where is the roller coaster
The opening of a tunnel that travels through a mountainside can be modeled by [tex]y = - \frac {2}{15} (x - 15)(x + 15)[/tex], where x and y are measured in feet. The x-axis represents the ground.
a. Find the width of the tunnel at ground level.
b. How tall is the tunnel?
Answer:
(a) 30 feet
(b) 30 feet.
Step-by-step explanation:
Given that the opening of a tunnel that travels through a mountainside can be modeled by
[tex]y=\frac{-2}{15} (x-15)(x+15)[/tex], where x and y are measured in feet.
[tex]\Rightarrow y=\frac{-2}{15}(x^2-15^2}[/tex]
[tex]\Rightarrow y=\frac{-2}{15}{x^2-225}\cdots(i)[/tex]
(a) At the ground level, [tex]y=0[/tex]
So, the width of the tunnel at ground level is distance between the extreme point of the tunnel on the grount.
For, [tex]y=0[/tex], the extreme points of the tunnel.
[tex]0=\frac{-2}{15} (x-15)(x+15)[/tex]
[tex]\Rightarrow (x-15)(x+15) =0[/tex]
[tex]\Rightarrow x= 15, -15[/tex]
So, the extreme points of the tunnel are, [tex]x_1=15[/tex] and [tex]x_2=-15[/tex].
Hence, the width of the tunnel at the ground level
[tex]= | x_1 - x_2 |[/tex]
[tex]=|15-(-15)|[/tex]
[tex]=30[/tex] feet.
(b) The maximum height of the tunnel can be determiment by determining the maxima of the given function.
First determining the value of x for which the slope of the graph is zero.
[tex]\frac{dy}{dx}=0[/tex]
From equation (i),
-2x=0
[tex]\Rightarrow x=0[/tex]
And [tex]\frac{d^2y}{dx^2}= -2[/tex]
which is always negative, so at x=0 the value of y is maximum.
Again, put x=0 in equation (i), we have
[tex]y=\frac{-2}{15}{0^2-225}[/tex]
[tex]\Rightarrow y=30[/tex] feet.
Hence, the tunnel is 30 feet tall.
Jill spends $525 for monthly bills. Of this amount she spends 110 on her cell phone bill and 25% on her car payment. The remainder pays her utilities. How much money does she spend on utilities?
Answer:
283.75
Step-by-step explanation:
525/4=131.25
131.25+110=241.25
525-241.25=283.75
[tex] \frac{100}{1} = {10}^{x} [/tex]
Please Help!! Due in 5 minutes!
Answer:
I may be wrong but I beileve its A(-20)
Step-by-step explanation:
Answer: Hey there The answer is simple is -20
Step-by-step explanation:
(2)(12)/-3-12=-20
hope this helps
Solve for x:
logx=3log2
(I forgot how to do simple logarithmic equations lol)
thanks in advance!
Use mental math to find the quotient of 397.3 ÷ 103.
A. 0.03973
B. 0.3973
C. 3.973
D. 39.73
Answer:
Your answer is: I think C) 3.973
Because ↓
Step-by-step explanation:
Hope this helped : )
simplify 6^-3
Please I need this asap!!!!
Answer:
Exact Form:
1 /216
Step-by-step explanation:
I need some help with geometry.
Answer:
x = 17, angle 1 and 2 = 45
Step-by-step explanation:
Question 13
Find the value of x.
need help, plz answer
Answer:
55 r5
Step-by-step explanation:
Answer:
390/7=55 with a remainder of 5.
Step-by-step explanation:
we can get this answer by subtracting fifty-five sevens from three-hundred ninty.
390-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7=5
Write the following equation in slope intercept form.
7x-4y=22
y= x+
Answer:
y= -7x+22/-4
Step-by-step explanation:
Answer:
y=7/4x-11/2
Step-by-step explanation:
Move the Y and x values to separate sides
-4y=-7x+22
divide whatever it takes to make y alone (dived by -4)
y=7/4x-11/2
Help me...PLEASE... :(
Answer:THE ANSWER IS BLOCKED AND DELETED FROM THE ACCOUNT OR THE INTERNET ACCESS IS LOW OR YOUR BATTERY IS NOT WORKING PROPERLY TRY AGAIN LATER
Multiply. Write your answer as a fraction in simplest form.
5/6⋅(−4 1/2)⋅(−2 1/5)=
Answer:
7425
Step-by-step explanation:
First let's make the last two fractions improper.
-4 1/2 = -9/2 -2 1/5 = -11/5
Now we have to find the least common denominator.
[tex]\frac{5}{6} *\frac{-9}{2}*\frac{-11}{5}[/tex]
The least common denominator is 30 because all the denominators can be multiplied by something to get 30.
[tex](\frac{5}{5})*\frac{5}{6}* (\frac{15}{15})*\frac{-9}{2}* (\frac{6}{6})*\frac{-11}{5}[/tex] Simplify
[tex]\frac{25}{30}*\frac{-135}{30}*\frac{-66}{30}[/tex] simply
[tex]\frac{-3375}{30}*\frac{-66}{30}[/tex]
[tex]\frac{222750}{30}[/tex] simply
7425
What is the slope of the line that passes through the points (8,7) and (4, 5)? Write
your answer in simplest form.
Answer: 1/2
Step-by-step explanation: got it right
The slope of the line that passes through the points (8,7) and (4, 5) is 1/2.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).
The given coordinate points are (8, 7) and (4, 5).
Substitute (x₁, y₁)= (8, 7) and (x₂, y₂)= (4, 5) in slope formula, we get
Slope = (5-7)/(4-8
= -2/(-4)
= 1/2
Therefore, the slope of the line that passes through the points (8,7) and (4, 5) is 1/2.
To learn more about the slope of a line visit:
https://brainly.com/question/14511992.
#SPJ6
Hi, i would really appreciate if someone helped me out!
A corner store sells two kinds of baked goods: cakes and pies. A cake costs $11 and a pie costs $10. In one day, the store sold 11 baked goods for a total of $117. How many cakes did they sell?
Answer:
7cakes and 4 pies
Step-by-step explanation:
The answers are on the pic
please answer fast!!
Answer:
27
Step-by-step explanation:
Jane decided she would spend the
of her money on Sweet Tarts. About how
many pounds of Sweet Tarts did Jane
purchase?
. Between the gum balls, Pixie Sticks, and
that she would spend the rest
Sour Patch Kids, how much money will
Nicholas have left of his allowance?
Answer:
can you comment the real question because this is just gibrish
Step-by-step explanation:
Find the slope of the line that passes through the following pair of coordinates: (15,18) (0,6)
Answer: y= (4/5)x+6
Step-by-step explanation:
(0,6) is the y intercept/b . Use y2-y1 for the slope/m. Y= Mx+b now is y=(4/5)x+6.
The sum of three numbers is 79. The sum of five times the first number and two times the
second number increased by the third number is 859. Two time the first number, increased by
three times the second number plus nine times the third number is 498. Write a system.
Answer:
(x+y+z)=79
5x+2y+z=859
2x+3y+9z=498
Step-by-step explanation:
Its writing 3 different equations that have the same value for the same variable.
Which of the following best describes the English expression fourteen less
than the quantity of a number plus one?
A. (1 - x) +14
O B. 4 - 1
O C. (x + 1) - 14
D. (x - 1) +14
Answer:
c
Step-by-step explanation:
Mandi has $40 to spend at the fair. The admission to get into the fair is $5 and each ride is $1.75
Write an inequality to represent the situation using r for the number of rides
What value of x makes this equation true? 0.6x − 5 = 0.1x + 7
Answer:
Step-by-step explanation:
0.6x − 5 = 0.1x + 7
.6x-.1x=.5x
.5x -5 = 7
7 + 5 = 12
.5x = 12
12/.5 = 24
x = 24
Samantha paid $10 to join an online book club. Then she paid $3 per e-book that she read. She has spent more than $40. How many e-books did she read? Show how you would set the problem up and the answer. * Your answer Submit Jer submit passwords through Google Forms. This form was created inside of River Grove School District 85.5. Report Abuse
Answer:
13/13.3 or 10
Step-by-step explanation:
You said she paid $10 to join, if she spent at least $40, then we subtract 10, then divide 30 by 3 then you would get 10.
If we don't have to subtract and she spent around $40 on only books, it would be 13/13.3
Mrs. Flossi is hosting a trivia contest for 40 students and 24 staff members. To be fair,
Mrs. Flossi wants there to be the same number of students and the same number of
staff members on each team.
What is the greatest number of teams Mrs. Flossi can make?
1. 3 teams
2. 4 teams
3. 5 teams
4.8 teams
(I WILL GIVE BRAINLIEST)
Answer:
8 teams is answer
Step-by-step explanation:
If you were to roll the
dice two times what is the
probability it will land on a
3 both times?
Answer:
1/36
Step-by-step explanation:
A dice have 6 faces, each face have 1/6 chance to land on, so the chance of landing on 3 two times in a row is 1/6 x 1/6 = 1/36
The price of stock market in at 9 AM was 13.17 then the price has been increasing at a rate of 0.11 each hour at noon the price of stuff he was 13.67 it begins to decrease at the rate of 0.12 each hour if the two rates continue and how many hours were the prices of the two stocks with the same
Answer:
2.26 hours
Step-by-step explanation:
Given that:
Stock 1:
Initial price = 13.17
Rate of increase = $0.11 per hour
13.17 + 0.11h - - - (1)
Stock 2 :
Initial price = 13.69
Rate of decrease = 0.12 per hour
13.69 - 0.12h - - (2)
13.17 + 0.11h = 13.69 - 0.12h
0.11h + 0.12h = 13.69 - 13.17
0.23h = 0.52
h = 0.52 / 0.13
h = 2.26 hours
Simplify -5(20 + 3).
85
-115
-97
-103
ill give brainliest
Answer:
The answer is -115
Step-by-step explanation:
Answer:
-115
Step-by-step explanation:
Ur welcome
please please help me i dont know
Answer:
O-O omg i feel u i have like the same question
Step-by-step explanation:
sorry couldn't help
Answer:
Hello! I'm pretty sure you aren't expecting an answer now. If no one else answers the points would be lost so I'm answering right now. If you were, I'm really sorry and you can report this answer so that it gets deleted and another person can answer! :)
Solve.
24 + d = 30 fastt
What is the measure of angle Y, in degrees?
Answer:
B
Step-by-step explanation: