Answer:
Answer : 1/8.
Step-by-step explanation:
Hey there!
Please see the attached picture for your answer.
Hope it helps!
A one lane highway runs through a tunnel in the shape of one half a sine curve cycle
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.
Learn more about the sine curve here;
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A collection of 30 coins consists of dimes and nickels. The total value is $1. 95How many dimes are there?
A swimmer dove off a board that was 50 ft above the water. The swimmer reached a depth of 15 ft in the pool. What number represents the swimmer's original height, in feet?
9514 1404 393
Answer:
50
Step-by-step explanation:
The number you choose depends on the location you consider to be zero height.
If we consider the surface of the pool to be zero height, and "up" to be the positive direction for measuring height, then the appropriate number for the original 50-ft height is 50.
50% of 80
50% of 48
50% of 15
25% of 120
25% of 90
Write a 6-digit number that fits the description.
1. The value of its thousands digit is 5,000.
2. The value of its hundreds digit is 700.
3. Its tens digit is 2 less than the thousands digit.
4. Its hundred thousands digit is the same as the hundreds digit.
The number is?
Answer:
175731 is one of the answers of the 6 digit number
some others are:
275732
375733
475734
575735
675735
775734
875732
The 6-digit number is 175731.
What is the place value strategy?The place value strategies are defined as math strategies that use to assist you in resolving your elementary math problems, use your places values, such as tens and hundreds. It is possible to employ enlarged notation or compensation. Using regrouping techniques, you can make the problem easier by compensating for addition.
Let the number would be ABCDEF
Given the condition that the value of its thousands of digits is 5,000.
So C = 5
Given the condition that the value of its hundreds of digits is 700.
So D = 7
Given the condition that Its tens digit is 2 less than the thousand digits.
So E = 5-2 = 3
Given the condition that Its hundred thousand digits is the same as the hundred digits.
So B = 7
Therefore, all possible answers:
275732
375733
475734
575735
675735
775734
875732
Hence, the 6-digit number is 175731
Learn more about the place value strategy here:
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Two cards are selected with replacement from a standard deck of 52 cards. Find the probability of selecting a heart and then selecting a diamond.
Answer: 50.2 is it
Step-by-step explanation: thats easy
Probability helps us to know the chances of an event occurring. The probability of selecting a heart and then selecting a diamond is 144/2652.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that Two cards are selected with replacement from a standard deck of 52 cards. Therefore, the probability of selecting a heart and then selecting a diamond is,
Probability = (12/52) × (12/51)
Probability = 144/2652
Hence, The probability of selecting a heart and then selecting a diamond is 144/2652.
Learn more about Probability:
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Find the missing side. Round your answer to the nearest tenth
Answer:
14.7
Step-by-step explanation:
tan(73)=48/x
or, x=48/tan(73)
or, x=14.7 (rounded to the nearest tenth)
Answered by GAUTHMATH
Find the surface area of a rectangular prism with a height of 16 feet, a width of 10 feet, and a length of 13 feet.
988 ft2
996 ft2
980 ft2
1000 ft2
Answer: 996 ft2
Step-by-step explanation:
Add up the area of all 6 sides of the prism:
(10 · 13) + (10 · 13) + (10 · 16) + (10 · 16) + (16 · 13) + (16 · 13)
= 130 + 130 + 160 + 160 + 208 + 208
=996 ft²
Answer:
B) 996 ft2
Step-by-step explanation:
What is the solution to the system of equations below?
2x+3y=6
x-3y=9
Answer:
Step-by-step explanation:
2x + 3y = 6
2x = 6-3y
x = (6-3y)/2
x - 3y = 9
(6-3y)/2 -3y = 9
(6-3y)/2 -6y/2 = 9
(6-9y)/2 = 9
6 - 9y = 9×2
-9y = 18-6
y = 12/-9
y = -4/3
2x + 3y = 6
2x + 3(-4/3) = 6
2x -4 = 6
2x = 6+4
2x = 10
x = 10/2
x = 5
Therefore x = 5 and y = (-4/3)
I used subsitution method
please click thanks and mark brainliest if you like :)
Answer:
x = 5; y = -4/3
Step-by-step explanation:
One equation has 3y. The other equation has -3y. Add the equations to eliminate y and solve for x.
2x + 3y = 6
(+) x - 3y = 9
---------------------
3x = 15
x = 5
2x + 3y = 6
2(5) + 3y = 6
3y + 10 = 6
3y = -4
y = -4/3
Answer: x = 5; y = -4/3
Please help‼️
Given O below, if XY and YZ are congruent, what is the measure of chord XY?
Answer:
11.2
Step-by-step explanation:
yz = 11.2
since the corresponding arc of yz and xy are same, their measures will ba same too
Answered by GAUTHMATH
Answer:
11.2
Step-by-step explanation:
good luck!
Can someone please help
Me
Answer:
$3735
Step-by-step explanation:
2/5 = 8/20
8/20 + 7/20 = 15/20 = 3/4
3/4*4980 = 3735
please help me with this
9514 1404 393
Answer:
92°
Step-by-step explanation:
The "givens" tell you the E and F are midpoints of their respective segments. That means EF ║ AB and angles DBF and EFC are "corresponding" angles with respect to transversal BC and those parallel lines. Corresponding angles are congruent, so ...
m∠DBF = m∠EFC = 92°
the image is located below
Answer:
288 ft³
Step-by-step explanation:
Volume of the pyramid,
base area × height × (1/3)
= (9×8)×12/3
= 72×4
= 288 ft³
please help me asap!!!!!
Answer:
392
Step-by-step explanation:
1.49×10⁸/3.8×10⁵ = 392
What is the volume of this regular prism?
54.97 cubic inches
8.91 cubic inches
109.95 cubic inches
21.99 cubic inches
Answer:
A
Step-by-step explanation:
The volume of prism is b*h, base area is (2.5)*(3.24*(1.1)=8.91. Hence volume is 8.91*6.17=54.97
Tại sao số mắt xích không được là bội số của số răng đĩa xích
Answer:
Nên sử dụng số răng lẻ cho đĩa xích dẫn động kết hợp với số lượng mắt xích chẵn để mài mòn đồng đều trên răng và trục lăn. Trong trường hợp này, một răng cụ thể của bánh xích không tiếp xúc với một mắt xích cụ thể của xích trong mỗi lần quay.
Step-by-step explanation:
Translated
It is preferable to use an odd number of teeth for the driving sprocket in combination with an even number of chain links for uniform wear and tear on the teeth and rollers. In this case, a particular tooth of the sprocket wheel does not come in contact with a particular link of the chain for every rotation.
Joes bait shop brought in a gross profit in sales of $4,100.00 in the month of June. During the same month their operating expenses totaled $1990.00. Calculate the net income of the bait shop for the month of June
Answer:
2110
Step-by-step explanation:
4100-1990=2110
Hey I need helping with solving thank you
Answer:
the answer to this equation is c (10)
Help
Plz!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
angle G
sin inverse (21/29) = 46.4
GH
c^2 - b^2 = a^2
29^2 - 21^2 = a^2
a = √(29^2 - 21^2)
GH = 20
therefore ans is B) <G = 46.4º, <I = 43.6º, GH = 20
Which of the following shows the extraneous solution to the logarithmic equation below?
2 log Subscript 5 Baseline (x + 1) = 2
Answer:
x=4
Step-by-step explanation:
log5(x+1)=1, (x+1)=5, x=4
Answer:
x= -6
Step-by-step explanation:
i got it wrong and the answer is -6
What is the distance between point C and point D?
Question 5 options:
A)
17 units
B)
13 units
C)
12 units
D)
√85 units
Answer:
B. 13 units
Step-by-step explanation:
let
(x1 , y1) = (-4 , -6)
(x2 , y2) = (1 , 6)
distance between CD = root (x2 - x1)^3 + (y2 - y1)
= root {1 - ( -4)}^2 + {6 - ( -6)}^2
= root {1 +4}^2 + {6+6}^2
= root 5^2 + 12^2
= root 25 + 144
= root 169
= 13 units ans
A speed training service wants to explore the effectiveness of some of the classes offered to their clients. They randomly select 300 high school athletes and record their 50-meter dash time. The 300 high school athletes are then randomly assigned to three groups with 100 in each. One hundred athletes will take a circuit training class, 100 athletes will take an interval training class, and 100 athletes will take a plyometrics training class. At the end of 10 weeks of taking these classes, their 50-meter dash time will be recorded a second time. Their times will be analyzed to see which class showed the greatest overall improvement in times.
Select all the sentences that correctly identify the components of the experiment.
The experimental units are subjects.
The subjects are the 50 athletes.
There is one treatment, the 50-meter dash.
There are three treatments.
One treatment is a circuit training class.
The factor is the type of class.
There are 10 levels of the factor.
Answer:
A,D,E,F
1,4.5,6
The experimental units are subjects.
There are three treatments.
One treatment is a circuit training class.
The factor is the type of class.
ED2021
During a one-month promotional campaign, Fran's Flix gave either a free DVD rental or a 12-serving box of microwave popcorn to new members. It cost the store $1 for each free rental and $2 for each box of popcorn. In all,46 new members were signed up and the store's cost for the incentives was $86. How many of each incentive were given away?
Given the linear function f(x) 2/3x + 6 evaluate f(-6)
the answer is on the photo
Mariah swam her leg of the race in 24.98 seconds and Janet swam her leg of the relay race in 25.874 seconds. What was their combined time for their part of the relay?
Answer:
50.854 seconds
Step-by-step explanation:
24.98 + 25.874 = 50.854 seconds
Y=square root of x compare to y= - square root of x how they differ and why
Answer:
Simply because x=y2 doesn't imply that y=
√
x
.
(a) How many different three-letter initials can people have: , (b) How many different three-letter initials with none of the letters repeated can people have: , (c) How many different three-letter initials with letters repeated begin with an X: , (d) How many different three-letter initials begin with a F and end in a D: .
Answer:
Step-by-step explanation:
A) 26*26*26 =17576
B)26*25*24=15600
C)26*26=676
D) 26
using the unit circle what is the exact value of tanpi/6
Answer:
[tex] \frac{ \sqrt{3} }{3} [/tex]
Step-by-step explanation:
[tex]\frac{1}{3} \div \sqrt{3} [/tex]
help please i’ll give brainliest
Answer:
3rd option
..................[tex]A) \frac{4-2}{2-1} =2[/tex]
[tex]B)\frac{1-0.5}{4-2} =0.25[/tex]
[tex]C)>2[/tex]
[tex]D) 1[/tex]
~OAmalOHopeO
Answer:
The third one is your answer
if 2x + 1=7 what is the value of x
Answer:
x=3
Step-by-step explanation:
2x+1=7
2x=7-1
2x=6
x=6/2
x=3
Answer:
Solution,
2x + 1=7
or 2x = 7 - 1
or, 2x= 6
or, x = 6
2
or, x = 3
.:. x = 3
