Mario measured the depth of the river as a function of time and graphed his findings. Use this graph to answer the following question.



What is the maximum depth of the river?

1 meter


22 minutes


10 meters


9 minutes

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.

For further details,please prefer this link:

https://brainly.com/question/13447584

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:

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

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:

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:

x = 33

Step-by-step explanation:

Pls brainliest I knew it because of K12

Answer:

A. none of these

Step-by-step explanation:

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

Answer:

12.6

Step-by-step explanation:

You would get 12.6315789474 but you round to the nearest tenth.

Answer:

[tex]\frac{12}{40\\}[/tex]

Step-by-step explanation:

[tex]\frac{3}{10}[/tex] × [tex]\frac{4}{4} =\frac{12}{40}[/tex]

Answer:32-2=30 30+1+3=34 . Ans:34

Step-by-step explanation:

Answer:

32-3(4)

24

24 squared is

576

Answer:

2 1/12

The answer should be 2 1/12

(Two and one over twelve)

or

(Two and a one twelfth)

Answer:

2.1

Step-by-step explanation:

...........................

Hello haohaoxNienie!

[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]

Use the remainder theorem to determine whether x = - 4 is a solution of x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8.

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

Refer to the attached picture.

Answer :- Yes, x = - 4 is a solution of x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8.

__________________

Hope it'll help you!

ℓu¢αzz ッ

Answer: y = -4

Step-by-step explanation:

If x = 1

1 = 2y + 9

1 - 9 = 2y

-8 = 2y

y = -8/2

y = -4

please give me a brainliest answer

Answer:

[tex]y = ( - 4)[/tex]

Step-by-step explanation:

Given that,

[tex]x = 1[/tex]

Question :

[tex]x = 2y + 9[/tex]

You have to find the value of y. So, make the y as the Subject

[tex]x = 2y + 9 \\ x - 9 = 2y \\ \frac{x - 9}{2} = \frac{2y}{2} \\ \frac{x - 9}{2} = y[/tex]

Now replace 1 instead of x

[tex]y = \frac{x - 9}{2} \\ y = \frac{1 - 9}{2} \\ y = \frac{ - 8}{2} \\ y = - 4[/tex]

Hope this helps you.

Let me know if you have any other questions :-)

Answer:

The measure of the angle ∠ABC is 108°

Step-by-step explanation:

An isosceles triangle has two equal sides and two equal angles

In this problem

∠BDA=∠BAD= 66° ----> the angles of the base are equals

Find the measure of the vertex angle

∠ABD = 180° - 2×66° = 48° (the sum of the internal angles of a triangle is                                              equal to 180°)

then. Find the measure of the angle  ∠CBD in the equilateral triangle we know that

The measure of the internal angle in a equilateral triangle is 60° so

∠CBD= 60°

Then find the measure of the angle ∠ABC

∠ABC=∠ABD+∠DBC

substitute the values

∠ABC= 48°+60° = 108°

The answer is 108°

The measure of the angle ∠ABC is 108°

Answer:

108 degrees

Step-by-step explanation:

Hi there!

1. Determine the measure of angle DBC

2. Determine the measure of angle ABD

3. Add them to determine the measure of angle ABC

We're given that triangle ABD is isosceles and triangle BCD is equilateral.

Because BCD is an equilateral triangle, all of its interior angles at 60 degrees.

Therefore, the measure of angle DBC is 60 degrees.

Triangle ABD is isosceles, so therefore, angle ADB is also 66 degrees.

The sum of the interior angles of a triangle is 180 degrees. Therefore, the measure of angle ABD is 180-66-66, which is 48 degrees.

To find ABC, add 60 and 48:

60+48 = 108

Therefore, angle ABC measures 108 degrees.

I hope this helps!

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:

$ 500

Step-by-step explanation:

Básicamente divides 125 entre 2 (para saber el precio de la mensualidad, asumiendo que no hay descuentos) y luego ese resultado lo multiplicamos por 8, ya que es la cantidad de meses que nos interesa pagar (no se hace por 6 porque en ninguna parte dice que ya ha pagado esos 2 meses)

Answer:

c right triangle

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A: Method that is used to find either the legs or the hypotenuse of a right triangle.

B: Diagonal line of a right triangle, also used in the Pythagorean Theorem

C: 3-sided shape with a 90-degree angle

D. Lenth and height of a right triangle, used in the Pythagorean Theorem

___________

[tex] \: [/tex]

[tex]\boxed{ \rm{answer \: by \: { \boxed{ \rm{☆HayabusaBrainly}}}}}[/tex]

x² = (6,9)² + (5,3)²

x² = 47,61 + 28,09

x² = 75,7

x = 8,7yd✔

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.

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)

9514 1404 393

Answer:

  sum = 1

Step-by-step explanation:

The method of partial sums has you look at sums of various numbers of terms of the series to see if there is a pattern that suggests either divergence or a limit. Here, the partial sums suggest the series sum is 1.

__

In the attachment, we have computed sums of 1 term, 10 terms, 100 terms, and so on up to 10^8 terms. These sums seem to approach the value 1.

Individual terms get small faster than for a harmonic series, which his known not to converge, but more slowly than a quadratic series. Large numbered terms are approximately proportional to n^-(3/2).

_____

You can actually compute the sum exactly, without reference to partial sums. Each term of the sum can be rewritten as ...

  [tex]\dfrac{1}{(n+1)\sqrt{n}+n\sqrt{n+1}}=\dfrac{1}{\sqrt{n(n+1)}(\sqrt{n+1}+\sqrt{n})}\\\\=\dfrac{\sqrt{n+1}-\sqrt{n}}{\sqrt{n(n+1)}}=\dfrac{1}{\sqrt{n}}-\dfrac{1}{\sqrt{n+1}}[/tex]

Then successive terms will cancel the intermediate fractions. So, for example, the sum of the first 3 terms is ...

  (1/√1 -1/√2) +(1/√2 -1/√3) +(1/√3 -1/√4) = 1 -1/√4

This means the given sum will evaluate to ...

  1 -1/√∞ = 1 -0 = 1 . . . sum of the infinite series

Answer:

10800

Step-by-step explanation:

Answer:

9220 Yan na ang true answer

Answer:

It is c

Step-by-step explanation:

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:

y = -3x + 1

Step-by-step explanation:

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

Answer:

the answer is x=11......

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:

385

Step-by-step explanation:

1 1/4 meters = 125 cm

125+260 = 385

Answer:

sum = 260 + 270  = 535  cm or = 5,35 m

Step-by-step explanation: take 11/4m = 2,75m * 100 = 275 cm

Answer:

5 shirts

Step-by-step explanation:

we can use the problem to get an equation:

65+15x=50+20x

subtract 50 from each side to get:

15+15x=20x

subtract 15x from each side to get:

15=5x

divide each side by 5 to get your answer:

x=5