Given below is an equation of a parabola. What are the coordinates of the vertex?
y = (x + 2)^2

a (–2, 0)
b (2, –2)
c (–2, 2)
d (2, 0)

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!

Answer:

one

Step-by-step explanation:

y = (x + 3)^2

Start with the parent function y = x^2.

y = x^2 touches the x-axis at only 1 point, (0, 0).

The difference between y = (x + 3)^2 and its parent function y = x^2, is that in y = (x + 3)^2, x was replaced by x + 3. That is a translation of 3 units left. The function y = (x + 3)^2 still only touches the x-axis once, but at x = -3.

Answer: one

Answer:

Step-by-step explanation:

To answer this, set the function y = (x + 3)^2 touch the x-axis (where y = 0) and find the actual value(s) of x:

y = (x + 3)^2 = 0

Taking the square root of both sides, we get x + 3 = ±0, or x = -3.  As this equation is a quadratic, there MUST be two roots; the roots are {-3, -3}.  Thus in theory, the graph touches the x-axis in two places, but these two places are identical:   (-3, 0)

Answer:

25x + 75 ≥ 30

Hope this helps!

Answer:

44.8

Step-by-step explanation:

Take the second number and subtract the first number

44.4 - (-.4)

Subtracting a negative is like adding

44.4 +.4

44.8

Answer:

[tex]D.44.8[/tex]

Step-by-step explanation:

The difference between two numbers can be obtained by subtracting the smaller number from the bigger number.

- 0.4 is the smaller number, and 44.4 is the larger number. Therefore, the difference between the two is 44.4 - (- 0.4).

Answer:

42 = 2*3*7

Step-by-step explanation:

42 can be rewritten as 2*21, for example.  

2 is prime.  21 = 3*7.

Then 42 = 2 * 21 is also equal to:

         42 = 2*3*7. where these factors are ordered from least to greatest.  The prime factors of 42 are {2, 3, 7}.

Answer:

A) Akash (1.5m), Meera (1.52), Rahul (1.54m), Lakshmi (1.56m)

B) Lakshmi is the tallest, 1.56m tall

Step-by-step explanation:

Rahul- 1.54m

Akash- 1500mm

Meera- 152cm

Lakshmi- 1560mm

Let's start by converting all the measurements to meters.

Rahul is already in meters, so he can just stay the same.

1500mm = 1.5m

152cm = 1.52m

1560mm = 1.56m

So our new measurements are:

Rahul- 1.54m

Akash- 1.5m

Meera= 1.52m

Lakshmi= 1.56m

We can now make our conclusions.

A) Akash (1.5m), Meera (1.52), Rahul (1.54m), Lakshmi (1.56m)

B) Lakshmi is the tallest, 1.56m tall

Answer:

Step-by-step explanation:

Let's convert all the heights to meters:

Rahul 1.54m

Akash 1.50 m

Meera 1.52 m

Lakshmi 1.56m

Now, let's arrange their heights in ascending order (shortest to tallest):

Akash 1.50 m

Meera 1.52 m

Rahul 1.54m

Lakshmi 1.56m

a) 1500 mm, 152 cm, 1.54 m, 1560 mm

b) therefore Lakshmi is the tallest.

Answer:

-3x-6

Step-by-step explanation:

you multiply x by -3 getting -3x then you multiply -3 by positve 2 getting -6

Hello skm413002!

[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]

Apply the distributive property:

-3(x+2) =

[tex] \large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}[/tex]

By applying the distributive property, we can solve it as....

[tex] \sf \: - 3(x + 2) \\ = \sf \: (- 3 \times x) -( 3 \times 2) \\ = \large \boxed{\boxed{ \bf - 3x - 6}}[/tex]

__________________

Hope it'll help you!

ℓu¢αzz ッ

Answer:

B) 5/8

Step-by-step explanation:

Because we are working with fractions that have different denominators, we need to find the lowest common denominator, which would be 8, because 1/8 cannot be divided anymore in 2 or 4, but 1/2 can be multiplied in eighths.

So, to make 1/2 into eighths, we have to multiply both the numerator and denominator by 4 in order for 2 to become 8:

1/2 * 4 = 4/8

Now, we can add the amounts of the total granola bar that he consumed:

4/8 + 1/8 = 5/8

Because 5/8 cannot be simplified any further, that is our final answer.

Hope this helps :)

Answer:

11th term is 0

Step-by-step explanation:

30, 27 , 24 ,......0

a = first term = 30

Common difference = second term - first term = 27 - 30 = -3

nth term = a+(n-1)*d

a + (n-1)d = 0

30 + (n - 1) *(-3) = 0

30 + n*(-3) -1*(-3) = 0

30 - 3n + 3 = 0

      -3n + 33 = 0

               -3n = -33

                   n = -33/-3

n = 11

Answer:

he  spent $75.80

Step-by-step explanation:

hope this helps:D

Answer:

A

Step-by-step explanation:

not sure if it is correct

Answer:

the answer is c :)

Step-by-step explanation:

Answer:

A. none of these

Step-by-step explanation:

It's an absolute value function such as : y = 3*| x-1 |

Answer:

It is c

Step-by-step explanation:

Answer: 14 cm

Step-by-step explanation:

Answer:

R=14 cm

total area= πr²

=22/7*196=616 cm²

r2= 3.5 cm

area of the small circles= 2*πr²=2*12.25*22/7=77 cm²

length of rectangle=3

breadth=1

area =lb=3 cm²

area of the small circles+area of rectangle=77+3=80 cm²

remaining area=616-80=536 cm²

Answer:

10

8+40÷20=8+2=10

,.,.......

Answer:

y = -3x + 1

Step-by-step explanation:

see if that's correct? I'm not quite sure

7249jwnsnjdkwlskjeiwiwo1ñwlld

Answer:

I think it's about 15 to 22.

Step-by-step explanation: So first I checked the length for the unknown number and I added the 12 and 10 together but that didn't work and so i'm just estimating the number for x yo.

Sorry if I didn't helped you yo.

Answer:

35

Step-by-step explanation:

Numbers that add up to 8 and number combinations

0 and 8: 80, 08

1 and 7: 17, 71

2 and 6: 26, 62

3 and 5: 35, 53

4 and 4: 44

Since the number must be between 25 and 40, the only possible numbers are 26 and 35

Since 26 is not the answer, the number is 35

Answer:

x = - [tex]\frac{5}{6}[/tex] , x = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

To find the zeros let f(x) = 0 , that is

12x² + 4x - 5 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 12 × - 5 = - 60 and sum = + 4

The factors are - 6 and + 10

Use these factors to split the x- term

12x² - 6x + 10x - 5 = 0 ( factor first/second and third/fourth terms )

6x(2x - 1) + 5(2x - 1) = 0 ← factor out (2x - 1) from each term

(2x - 1)(6x + 5) = 0

Equate each factor to zero and solve for x

6x + 5 = 0 ⇒ 6x = - 5 ⇒ x = - [tex]\frac{5}{6}[/tex]

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]

Answer:

28.1 units

Step-by-step explanation:

Area of circle= πr², where r is the radius.

Given that the area is 20π,

20π= πr²

Divide both sides by π:

20= r²

Square root both sides:

[tex]r = \sqrt{20} [/tex]

[tex]r = \sqrt{4(5)} [/tex]

[tex]r = ( \sqrt{4} )( \sqrt{5} )[/tex]

[tex]r = 2 \sqrt{5} [/tex]

Circumference of circle= 2πr

Substitute the value of r:

Circumference of the circle

[tex] = 2(\pi)( 2\sqrt{5} )[/tex]

[tex] = 4\pi \sqrt{5} [/tex]

= 28.1 units (3 s.f.)

Answer:

Hi I hope this helps

A = X : -3 Y : -3

B = X : -2 Y : 1

Step-by-step explanation:

please let me know if it's right or wrong

Notice that

4/9 = 2²/3² = (2/3)²

so that

(2/3)³ (4/9)⁴ = (2/3)³ ((2/3)²)⁴

… = (2/3)³ (2/3)⁸

… = (2/3)¹¹

Answer:

Perpendicular

neither

[tex]y=\frac{4}{5}x-2[/tex]

Step-by-step explanation:

The midpoint is the middle of the line. Thus for a line segment, it is finding the halfway point between the x and y values.

Midpoint = ( [¹/₂ (x₁ + x₂)] , [¹/₂(y₁ + y₂)])

∴ for a line segments with endpoints (4,-7) and (12, -1),

 Midpoint = ( [¹/₂ (12 + 4)] , [¹/₂(-7 - 1)])

                = ( [¹/₂ (16)] , [¹/₂(-8)])

                = (8, -4)  (OPTION A)

Answer:

10/21

Step-by-step explanation:

Number of minutes required for printing 21 pages: 10

So, number of minutes required for printing 1 page

= 10/21

(= 0.47 = 0.5 [approximately])

Answer:

the slope is -2

Step-by-step explanation:

Answer:

1/1 = 1

Step-by-step explanation:

Use rise/run.

The x value increases by 1 in the same amount of time that the y value increases by 1. This gives you the slope 1/1 (y increase/x increase).

1/1 can then be converted to 1.