A one lane highway runs through a tunnel in the shape of one half a sine curve cycle
Answers
The sine curve equation, y = 10·sin(x·π/24), that models the entrance of the
tunnel with a cross section that is the shape of half of a sine curve and the
height of the tunnel at the edge of the road, (approximately 7.07 ft.) are
found by applying the following steps
(a) The equation for the sine curve is y = 10·sin(x·π/24)
(b) The height of the tunnel at the edge of the road is approximately 7.07 feet
The reason for the above answers are presented as follows;
(a) From a similar question posted online, the missing part of the question
is, what is the height of the tunnel at the edge of the road
The known parameters;
The shape of the tunnel = One-half sine curve cycle
The height of the road at its highest point = 10 ft.
The opening of the tunnel at road level = 24 ft.
The unknown parameter;
The equation of the sine curve that fits the opening
Method;
Model the sine curve equation of the tunnel using the general equation of a sine curve;
The general equation of a sine curve is y = A·sin(B·(x - C) + D
Where;
y = The height at point x
A = The amplitude = The distance from the centerline of the sine wave to the top of a crest
Therefore;
The amplitude, A = The height of half the sine wave = The height of the tunnel = 10 ft.
D = 0, C = 0 (The origin, (0, 0) is on the left end, which is the central line)
The period is the distance between successive points where the curve passes through the center line while rising to a crest
Therefore
The period, T = 2·π/B = 2 × Opening at the road level = 2 × 24 ft. = 48 ft.
T = 48 ft.
We get;
48 = 2·π/B
B = 2·π/48 = π/24
By plugging in the values for A, B, C, and D, we get;
y = 10·sin((π/24)·(x - 0) + 0 = 10·sin(x·π/24)
The equation of the sine curve that fits the opening is y = 10·sin(x·π/24)
(b) The height of the tunnel at the edge of the road is given by substituting
the value of x at the edge of the road into the equation for the sine curve
as follows;
The width of the shoulders = 6 feet
∴ At the edge of the road, x = 0 + 6ft = 6 ft., and 6 ft. + 12 ft. = 18 ft.
Therefore, we get;
y = 10 × sin(6·π/24) = 10 × sin(π/4) = 5×√2
y = 10 × sin(18·π/24) = 10 × sin(3·π/4) = 5×√2
The height of the, y, tunnel at the edge of the road where, x = 6, and 18 is y = 5·√2 feet ≈ 7.07 ft.
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Related Questions
Write five other iterated integrals that are equal to the given iterated integral. 8 0 x2 0 y f(x, y, z) dz dy dx 0
Answers
An iterated integral is the outcome of taking integrals toward a function of more than one variable in such a way that part of the variables is treated as constants for each of the integrals.
From the given parameters, we are to write out five iterations for a triple integral;
[tex]\mathbf{\int ^8_0\ \int^{x^2}_{0} \ \int^y_0 \ \ f(x, y, z) \ dz dy dx }[/tex]
where;
the region is bounded by 0 ≤ z ≤ y, 0 ≤ y ≤ x², 0 ≤ x ≤ 8.Thus, since x, y, z are functions of at least one variable, we can have the following iterations:
[tex]\mathbf{\int^{64}_{0} \ \int^{8}_{\sqrt{y}} \ \int^{y}_{0} \ \ f(x,y,z) dz dxdy}[/tex] [tex]\mathbf{\int^{64}_{0} \ \int^{y}_{0} \ \int^{8}_{\sqrt{y}} \ \ f(x,y,z)\ dxdzdy}[/tex] [tex]\mathbf{\int^{64}_{0} \ \int^{64}_{z} \ \int^{8}_{\sqrt{y}} \ \ f(x,y,z)\ dxdydz}[/tex] [tex]\mathbf{\int^{8}_{0} \ \int^{x^2}_{0} \ \int^{x^2}_{z} \ \ f(x,y,z)\ dydzdx}[/tex] [tex]\mathbf{\int^{64}_{0} \ \int^{8}_{\sqrt{z}} \ \int^{x^2}_{z} \ \ f(x,y,z)\ dydxdz}[/tex]Learn more about iterated integrals here:
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-2/7 × 9.75 what is answer
Answers
Answer:
-2.78
Step-by-step explanation:
You first divide and then multiply.
If there are 10,000 people on a space ship and 7.5 potatoes grow out of 1 potato plant. How many potato plants are we going to need per person?
Answers
This can be answered by the equation 10,000 / 7.5 = 1,333.33, so we can round to 1,333.
Hope this helps!
Answer: 1333
Step-by-step explanation:
Graph the solution to the following system of inequalities.
-7x + 5y < -10
5x + 4y > 8
Then give the coordinates of one point in the solution set.
Answers
Graph attached
Solution is (1.6,0)NO NEED FOR LINKS NEED THE ANSWER RIGHT NOW
Answers
Answer:
a. y= 16+ 7x
b. y=19+9x
c. y= 10+5x
Step-by-step explanation:
a.) adds 7 each time
b.) adds 9 eah time
c.) adds 5 each time
Answer:
hope it helps you......
order of operations : simplify completely (6-2X2)X3
Answers
Answer:
6 is the answer.
Step-by-step explanation:
Using PEMDAS, let's solve.
(6 - 2 x 2) x 3(6 - 4) x 32 x 36Therefore, 6 is the answer.
Hoped this helped.
hello comment anything
Answers
I like anime and sleeping✌
Answer:
i like food, money, and games
Step-by-step explanation:
E
Floretta, a pitcher, claims that her pitch speed is less than 46 miles per hour, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 5% significance level, to persuade them. She throws 24 pitches. The mean speed of the sample pitches is 37 miles per hour. Floretta knows from experience that the standard deviation for her pitch speed is 5 miles per hour.
H0: μ≥46; Ha: μ<46
α=0.05 (significance level)
What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?
Answers
Which statement below is TRUE about |-2| and |-5|?
|-5| is greater than |-2|
|-2| is greater than the |-5|
Neither statement is true
Answers
Answer:
|-5| is greater than |-2|
Step-by-step explanation:
the absolute value of -5, is 5, which is greater than the absolute value of -2, which is 2. Have a wonderful rest of your day! I hope this helps!
Answer all of them plzz
Answers
Answer:
a) (2x+3) (x+4)
b) (5x-3) (x-1)
c) (-2x-3) (x-3)
d) 3(x-1) (3x-8)
e) -2(3x+5) (x-2)
f) h(4x-3) (3x-4)
g) -(x-3) (x+7)
h) (3x-2) (x+3)
i) 2(2x+1) (x-2)
j) (3h+2) (h-7)
Step-by-step explanation:
your welcome :)
Answer:
a)
(x+4)(2x+3)
b)
(x-2)(5x-3)
c)
(-x+3)(2x-3)
d)
3(x-1)(3x-8)
e)
2(-x+2)(3x+5)
f)
h(3x-4)(4x-3)
g)
(x+7)(-x+3)
h)
(x+3)(3x-2)
i)
2(x-2)(2x+1)
j)
(h-7)(3h+2)
Hope this helps!
Don’t know the answer
Answers
Answer:
log a + 3 . log c - log b
Step-by-step explanation:
2nd option is the correct answer
Answer:
log a + 3 . log c - log b
Step-by-step explanation:
✌️❤️✌️
NO NEED FOR LINKS NEED HELP RIGHT NOW
Answers
Answer:
1a.2
2a. 9
3a. 6000
1b. 9000
2b. 3000
3b. 9
Step-by-step explanation:
Hope you could get an idea from here.
Doubt clarification - use comment section.
if you help me with this i’ll mark you brainlest if you are the first to answer.
Answers
Answer:
m∠1 = 97
m∠2 = 83
m∠3 = 97
m∠4 = 83
Answer:
m∠1 = 97°
m∠2 = 83°
m∠3 = 97°
m∠4 = 83°
Step-by-step explanation:
180 - 97 = 83°
180 - 83 = 97°
Which answer shows the correct solution for 6x + 19x - 4 = 5(5x + 4)?
No solution
Infinitely many
One solution
Answers
Answer:
No solution
Step-by-step explanation:
25x-4=5(5x+4)
Distributive Property= 25x-4=25x+20
Solve for x
-4=20
Not possible so no solution.
Answer:
A
Step-by-step explanation:
6x + 19x -4 = 5(5x+4)
6x + 19x -4 = 25x+20
6x + 19x- 25x = 20+4
Combine Like terms
0 = 20 +4
0 = 24
0 = 24 = No solution
Help help math math help help
Answers
Answer:
102 degrees below horizontal
Step-by-step explanation:
if the first angle is 78 degrees, the angle on the other side of the line is 102 degrees because a straight line is 180 degrees, and a box would have a total of 360 degrees in it
because the same line passes through both horizontal lines, the angle 3 is equal to the opposite angle to the 78
180-78 = 102
another way to look at it is that the 78 degrees is the same angle directly above angle 3 because the horizontal lines are parallel, and if it is 78 degrees, that makes the angle below it (angle 3) 102 degrees since a straight line must add to 180 degrees
Answer:
102
Step-by-step explanation:
please help me on this, thank you
Answers
45 - 4 =41 and x is 20.5 or 20 1/2
75° b Arrange the three side lengths in increasing order. 350 c [?]
Answers
Answer:
a < b < c
Step-by-step explanation:
The side opposite the larger angle measure is the longer side.
The side opposite the smallest angle measure is the shortest side.
The sum of the three angles = 180° ; (75° + 35° + ? = 180°). The missing angle is 70°
The angles in order from the smallest to the largest:
35° < 70° < 75°
The side for the shortest to the largest
side opposite 35° is a
side opposite 70° is b
side opposite 75° is c
Answer a < b < c
Using angle sum property in △ABC
∠A+∠B+∠C=180
∘
⇒50
∘
+60
∘
+∠C=180
∘
⇒∠C=70
∘
In any triangle side opposite to the largest angle is the longest side.
Here ∠C is largest and side opposite to it is AB
∴AB is the longest side.
Then comes ∠B and side opposite to it is AC
∴AC is the second longest side.
Then comes ∠A and side opposite to it is AC
∴BC is the shortest side.
So the increasing order of sides is
BC
The formula for the area of an ellipse is Arnab. Using a + b = 20 write the area of
the ellipse as a function of a by solving for a and then plugging in your results
into the formula for the area of an ellipse to replace b.
Answers
[tex]A=\pi ab\qquad \qquad \begin{array}{llll} a+b=20\\ b=20-a \end{array}\qquad \qquad \stackrel{\textit{substituting}}{A=\pi a(20-a)}\implies A=\pi (20a-a^2)[/tex]
The area of the ellipse is given by the function A(a) = 20πa - πa², where a is a parameter representing one of the semi-major axes of the ellipse.
To write the area of the ellipse as a function of a using the given constraint a + b = 20, we first need to solve for b in terms of a and then substitute the expression for b into the formula for the area of the ellipse.
Given the equation for the ellipse:
x²/a² + y²/b² = 1
We have the constraint: a + b = 20
Now, let's solve for b in terms of a:
b = 20 - a
Now, we'll substitute this expression for b into the formula for the area of the ellipse:
Area (A) = πab
Area (A) = πa(20 - a)
Area (A) = 20πa - πa²
So, the area of the ellipse is given by the function A(a) = 20πa - πa², where a is a parameter representing one of the semi-major axes of the ellipse.
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Select the correct answer from each drop-down menu. Identify the type of chart described and complete the sentence. A (blank) chart shows open and close prices and highs and lows, but over a long time period it can also show pricing (blank) .
Answers
Based on the information given, it can be deduced that the chart that is being described is the OHLC chart.
It should be noted that an open-high-low-close chart(OHLC) chart simply means a type of chart that's used to illustrate the movements in the price of a financial instrument for a particular period of time.
The vertical line on the chart illustrates the price range over a unit of time. It's useful in assessing volatility as it shows the full price range of the period.
Learn more about charts on:
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Answer:
Candlestick & trends.
Step-by-step explanation: Got it correct on edmentum!
Rapid Rental Car charges a $40 rental fee, $15 for gas, and $0.25 per mile driven. For the same car,
Capital Cars charges $45 for rental and gas and $0.35 per mile. For bow many miles is the rental cost at
both companies the same?
Answers
Answer:
Step-by-step explanation:
40 + 15 + 0.25m = 45 + 0.35m
55 + 0.25m = 45 + 0.35m
10 = 0.10m
m = 100 miles
3 divided by 4 1/2 write in simplest form
Answers
[tex]3 \div 4 \frac{1}{2} \\ = 3 \div \frac{9}{2} \\ = 3 \times \frac{2}{9} \\ = \frac{2}{3} [/tex]
Answer:
[tex] \frac{2}{3} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
2 procedimientos por favor
Answers
Answer:
184.8
Step-by-step explanation:
385/25×12
385÷25=15.4
15.4×12=184.8
identify whether the given mathematical sentences below is true or false, then write your reason. If false , write the correct answer.
Answers
Answer:
Step-by-step explanation:
General admission to the fair is $8.00, and rides cost $3.00 each.
Answers
Answer:
$24.00
Step-by-step explanation:
8x3=24
Ordering decimals
Order these numbers from least to greatest.
1.509, 1.4062, 1.6, 1.56
Answers
Answer:
1.4062, 1.509, 1.56, 1.6
Step-by-step explanation:
1509/1000, 14062/10000, 16/10, 156/100
15090, 14062, 16000, 15600
1.4062, 1.509, 1.56, 1.6
(8,4) and has a slope of 5/2
Answers
Which equation represents this statement?
The product of 1/5 and a number is equal to 1/1 2.
1/5n=1/1 2
1/5÷n=1/1 2
1/5−n=1/1 2
1/5+n=1/1 2
Answers
Answer:
answer is B
Step-by-step explanation:
the difference of 16 and 2 divide by 7
make the equation
Answers
Answer:
(16-2)/7
Step-by-step explanation:
16-2=14
14/7=2
Equation: (16-2)/7
The difference of 16 and 2 divide by 7 gives result 2 and required equation is x = (16 - 2) / 7.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given numbers are 16, 2 and 7.
Let the difference of 16 and 2 divide by 7 gives result x,
The equation for the difference of 16 and 2 which is 14, divide by 7.
x = (16 - 2) / 7
The equation x = (16 - 2) / 7 can be simplified as,
The difference between 16 and 2 = 16 - 2 = 14
x = 14 / 7 = 2.
The required equation is x = (16 - 2) / 7 and simplified answer is 2.
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Josh was issued a traffic ticket for speeding. The court cost
was $40 and he had to pay $10 for every mile per hour
over the speed limit. Determine how fast Josh was driving
if the speed limit was 65 mph and his fine was $110.
Answers
Answer:
72 mph
Step-by-step explanation:
i did this on achievemath3000 and 72 was the answer
The quotient of 2 numbers, p and q.
Answers
Answer:
p/q = x
Step-by-step explanation:
