make the equation true. It is an infinite solution.
The radius of the bulls-eye of the dartboard is 8 inches. The radius of each concentric circle (there are 4 labeled A, B, C, D from the inside out) is 14 inches more than the radius of the circle inside it. If a dart lands at random on the dartboard, the probability that the dart will hit in area C is what percent?
HELP!!!!!!!!!Which geometric series converges?
Answer:
its b
Step-by-step explanation:
Classify the model as exponential growth or exponential decay. Identify the growth or decay factor AND the percent of increase or decrease per time period.
y=2(1/2)^t
Plz help!
Which sets of the real number system does − 2 belong to?
Larry wants to inscribe an equilateral triangle in a circle using only a compass and straightedge. He will first construct a circle and locate its center. He will then perform the following steps.
Step 1: Set the width of the compass to the diameter of the circle.
Step 2: Plot a point on the circle. Place the compass on this point and draw two arcs to cut the circle. These two points of intersection between the arcs and the circle represent two of the vertices.
Step 3: Draw a segment between the two vertices. Adjust the width of the compass to the length of the segment. Place the compass on one vertex and draw an arc to construct the third vertex.
Step 4: Draw a line from one vertex to the next to form an equilateral triangle.
What is the error in Larry's construction?
A. He did not draw a pair of perpendicular bisectors to construct two diameters of the circle.
B. He drew only two arcs.
C. He set the width of the compass to the diameter of the circle.
D. He did not ensure that the length of the sides of the triangle was the same as the diameter of the triangle.
The error in Larry's construction is:
C. He set the width of the compass to the diameter of the circle.
Step-by-step explanation:The steps for the construction of an inscribed equilateral triangle is as follows:
Step 1: Draw a circle on a piece of paper.Take a point anywhere on the circumference of the circle and take that point as a starting point.Step 2: Now without changing the span of the circle we have draw two arcs to cut the circle.These two points of intersection between the arcs and the circle represent two of the vertices. Step 3: Draw a segment between the two vertices. Adjust the width of the compass to the length of the segment. Place the compass on one vertex and draw an arc to construct the third vertex. Step 4: Draw a line from one vertex to the next to form an equilateral triangle.Hence, the error he that he set the width of compass equal to the diameter of circle.
Instead he should have set the width of the compass equal to the radius of the circle.
Find the supplement to the angle whose measure is 70 degrees. Show all your work
35 POINTS!!
The scatter plot shows the relationship betweeen the number of hours students spend watching television and the numer of hours they spend playing outdoor sports each week.
A graph is titled Television and Sport. On the x axis, the label is Weekly Hours of
What is the y-intercept of the line of best fit and what does it represent?
A 10.4 hours; the number of hours students play outdoor sports in a week when they do not watch television
B 7.2 hours; the number of hours students play outdoor sports in a week when they do not watch television
C 10.4 hours; the number of hours students watch television in a week when they do not participate in any outdoor sports
D 7.2 hours; the number of hours students watch television in a week when they do not participate in any outdoor sports
Answer:
D 7.2 hours; the number of hours students watch television in a week when they do not participate in any outdoor sports
Step-by-step explanation:
Given is a scatter plot which shows the relationship betweeen the number of hours students spend watching television and the numer of hours they spend playing outdoor sports each week.
From the graph showing the regression line, the regression line has y intercept as 7.2
(When x=0, y =7.2)
Hence correct answer is
D 7.2 hours; the number of hours students watch television in a week when they do not participate in any outdoor sports
A square banner has an area of (4x^2-12x+9) square inches. Write an expression for the perimeter of the banner.
A wedding planner purchased small and large lanterns for a wedding reception. The small lanterns cost $25 each, and the large lanterns cost $40 each. The planner purchased a total of 40 lanterns for a total of $1180.
Answer:
The wedding planner must have purchased 28 small lanterns and 12 large lanterns.
Step-by-step explanation:
Let the number of small and large lanterns purchased be S and L respectively.
S + L = 40 ........ Equation 1
L = 40 - S
25S + 40L = 1180 ....... Equation 2
25S + 40(40 - S) = 1180
25S + 1600 - 40S = 1180
-15S = 1180 - 1600
-15S = -420
S = 28
L = 40 - S
L = 40 - 28
L = 12
The wedding planner must have purchased 28 small lanterns and 12 large lanterns.
Which diagram shows parallel lines cut by a transversal?
Answer:
The third diagram.
Step-by-step explanation:
When we have two parallel lines cut by a transversal, vertical angles are congruent; alternate interior angles are congruent; alternate exterior angles are congruent; corresponding angles are congruent; and same-side interior angles are supplementary.
In the first diagram, we have two angles on the same side of their respective parallel lines and the same side of the transversal. These are by definition corresponding angles. Since they are not congruent, these lines are not truly parallel.
In the second diagram, we have two angles on opposite sides of the transversal and outside the block of parallel lines. These are by definition alternate exterior angles. Since they are not congruent, these lines are not truly parallel.
In the third diagram, we have two angles inside the block of parallel lines and on the same side of the transversal. These are by definition same-side interior angles. Since they are congruent, these are parallel lines.
What is the value of e^In7x a.1 b.7e c.7x d.7
There are 454 grams in a pound. There are 16 ounces in a pound. How many grams are in an ounce?
Answer: There are 28.375 grams in an ounce.
Step-by-step explanation:
Given: Total grams in a pound =454 grams
Total ounces in a pound = 16 ounces
Therefore, 16 ounces = 454 grams
To find grams in an ounce, we need to divide 454 grams by 16, we get
The total grams in an ounce=[tex]\frac{454}{16}=28.375\ grams[/tex]
∴The total grams in an ounce= 28.375 grams
Hence, there are 28.375 grams in an ounce.
28.375 grams in an ounce.
To calculate how many grams are in an ounce, divide 454 (grams in a pound) by 16 (ounces in a pound) to get 28.375 grams in an ounce.
To find out how many grams are in an ounce:
Given: 1 pound = 454 grams and 1 pound = 16 ounces.Since 1 pound = 454 grams and 1 pound = 16 ounces, divide 454 by 16 to find out how many grams are in an ounce.454 grams ÷ 16 = 28.375 grams in an ounce.A soccer ball has a radius of 6 inches, what is the approximate volume of the ball? Pi =3.14 *
Your school raise 125% of its fundraising goal. The goal raised $6,750. What was the goal?
can you please help me with this I will crown you brainly
Select the statements that are true for the graph of y=(x−1)^2(−6)
The vertex is (1, −6) .
The vertex is (−1, −6) .
The graph has a minimum.
The graph has a maximum.
From the graph of given function, we have vertex (1, -6). Therefore, option A is the correct answer.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is y=(x-1)²-6.
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (1, -6)
Focus: (1, -23/4)
Axis of symmetry: x=1
Directrix: y=-25/4
The coordinate points to plot are (-1, -2), (0, -5), (1, -6), (2, -5) and (3, -2).
Therefore, option A is the correct answer.
To learn more about the function visit:
https://brainly.com/question/28303908.
#SPJ2
PLEASE HELP ASAP!!! 42 POINTS
Gina sells 216 cakes in the ratio small :medium:large 5:7:12. The profit for one medium cake is twice the profit for one small cake. The profit for one large cake is three times the profit for one small cake. Her total profit id £648.45. Work out the profit for one small cake.
Answer:
£1.31
Step-by-step explanation:
5+7+12=24
216÷24=9
Small=9x5=45
Medium=9x7=63
Large=9x12=108
2x= Medium, Large= 3x, Small=x
Small=45x, Medium= 63x2=126x, Large=108x3=324x
45x+126x+324x=495x
£648.45=495x
£648.45÷495=x
£1.31=x
The profit for one small cake will be £ 1.31. The profit of the one small cake is the amount of benifit obtained to sell one cake.
What is profit?When money generated from a commercial activity exceeds the expenses, costs, and taxes involved in maintaining the activity in question, profit is earned.
The ratio of the small :medium: large cake is 5:7:12.
Let the cake is considered to be x;
The sum of alll the cakes is;
5x+7x+12x=24 x
The total no of cake is 216
Each no of cake is found as;
[tex]\rm 24 x = 216 \\\\ x = 9[/tex]
The number of the small cake;
N(s) = 9 ×5 =45
N(m)=9×7=63
N(l)=9×12=108
Let the small cake is x
The profit for one medium cake is twice the profit for one small cake;
P(m)=2x
P(l)=3x
P(s)=x
The small medium and the large cake according to the new condition will be 45 x,126x,324x respectively.
The sum of all the cakes according to the new condition is found as;
[tex]4s x +126 x+324 c \\\\ 495 x=648.45 \\\\ x=\£ \ 1.31[/tex]
Hence the profit for one small cake will be £ 1.31.
To learn more about the profit refer to the link;
https://brainly.com/question/15036999
#SPJ3
A sphere has a radius of 26 inches. a horizontal plane passes through the center of the sphere describe the cross section formed by the plane and the sphere.
When a horizontal plane passes through the center of a sphere with a radius of 26 inches, the cross-section formed is a circle with a radius of 26 inches.
let's break down the problem into two parts:
Describe the cross-section: We'll describe the shape formed when a horizontal plane passes through the center of the sphere.
Calculate the dimensions of the cross-section: We'll calculate the dimensions of the cross-section, such as its radius or diameter.
1. Describe the cross-section:
When a horizontal plane passes through the center of a sphere, it divides the sphere into two equal halves. The cross-section formed by this plane and the sphere will be a circle. Since the plane passes through the center of the sphere, the circle will be perfectly centered.
2. Calculate the dimensions of the cross-section:
Since the radius of the sphere is given as 26 inches, the radius of the cross-section (which is also the radius of the circle formed) will also be 26 inches.
So, the cross-section formed by the plane and the sphere is a circle with a radius of 26 inches.
Mr Daniels is organizing a class field trip on a budget of $900.The bus rental costs $600. Mr.daniels will also buy tickets that will cost $9.50 per student. Write an inequality to represent the number students,y, that he can bring on the trip.
Answer:
y ≤ 31 students
Step-by-step explanation:
The rental cost is a fixed cost that will be incurred irrespective of the number of students embarking on the class field trip. This cost added to the total ticket cost must be less than or equal to the budget.
the total ticket cost for y number of students
= 9.5y
Hence the total cost = 9.5y + 600 ( measured in $)
In inequality form,
9.5y + 600 ≤ 900 (all in $)
9.5y ≤ 900 - 600
9.5y ≤ 300
y ≤ 300/9.5
y ≤ 31 students
help with these two please....
Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. heidi rented a car one day and paid $58 for 190 miles. on another day she rented a car from the same agency and paid $86 for 330 miles. find the linear function f(x) (where x is in miles and f(x) is in dollars) that the agency could use to determine its daily rental charges.
The linear function f (x) hat the agency could use to determine its daily rental charges will be;
⇒ f (x) = 0.2x + 20
Where, f (x) is in dollars and x is in miles.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
Heidi rented a car for one day and paid $58 for 190 miles.
And, On another day she paid $86 for 330 miles.
Now,
We find the linear function for f (x), where f (x) is in dollars and x is in miles as;
Here the two situations are given for miles and dollars as;
(190, 58) and (330, 86)
Thus, The linear function with two points (190, 58) and (330, 86) is defined as;
⇒ y - y₁ = (y₂ - y₁)/(x₂ - x₁) (x - x₁)
⇒ y - 58 = (86 - 58) / (330 - 190) (x - 190)
⇒ y - 58 = 28 / 140 (x - 190)
⇒ y - 58 = 1/5 (x - 190)
⇒ y - 58 = 0.2 (x - 190)
⇒ y - 58 = 0.2x - 38
⇒ y = 0.2x - 38 + 58
⇒ y = 0.2x + 20
⇒ f (x) = 0.2x + 20
Thus, The linear function f (x) hat the agency could use to determine its daily rental charges will be;
⇒ f (x) = 0.2x + 20
Where, f (x) is in dollars and x is in miles.
Learn more about the linear expression visit:
https://brainly.com/question/18831322
#SPJ5
To determine the daily rental charges at a car rental agency based on fixed and per mile fees, the linear function f(x) is found to be $40 + $0.15 per mile.
Linear function f(x):
Define variables: Let d = daily rental charge, m = per mile charge.Form equations based on given data: $58 = d + 190m and $86 = d + 330m.Solve the system of equations to find f(x): d = $40 and m = $0.15. Therefore, f(x) = 40 + 0.15x.Write an expression to show the sum of fourteen and triple eight.