This can be determined by ellipse formula. Therefore, the height of the tunnel 4 feet from the edge is 13.08 feet.
Given:
A tunnel is constructed with a semi-elliptical arch. The width of the tunnel is 80 feet, and the maximum height at the center of the tunnel is 30 feet.
Find:
The height of the tunnel 4 feet from the edge is.
Let us consider,
The center of the concerned ellipse at the centre of its width of 80 feet. Let us consider
[tex]\begin{alligned}2a&=80\\\\a&=\dfrac{80}{2}&=\bold{40\:feet}\end{aligned}[/tex]
Since the maximum height at the centre of the tunnel is 30 feet, we can say that b = 30 feet.
Now, considering the centre of the tunnel as origin, we can write the equation of the ellipse as:
[tex]\bold{\dfrac{x^{2} }{a^{2} } +\dfrac{y^{2} }{b^{2} } =1}[/tex]
If we need to find the height of the tunnel 4 feet from the edge, we are looking for the height of the tunnel at 40 - 4 = 36 feet from the center of the tunnel.
Therefore, we need to find y from the equation of the ellipse, when x = 36 feet.Hence,
[tex]\begin{aligned}\dfrac{36^{2} }{40^{2} } +\dfrac{y^{2} }{30^{2} }&=1\\\dfrac{1296}{1600} +\frac{y^{2} }{900}&=1\\y^{2}&=(1-\frac{1296}{1600} )\times900\\y^{2}&=(1-0.81)\times900\\y^{2}&=0.19\times900\\y^{2}&=171\\y &=\sqrt{171\\\bold{y&=13.08}\end{aligned}[/tex]
Therefore, the height of the tunnel 4 feet from the edge is 13.08 feet.
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Answer:
This can be determined by ellipse formula. Therefore, the height of the tunnel 4 feet from the edge is 13.08 feet.
Step-by-step explanation:
because of the reason that the other one said so, and im answering cause i want more points and to maintain my streak, and brainly stop taking down my answers!
Please
Helppp!!
Geometry
Answer:
m∠6 = 54°
Hope this helps!
Step-by-step explanation:
( 13x+9 ) and angle 4 are congruent meaning the same. That means angles 5 and 8 are also congruent to ( 13x + 9 ).
Angle 5 or angle 8 are Supplementary to angle ( 5x + 9 ) so a Supplementary angle is 180° and we need to find out x. ( 13x + 9 ) + ( 5x + 9 ) = 18x + 18.
Because Supplementary angles equal 180°, 18x + 18 = 180
18x = 162 x = 162/18 x = 9
Because ∠6 is congruent to angle ( 5x + 9 ), ∠6 = ( 5(9) + 9 )
∠6 = 45 + 9 ∠6 = 54
can someone please help me as soon as possible
Answer:
a quadratic function is letter A
Which graph represents the piecewise-defined function f(x) = { -x + 4, 0 ≤ X< 3
6,
X ≥ 3
9514 1404 393
Answer:
(d)
Step-by-step explanation:
The second line of the function is ...
f(x) = 6, x ≥ 3
This tells you that portion of the graph is the horizontal line y = 6, extending to the right from x = 3, and that there will be a solid dot at (3, 6).
This shows only on the attached graph.
Answer:
4th graph
Step-by-step explanation:
write the volume of a cylinder with a base radius 3 m and height 8 m in terms of pi
Show your work and leave your answer it terms of pi
Answer:
72π (in terms of pi)
Step-by-step explanation:
V = π·r²·h
Plug in the values.
V = π·3²·8
Solve.
V = 72π
To leave an equation in terms of pi, just square, multiply, and leave pi at the end.
3² = 9·8 = 72
72π
If you need the answer fully simplified, it is 226.19 (rounded up).
hello
Michael cycled 15 km at an average speed of 18 km/h.
How many minutes did his journey take?
Answer:
50 minutes
Step-by-step explanation:
Amount of time his journey took = 15km ÷ 18km/h
= 0.833h (to 3sf)
= 50 minutes
Robin earned $4,581 in 9 weeks. How much does he earn per week?
Answer:
$509 per weekStep-by-step explanation:
Well, in order to find the unit rate we simply do the following steps:
4,581 ÷ 9 = 509
So to answer the question, each week Robin earns $509.
Hope this helps! : )
Answer:
they earn 509 a week
Step-by-step explanation:4581 divided by 9
8 liters is the same as how many gallons? round anwer to the nearst tenth
Answer:
3.785, but rounded to the nearest tenth is 3.8
Step-by-step explanation:
Hope this helps!
Answer 1,76211454 gallons
Step-by-step explanation: if you are in the UK , 1 gallon = 4,54 liters , in America is 3,78
PLEASE HELP what is the next term what is A in the sequence and what is the common ratio for 2 4 8 16 32
Answer:
The next term is 64, a is 2, and the common ratio is 2.
Step-by-step explanation:
Look at what's happening from each number to the next. What do you need to do to get from 2 to 4, or 4 to 8? Multiply by 2. That's your common ratio. To get the next number in the sequence, multiply the last number by the common ratio of 2. 32 x 2 = 64, so the next number in the sequence is 64. "a" is just the very first term, meaning it's 2.
Mable earns $180 in 18 hours. at this rate how many dollars will she earn in 30 hours
Step-by-step explanation:
18 hours = $180
1 hour = 180/18 = $10
so 30 hours = 30 × 10 = $300
please give me a brainliest answer
PLEASE HELP!!!!! You are given an isosceles trapezoid ABCD with median XY. Complete the following.
m
A baker used 3kg of baking powder every for every 12kg of flour. if he used 180kg of flour for the Christmas season. how many kg of baking powder did he use in all. help now, please
Answer:
Step-by-step explanation:
12 kg of flour for 3 kg of baking powder
so 1 kg of flour = 3/12 or 1/4 of baking powder
180 kg of flour = [tex]\frac{1}{4}[/tex] × 180 kg of baking powder
= 45 kg of baking powder for 180 kg of flour
please give me a brainliest answer
Step-by-step explanation:
Step-by-step explanation:
12 kg of flour for 3 kg of baking powder
so 1 kg of flour = 3/12 or 1/4 of baking powder
180 kg of flour = 14\frac{1}{4}
4
1
× 180 kg of baking powder
= 45 kg of baking powder for 180 kg of flour
please give me a brainliest answer
PLEASE HELP MEE!!! I WILL GIVE YOU THE BRAINLIEST
Answer:
Domain (-infinity, infinity) Range (-4, infinity)
Step-by-step explanation:
look at the x axis. the graph is going forever out, so infinity.
now look at the y axis. where does it stop? -4. you might need to use [ instead of ( when answering your problem (that just means including) hope this helps!
PLEASE HELP!!
Josh works for MooMoo Milkshakes. The company wants to know what milkshake flavor is the most popular. Today, he surveyed
every third female customer on their favorite milkshake flavor. Eighteen customers
(out of 60 total) were surveyed, and 7 customers
prefer MooChooChocolate, 5 customers prefer VeryStrawberry, and 6 customers prefer BananaBoBanna.
What type of sampling is demonstrated in the situation above?
A. census
B. random sampling
C. negative sampling
D.convenience sampling
Answer: random sampling
Step-by-step explanation: Random sampling is where each member of the sample is randomly selected from the population. Since Josh chose every third female customer, he randomly chose the sample.
Answer: B random sampling .
Step-by-step explanation:
A student from last year got an answer of 36 when asked to simplify the expression below. Identify the student’s mistake? Then solve it correctly.
`2+10\ \times\ 3`
Confused ;-; please help me
Answer:
1)sss
2)asa
3)sas
Step-by-step explanation:
hope this helps
hi pls help me thanksss
pls provide me with workings thankss :)
Step-by-step explanation:
(i)
Using cos(a - b) = cos a cos b + sin a sin b
[tex]\frac{4}{5}[/tex] = cos a cos b + [tex]\frac{1}{5}[/tex]
cos a cos b = [tex]\frac{4}{5} -\frac{1}{5} = \frac{3}{5}[/tex]
(ii)
Using cos(a + b) = cos a cos b - sin a sin b
cos(a + b) = [tex]\frac{3}{5}-\frac{1}{5}=\frac{2}{5}[/tex]
(iii)
Using cot a = [tex]\frac{cos a}{sin a}[/tex]
[tex]=(\frac{cos A}{sin A} )(\frac{cos B}{sin B} )[/tex]
[tex]=\frac{cos A cos B}{sin A sin B}[/tex]
[tex]=\frac{\frac{3}{5} }{\frac{1}{5} }[/tex] [tex]=\frac{3}{5}[/tex] × [tex]5[/tex]
= 3
please give me a brainliest answer
X+2x-5+6= 0 How would you picture model this to solve for x?
Hey there!
x + 2x - 5 + 6 = 0
1x + 2x - 5 + 6 = 0
3x + 1 = 0
SUBTRACT 1 to BOTH SIDES
3x + 1 - 1 = 0 - 1
CANCEL out: 1 - 1 because that gives you 0
KEEP: 0 - 1 because that helps solve for the x-value
0 - 1 = -1
NEW EQUATION: 3x = -1
DIVIDE 3 to BOTH SIDES
3x/3 = -1/3
CANCEL out: 3/3 because that gives you 1
KEEP: -1/3 because it gives you the value of x
SIMPLIFY IT
x = -1/3
Therefore, your answer is: x = - 1/3
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Find f(x) if it is known that f(x-2)=2x-4
Answer:
f=2
Step-by-step explanation:
f(x-2)=2x-4
divide x-2 to 2x-4
f=2
f(2-2)=4-4
I've tried everywhere to get this answerrrrr ill give brainliest for the correct answer mate!!
Answer:
list out some of the difference between Mendeleev periodic table modern periodic table plz give ans
please if you can i urgently need help thank you very much
Answer:
1/4
Step-by-step explanation:
2^7/2^9 = 1/2^2
PLEASE HELP WE DON'T KNOW THE ANSWERS AND WE ARE ALL FAILING THIS CLASS PLS HELP//// I would like to thank you for helping us so much we greatly apricate this.
Answer:
leave unknown variables alone on one side. throw the numbers to the other side of the equation by changing sign
Need help! Solve for X on both
PLEASE HELP complete the construction a perpendicular line to segment AB through point P.
Answer:
.
Step-by-step explanation:
sorry i can't help
Toby picks a 4-digit number.
It is larger than 2999 and it is a multiple of 2.
How many different numbers could he have picked?
Let’s reduce this question into easier terminology.
The number is a multiple of 2, meaning it is an even number. It is larger than 2,999 and less than 10,000 (since it is a 4 digit number).
Thus, Toby could have picked any even number from 3000 to 9,999. So this question is asking how many even numbers (multiples of 2) are between 3000 and 9,999.
For every thousand, there are 1000/2 = 500 multiples of 2:
500 multiples between 3,000 and 3,999
500 multiples between 4,000 and 4,999
and so on until 9,999. So there are
7*500 = 3500 multiples of 2 in this range.
Toby could have picked 3500 possible numbers.
A company makes a profit of $1.38 million. This is $2.54 million more than last year. What was the profit last year?
The answer also asks for us to fill in the blank; "The profit last year was $__ million, so I need help filling in the blank.
The "million" part is already taken care of by your teacher.
====================================================
Explanation:
x = profit last year (millions of dollars)
x+2.54 = profit this year, which is 2.54 million more than last year
x+2.54 = 1.38
x = 1.38-2.54
x = -1.16
The profit last year was -1.16 million dollars
This is the same as writing -1,160,000 dollars of profit.
A negative profit indicates that the company lost money. This is when the company is spending more than what they earn (i.e. they are in some kind of debt).
jika abcd adalah jajar genjang dengan koordinat titik A(-2,-1). B(3,-1) dan C (5,3) maka koordinat titik d adalah
a. D (3,0)
b. D ( 2,3)
c. D (-4,3)
d. D (0,3)
jumlah bilangan genap antara 0 dengan 51
a. 100
b. 650
c. 2500
d. 98
jumlah bilangan genap kelipatan 3 antara 20 dengan 100 adalah
a. 78
b. 120
c. 780
d. 13
1. D. (0,3)
2. B. 650
3. C. 780
Bener semua kok
semoga membantu.
kasi brainliest oi wkwkwk
Jeff made 2 out of every 5 baskets he shot during basketball practice. If he took 25 shots, how many baskets did he make? You MUST show your proportion and work!
Answer:
30 many shoot basket did he make
A diver descends at an average speed of 10.4 m/min. Use rational numbers to write her depth after 3.6 min.
Answer: it’s just 2.89 there’s nothing else to it
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Miguel measured the town library and made a scale drawing. The scale he used was
1 millimeter : 7 meters. The parking lot is 7 millimeters long in the drawing. How long is the
actual parking lot?
Answer:
The parking lot is actually 49 meters.
Find the measures of a right triangle with one angle whose measure is 30
Answer:
The other measure is 60º
Step-by-step explanation:
a triangle= 180º total
a right triangle has one 90º angle
there is a 30º angle given
180-90=90
90-30=60
so 60º