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!
what is [4(30-5)]÷10/2
Answer:
5
Step-by-step explanation:
I think ;- ; sorry
Answer:
0.0032
Step-by-step explanation:
start with [4(30-5)]/10/2
simplify to get:
[4(25)]/10/2
simplify to get:
0.16/10/2
simplify to get:
0.016/5
simplify to get your answer:
0.0032
Given the following equation in point-slope form. Identify the slope and the point.
y - 5 = 3/4 (x+ 3)
M =
Answer:
point = (-3, 5)
slope = 3/4
Step-by-step explanation:
The formula for point slope is:
y - y1 = m (x - x1)
point (x1, y1)
slope m
So with your equation:
y - 5 = 3/4 (x+ 3)
point = (-3, 5)
slope = 3/4
Answer: M=0,75
Step-by-step explanation:
We have a linear function y=mx+bwhere m is slope ; by intercept Let's bring the functions to the standard form[tex]\displaystyle y-5 =\frac{3}{4} \cdot (x+3) \\\\ y=\frac{3x+9}{4} +5 \\\\ y=0,75x+2,25+5 \\\\ y=0,75x+7,25 \\\\ y=\boldsymbol {0,75}x+7,25 \\\\ \rm Then : \\\\ M=0,75[/tex]There is 20% of fat in a 280g 32 piece chocolate bar. How much fat is in 4 pieces?
Find the value of a if y=a/7x + c is parallel to y = 2x - 4
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Value of a is :
[tex]14[/tex][tex] \large \boxed{ \mathfrak{Explanation}}[/tex]
Please refer to attachment for the solution ~
Pls solve.. URGENT!!! Will give brainliest.
EXPLAIN IN STEPS
links will be reported
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Length of each side of each of these three equilateral triangle is :
[tex]1.5 \: \: cm[/tex]Solution is in attachment ~
find the value of
[tex] \frac{x + y}{xy} [/tex]
Please find attached photograph for your answer.
Hope it helps.
Please do comment whether it is useful or not.
ray4918 here to help.
6 exponent 2-4 for b=5
Answer
6 exponent 2 is 36
6 exponent 4 is 1296
Both added is 1332
Step-by-step explanation:
1. 6x6=36
2. 6X6X6X6= 1296
3 1296+36=1332
A coin weighs about 16^-2 pounds. Find the weight of 1000 of the coins. Round your answer to the nearest tenth.
25 - 3x = -8
what does x equal
Step-by-step explanation:
25-3x=-8
-8-25=-33
-3x=-33
-33/-3= 11
x=11
hope this helped =)
Answer:
[tex]\boxed{\bf x=11}[/tex]
Step-by-step explanation:
[tex]\bf 25-3x=-8[/tex]
[tex]\boxed{\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}}[/tex]
[tex]\bf 25-3x-25=-8-25[/tex]
[tex]\bf -3x=-33[/tex]
[tex]\boxed{\mathrm{Divide\:both\:sides\:by\:}-3}[/tex]
[tex]\bf \cfrac{-3x}{-3}=\cfrac{-33}{-3}[/tex]
[tex]\bf x=11[/tex]
A square has a perimeter of 20 ft. What is the length of each side?
Answer:
5
Step-by-step explanation:
the length is 5 because each side with equal to 5
5+5+5+5=20
What is a good estimate for 375% of 40? explain
150
um it is the closest estimate i could think of
Answer:
150
Step-by-step explanation:
375 x 40 divided by 100 = 150
(y^5 -3y^2 -20)/(y -2)
Use synthetic division
Answer:
The answer is y^4+2y^3+4y^2+5y+10
Step-by-step explanation:
I essentially just factored everything, as I'm certain this is right. :D
4x – 3y = -7
5x – 4y = - 8
The answer is x=−4 and y=−3
Perform the operation. Enter your answer in scientific notation.
(7 x 10^*9)(5.6 x 10^*8)
Answer:
3.92 × 10 ^18
Step-by-step explanation:
(7 x 10^*9)(5.6 x 10^*8)
(7000000000)(560000000)
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
If the decimal is moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
(6x + 1)(5x + 8) help please
Im not sure how to do this
Answer:
see explanation
Step-by-step explanation:
Since the figures are similar then then corresponding sides are in proportion , that is
[tex]\frac{NP}{ST}[/tex] = [tex]\frac{NM}{SR}[/tex] , substitute values
[tex]\frac{x}{25}[/tex] = [tex]\frac{18}{30}[/tex] ( cross- multiply )
30x = 450 ( divide both sides by 30 )
x = 15
Similarly
[tex]\frac{UT}{QP}[/tex] = [tex]\frac{NM}{SR}[/tex] , that is
[tex]\frac{y}{15}[/tex] = [tex]\frac{18}{30}[/tex] ( cross- multiply )
30y = 270 ( divide both sides by 30 )
y = 9
The similarity ratio is the ratio of corresponding sides , that is
[tex]\frac{NM}{SR}[/tex] = [tex]\frac{18}{30}[/tex] = [tex]\frac{3}{5}[/tex]
SRUT is [tex]\frac{3}{5}[/tex] of NMQP
A unit rate is a ratio that compares an amount of one quantity to _______________ unit of another quantity.
Answer:
one
Step-by-step explanation:
A unit rate compares a quantity to one unit of measure.
A farmer wants to fence a small rectangular yard next to a barn. Fence for side parallel to the barn will cost 55 per foot and the fence for the other two sides will cost 45 per foot. The farmer has a total of 1650 dollars to spend on the project. Find the dimensions for the yard that will have the largest possible area.
Answer:
55 divided by 45= 1.222222222222 1650 divided by 1.222222= anserw
Step-by-step explanation:
Find the area of the triangle below.
Carry your intermediate computations to at least four decimal places. Round your answer to the nearest hundredth
Answer:
20
Step-by-step explanation:
Since this is not a right angle, we can use the formula [tex]Area= Sin(y) (\frac{1}{2}ab)[/tex]
a=7
b=10
y=35
So, when we plug these values in, we get:
[tex]a=Sin(35)(\frac{(10)(7)}{2})\\\\=35sin(35)\\=20.075\\[/tex]
rounded to the nearest hundredth, I believe it's 20.
Write an equation representing the pound of clay, c, that jamal from the example needs to make b bowls.
explain how to find the amount of clay jamal needs to make 8 bowls.
Answer:
8=2/3c
Step-by-step explanation:
Each bowl requires 2/3 pounds of clay
To make 8 bowls, Jamal needs 5 1/3 pounds of clay
1. The equation to represent amount is, x= b*c
2. Amount of clay Jamal needs to make 8 bowls is 8c.
What is equation?A mathematical statement that is made up of two expressions connected by an equal sign.
let the amount of clay be x.
The number of bowls be b and c is pounds of clay.
So, Total cost
x= b * c
Now, if number of bowls are 8 then
x= 8*c
x=8c
So, the amount of clay Jamal needs to make 8 bowls is 8c.
Learn more about equation here:
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PLEASE PLEASE HELP ILL MARK BRAINLIEST!!!!
Answer:
3x+5y=35
Step-by-step explanation: 3 times how many pounds of apple he gets (5)and 5 times how many pounds of oranges he gets(4) equals the amount he spends on all.(3x5=15+5x4=20=35)
If I have 8 apples and I give Mark 4 apples , how many apples do I have left?
Answer:
four
Step-by-step explanation:
4 take away from 8 equals 4
A farmer has 15 boxes of eggs.
There are 6 eggs in each box.
Write, as a ratio, the number of eggs in three boxes to the total number of eggs.
Give your answer in its simplest form.
Answer:
1:5
Step-by-step explanation:
The total number of eggs would be 15×6, or 90.
The eggs in 3 boxes would be 18.
18:90
Then simplify.
1:5
D
Which of the following number Satisoy
the equation - 6+2=-12?
a) 2
b) 6
C) -6. D) -2
Answer:
C) -6
Step-by-step explanation:
-6 + 2 = -4 not -12.
But -6 + (-6) = -12.
Hope this is what you were looking for :)
9/2 + (-8)
Explain the steps
Answer:
nine divided by 2 plus negative eight
Step-by-step explanation:
9/2=4.5
4.5+(-8)= -3.5
Step-by-step explanation:
= 9/2 + -8/1
= 9/2 + 16/2
= 9 + (-16)/2
= -7/2
eight times the difference of a number and 7. write in algebraic expression.
Answer:
8(n - 7)
Step-by-step explanation:
let the number be n then the difference of n and 7 is n-7
8 times this difference is
8(n - 7)
Answer: 8(n-7)
Step-by-step explanation:
it should be that <3
The mean height of an adult giraffe is 17 feet. Suppose that the distribution is normally distributed with standard deviation 0.9 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.
c. What is the Z-score for a giraffe that is 18.5 foot tall?
d. What is the probability that a randomly selected giraffe will be shorter than 17.5 feet tall?
e. What is the probability that a randomly selected giraffe will be between 16.7 and 17.2 feet tall?
f. The 70th percentile for the height of giraffes is ___ ft.
Answer:
Median =17
Step-by-step explanation:
Given that the mean height of an adult giraffe is 17 feet. Suppose that the distribution is normally distributed with standard deviation 0.9 feet. Let X be the height of a randomly selected adult giraffe. X is a random variable.
a) X is N(17, 0.9)
b) Median giraffe height = 17 ft since in normal distribution mean = median
c) When x = 18.5, Z = 18.5-17/0.9 = Z= 0.1667
d) P( x < 18) = P( Z < 56)
= 0. 2877
e) P(16.9 < x < 17.9) = P(-0.11 < z < 1) = .0.438 + 0.3413
= 0.3851
f) 75th percentile for z is 0.675
x = 17.9 + 0.9 (0.675)
= 18.5075
Write an equation in slope-intercept form of the line that passes through (-2,5) and (-4, -5)
Answer:
b=-5
Step-by-step explanation:
<3
hii! could someone please help with a legit answer 'n explanation? Im soo confused. thank you so much!
Answer:
First part = 2.
Time to land = 6 seconds.
Step-by-step explanation:
The object is at h = 0 when it land so
-5x^2 + 20x + 60 = 0
-5(x^2 - 4x) = -60
-5[(x - 2)^2 - 4] = -60
(x - 2)^2 - 4 = -60/-5 = 12
(x - 2)^2 = 16.
Solving the above:
Take the square root of both sides:
x - 2 = 4
x = 2 + 4
x = 6 seconds
Given g(x)=-x-2 find g(-3)
Answer:
g(-3)=1
Step-by-step explanation:
substitude x=-3
g(-3)=-(-3)-2
=1
Answer:
g(-3) = 1
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Functions
Function NotationStep-by-step explanation:
Step 1: Define
Identify
g(x) = -x - 2
Step 2: Evaluate
Substitute in x [Function g(x)]: g(-3) = -(-3) - 2Simplify: g(-3) = 3 - 2Subtract: g(-3) = 1