A bridge constructed over a bayou has a supporting arch in the shape of an inverted parabola. Find the equation of the parabolic arch if the length of the road over the arch is 100 meters and the maximum height of the arch is 40 meters.

Answers

Answer 1

Answer:

y = (-2/125)(x - 50)² + 40

Step-by-step explanation:

The total length of the bridge is 100 meters.

Maximum height always occurs at midpoint of x.

So for x=50 meters , y = 40 meters.

As the vertex is given at the maximum height,  Vertex can be defined at the point (50,40)

We know that the general equation for vertical parabola is:

y = a(x - h)² + k

Where (h,k) = Vertex = (50,40)

Substitute in the equation:

y = a(x - 50)² + 40 ⇒ Equation (i)

We know 2 more points on the parabola. We know that when x=0 , y=0 and we also know that when x=100m, y=0 meters.

Substitute any point in the above equation

Substituting (100,0) in the equation

0 = a(100 - 50)² +40

Solve the equation for a:

a = - 2/125

Substitute a in Equation (i)

y = (-2/125)(x - 50)² + 40


Related Questions

(1−cos^2 x )·(1+tan^2 x)

Answers

Answer:

[tex](1-cos^2 x ).(1+tan^2 x) = tan^2x[/tex]

Step-by-step explanation:

Given

[tex](1-cos^2 x ).(1+tan^2 x)[/tex]

Required

Solve

[tex](1-cos^2 x ).(1+tan^2 x)[/tex]

In trigonometry;

[tex]1 - cos^2x = sin^2x[/tex]

So, make substitution

[tex](1-cos^2 x ).(1+tan^2 x)[/tex] becomes

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(1+tan^2 x)[/tex]

Also; in trigonometry:

[tex]1 + tan^2x = sec^2x[/tex]

Make another substitution

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(sec^2 x)[/tex]

Recall that [tex]secx = \frac{1}{cosx}[/tex]

So;

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(sec^2 x)[/tex] becomes

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(\frac{1}{cos^2 x})[/tex]

[tex](1-cos^2 x ).(1+tan^2 x) = \frac{sin^2 x }{cos^2 x}[/tex]

[tex](1-cos^2 x ).(1+tan^2 x) = (\frac{sin x }{cosx})^2[/tex]

In trigonometry;

[tex]tan x = \frac{sin x}{cos x}[/tex]

[tex](1-cos^2 x ).(1+tan^2 x) = tan^2x[/tex]

The expression cannot be further simplified

For an experiment, Marie brought a container filled with 30 grams of snow into a warm environment. After 5 minutes, 21% of the snow had melted. How many grams of snow were remaining in the container after the 5 minutes?

Answers

23.7 grams would be left in the container
23.7 grams

Explanation
30 grams —> 100%
X—> 79%

30x79=2370
2370/100 = 23.7

Susan wants to make 2 square flags to
sell at a crafts fair. The fabric she wants
to buy is 5 meters wide. She doesn't
want any fabric left over. What's the
least amount of fabric she should buy?

Answers

Answer:

10 meters

Step-by-step explanation:because they are square and they would have to be 5 meters long and she dose not want any left over so...

Help please and thank you

Answers

Answer:

73.72 ft Squared

Step-by-step explanation:

First you need to find the area of the rectangle the area of rectangle is 8x10=80. Then You take that 80=3.14x2. then you find the area by dividing it. so...

1.) 80=3.14x2

3.14x2=6.28       80=6.28              (Then you divide 6.28 by 80)

                             80    80                  

2. Which of the following methods can't be used to find the zeros of a function?
options:
A. Substitute x = 0 in the function and solve for f(x).
B. Graph the function using a table of values.
C. Factor the function and apply the zero-product property to its factors.
D. Apply the quadratic formula.

Answers

Answer:

The correct option is;

Substitute x = 0 in the function  and solve for f(x)

Step-by-step explanation:

The zeros of a function are the values of x which produces the value of 0 when substituted in the function

It is the point where the curve or line of the function crosses the x-axis

A. Substituting x = 0 will only give the point where the curve or line of the function crosses the y-axis,

Therefore, substituting x = 0 in the function  can't be used to find the zero's of a function

B. Plotting a graph of the table of values of the function will indicate the zeros of the function or the point where the function crosses the x-axis

C. The zero product property when applied to the factors of the function equated to zero can be used to find the zeros of a function

d, The quadratic formula can be used to find the zeros of a function when the function is written in the form a·x² + b·x + c = 0

Answer: Substitute x = 0 in the function and solve for f(x).

Step-by-step explanation:

Which of the following is not a property of a rhombus? Question 20 options: A) Diagonals are congruent. B) Opposite angles are congruent. C) All sides are congruent. D) Diagonals are perpendicular bisectors of each other.

Answers

Answer: A

Step-by-step explanation:

This is because  diagonals of a rhombus are perpendicular not congruent, ]

Pependicular means at an angle of 90°

If this helped please mark brainliest

Help will give brainliest

Answers

Answer:

70

Step-by-step explanation:

Answer:

70 fewer refrigerators  than television

Step-by-step explanation:

PLEASEEEEEE HELP ME 40 POINTS :((((((!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Deleted acc.. that’s sad I had the same work before

Answer:

hi

Step-by-step explanation:

I could use some more help

Answers

Answer:

[tex]\left[\begin{array}{ccc}-30&22&8\\-4&-4&16\\30&-28&18\end{array}\right][/tex]

Step-by-step explanation:

Given

[tex]A = \left[\begin{array}{ccc}-1&9&2\\10&-10&2\\-5&6&-5\end{array}\right][/tex]

[tex]B = \left[\begin{array}{ccc}7&-1&-1\\6&-4&-3\\-10&10&-7\end{array}\right][/tex]

Required

2A - 4B

To solve 2A - 4B, we first multiply matrix A by 2 and matrix B by 4

So, if

[tex]A = \left[\begin{array}{ccc}-1&9&2\\10&-10&2\\-5&6&-5\end{array}\right][/tex]

[tex]2A = 2 *\left[\begin{array}{ccc}-1&9&2\\10&-10&2\\-5&6&-5\end{array}\right][/tex]

[tex]2A = \left[\begin{array}{ccc}-2&18&4\\20&-20&4\\-10&12&-10\end{array}\right][/tex]

If

[tex]B = \left[\begin{array}{ccc}7&-1&-1\\6&-4&-3\\-10&10&-7\end{array}\right][/tex]

then

[tex]4B = 4*\left[\begin{array}{ccc}7&-1&-1\\6&-4&-3\\-10&10&-7\end{array}\right][/tex]

[tex]4B = \left[\begin{array}{ccc}28&-4&-4\\24&-16&-12\\-40&40&-28\end{array}\right][/tex]

So; 2A - 4B becomes

[tex]\left[\begin{array}{ccc}-2&18&4\\20&-20&4\\-10&12&-10\end{array}\right] - \left[\begin{array}{ccc}28&-4&-4\\24&-16&-12\\-40&40&-28\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-2-28&18-(-4)&4-(-4)\\20-24&-20-(-16)&4-(-12)\\-10-(-40)&12-40&-10-(-28)\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-30&18+4&4+4\\20-24&-20+16&4+12\\-10+40&12-40&-10+28\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-30&22&8\\-4&-4&16\\30&-28&18\end{array}\right][/tex]

Hence, 2A - 4B is equivalent to

[tex]\left[\begin{array}{ccc}-30&22&8\\-4&-4&16\\30&-28&18\end{array}\right][/tex]

Pls help summer homework :D C:

Answers

Answer:

C) None of the above

Step-by-step explanation:

Reason is V is a shorter distance and q is longer they need to be subtraction but the other way round to enable the correct subtraction we can show (q-V) which means the longer distance minus the shorter distance.

ΔABC has been translated right to create triangle ΔXYZ. Based on this information, which of the following is a true statement? answers: A) ≅ B) ≅ C) ∠A ≅ ∠C D) ∠B ≅ ∠X

Answers

Answer:

None. (or B)

Step-by-step explanation:

A)  AC≅ZY

B) AZ≅

C) ∠A ≅ ∠C

D) ∠B ≅ ∠X

Options C and D are not true and Options A is wrong and B is incomplete but using process of elimination, the answer is probably B.

The resulting information will be ∠ A ≅ ∠ X, ∠ B ≅ ∠ Y and ∠ C ≅ ∠ Z and AB ≅ XY, BC ≅ YZ and AC ≅ XZ

What is translation transformation?

A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.

Given that, Δ ABC has been translated right to create triangle Δ XYZ

We know that in translation transformation, in translation, only the position of the object changes, its size remains the same.

That means Δ ABC ≅ Δ XYZ Therefore, we get,

Congruent parts are;

Angles:-

∠ A ≅ ∠ X,

∠ B ≅ ∠ Y and

∠ C ≅ ∠ Z

Side:-

AB ≅ XY,

BC ≅ YZ and

AC ≅ XZ

Hence, The resulting information will be ∠ A ≅ ∠ X, ∠ B ≅ ∠ Y and ∠ C ≅ ∠ Z and AB ≅ XY, BC ≅ YZ and AC ≅ XZ

For more references on translation transformation, click;

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What is the end behavior of the function f(x)=54x2? As x→∞, f(x)→−∞ As x→−∞, f(x)→−∞ As x→∞, f(x)→∞ As x→−∞, f(x)→∞ As x→∞, f(x)→∞ As x→−∞, f(x)→−∞ As x→∞, f(x)→−∞ As x→−∞, f(x)→∞

Answers

Answer:

3f(x)  

3x^2  

12  

-x+6

0

Step-by-step explanation:

Fashoo

On a number line, the distance from zero to -8 is 8 units. Which equation demonstrates this concept? A. 82 = 64 B. |-8| = 8 C. |-8| = -8 D. 0 + 8 = 8

Answers

Answer:

Option B

Step-by-step explanation:

The absolute value of a number is how far a number is from zero. We can use ' | | ' to represent the absolute volume of a number.  The distance, or absolute value, of -8 is 8.

We can represent this by writing:

|-8| = 8

Option B should be the correct answer.

Answer:

B

Step-by-step explanation:

The absolute value of a number means the distance from 0.

For example, |-2| is 2 units from 0.

|-8| = 8

-8 is 8 units from 0.

Which number completes the inequality? 1.01 less-than blank less-than 1.17, less-than 1.20 1.008 1.08 1.18 1.8

Answers

Answer:

1.08

Step-by-step explanation:

1.01 < x < 1.17

x ≠ 1.20

x ≠ 1.008

x = 1.08

x ≠ 1.18

x ≠ 1.8

The number that completes the inequality is 1.08:

1.01 < 1.08 < 1.17, < 1.20

Option C is the correct answer.

We have,

To determine which number completes the inequality, we need to find the number that is greater than 1.01 but less than both 1.17 and 1.20.

Among the given options, the number that satisfies this condition is 1.08.

Thus,

The number that completes the inequality is 1.08:

1.01 < 1.08 < 1.17, < 1.20

Learn more about inequalities here:

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Line j is a straight line. Line j is a straight line. 2 lines come out of the line to form 4 angles. From top left, clockwise, the angles are: x, y, z, w. Which equation represents the relationship between the measures of Angle w and Angle z? Measure of angle w = measure of angle z Measure of angle w + measure of angle z = 90 degrees Measure of angle w + measure of angle z = 100 degrees Measure of angle w + measure of angle z = 180 degrees

Answers

Answer:

c

Step-by-step explanation:

In the given line the relationship between angle w and z is Measure of angle w + measure of angle z = 180 degrees.

What is a supplementary angle?

This is the type of angle that when measured, two of the angles would sum up to 180 degrees.

The supplementary angle is the sum of angle w + angle z = 180 degrees. Hence c is correct.

Read more on supplementary angles here:

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(a) The perimeter of a rectangular parking lot is 332 m.
If the width of the parking lot is 75 m, what is its length?
Length of the parking lot:
m

Answers

the answer should be 91 because for your total perimeter you add all the sides. So you already have your length of 75 which counts as 2 sides and equals up to 150. after you subtract your two sides from your perimeter you get 182. you then divide 182 by 2 to get your two remaining sides which gives you 91.

Answer:

Step-by-step explanation:

Perimeter of the rectangle = 332m

Perimeter of a rectangle = 2(L+b)

Breadth = 75m

= 2 ( L + 75) = 332

2L + 150 = 332

2L = 332-150

L = 182/2

L= 91m

What are the coordinates of the image of R for a dilation with center (0,0) and scale factor 3?

Answers

Answer:

(3, -3)

Step-by-step explanation:

If a point is dilated about the origin rule to be followed,

(x, y) → (kx, ky)

where k is a scale factor by which the point is being dilated.

If a point R having coordinates (1, -1) is dilated by scale factor of 3, coordinates of the image will be [3×1, 3(-1)]

Therefore, coordinates of the image R' will be (3, -3)


PLEASE HELP!!!!!!! i will give brainliest

Answers

Answer: Choice C

Yes they are independent because P(California) = 0.55 approximately and P(California | Brand B) = 0.55 approximately as well

===================================================

Explanation:

P(California) is notation that means "probability the person is from California". There are 150 people from California out of 275 total. Therefore, the probability is 150/275 = 0.5454 approximately which rounds to 0.55

Now if I told you "this person prefers brand B", then you would focus your attention solely on the brand B column. The other columns are ignored because you know they don't prefer anything else. With this narrower view, we see that 54 Californians prefer this brand out of 99 total. The probability becomes 54/99 = 0.5454 which rounds to 0.55. We get the same as before.

The notation P(California | Brand B) means "the probability they are from California given they prefer brand B". The vertical line is not the uppercase letter i or lowercase letter L. It is simply a vertical line. In probability notation that vertical line means "given".

We've shown that P(California | Brand B) = 0.55 approximately. The fact that they prefer brand B does not change the original probability. So the two events are independent. If liking brand B did change the probability, then the events would be dependent.

solve the equation (x-2)^2/3=9

Answers

Answer:

x = 2±3sqrt(3)

Step-by-step explanation:

(x-2)^2/3=9

Multiply each side by 3

(x-2)^2/3 *3=9*3

(x-2)^2=27

Take the square root of each side

sqrt( (x-2)^2)=±sqrt(27)

x-2 = ±3sqrt(3)

Add 2 to each side

x = 2±3sqrt(3)

Use the interactive to graph a line with the given points: (–1,7) and (1,–1) The coordinates of the y-intercept of the line are.

Answers

Answer:

The y-intercept would be 6.25

Step-by-step explanation:

I found this by taking the two points and making it into a y = mx + b line.

Answer:

(0,3)

Step-by-step explanation:

We can use the slope-intercept form to find the y-intercept.

First, we need to find the slope of the line.

We are given the points (-1,7) and (1,-1).

[tex]m=\frac{rise}{run}=\frac{-1-7}{1+1}=\frac{-8}{2}=-4[/tex]

The slope is -4.

Slope-intercept is [tex]y=mx+b[/tex].

We can replace 'y' and 'x' with one of the points given, 'm' with the slope, and solve for 'b'. "B" would be the y-intercept.

I will use (-1,7):

[tex]7=-4(-1)+b\\\\7=4+b\\\\7-4=4-4+b\\\\\boxed{3=b}[/tex]

The line's equation is [tex]y=-4x+3[/tex].

Therefore, the y-intercept is '3'. The coordinates of the y-intercept is (0,3).  

Classify the triangle by its angles. answers: A) Obtuse triangle B) Acute triangle C) Right triangle D) Equilateral triangle

Answers

Answer:

B) Acute triangle

Step-by-step explanation:

In acute triangles, all of the angles are less than 90°. This is true for this triangle :)

I hope this helps!!

Answer:

B) Acute triangle

Step-by-step explanation:

All the angles are less than 90 degrees so all the angles are acute

Consider the density curve below.

0.25

х

1

2

3

4

5

Find the percent of the area under the density curve where x is less than 4.

Answers

Answer:

Check Explanation.

Step-by-step explanation:

Although, the density curve for this question is missing and isn't available online, I would use an example of another density curve to explain how this could be easily done.

From the density curve attached to this question, the total area under the curve is the are of the triangular shape formed by this curve with the x-axis.

Total Area under the curve = ½×base×height

= ½ × (5-1) × 0.5 = 1 square unit

Area under the density curve where x is less than 4 is a trapezium.

Area of a trapezium = ½ (a+b) h

For the area under the density curve where x is less than 4,

a = 0.5, b = (0.5/4) = 0.125, h = (4-1) = 3

Area under the density curve where x is less than 4 = ½ (0.5+0.125) × 3 = 0.9375 square unit

In terms of the total area, Area under the density curve where x is less than 4 covers

(0.9375/1) × 100% = 93.75%

Hope this Helps!!!

Square ABCD has a side length of 12 centimeters . Find the area of the square Type a numerical answer in the space provided Do not include units or spaces in your answer

Answers

Answer:

144

Step-by-step explanation:

Area of a square is [tex]s^2[/tex]

The side length is 12 cm.

[tex]12^2=144[/tex]

Therefore, the area of the square is [tex]144 \: cm^2[/tex].

What is the area of the shaded part of the circle that has a diameter of 8 mm? Use 3.14 for
4 mm
8 mm
O 16mm?
O 32mm?
O 34 24 mm
50.24 mm?

Answers

Answer: 34.27 sq. mm.

Step-by-step explanation:

Area of a triangle = hb / 2

= 8 x 4 / 2

= 32 / 2 = 16 mm

Area of the circle = πr^2

= π x 4^2

= 50 27 sq. mm.

Area of the shaded part

= 50.27 - 16

= 34.27 sq. mm

Answer: the answer is c, 34.24 mm

Step-by-step explanation: I just did the test

a ferris wheel goes around once every 20 seconds . How many times will a rider be ag thetop during an 8-minuteride?

A.23
B.24
C.25
D.160

Answers

Answer:

The answer is B.

Step-by-step explanation:

There are three 20 second time periods in 1 minute. Three times eight is equal to 24.  

A group of students where asked about the number of e-mails they each send that day. The results are: 0, 1, 1, 2, 3, 3, 4, 4, 6, 7, 8, 10, 11, 14, and 15. Which histogram correctly shows the data set?

Answers

Answer:

Choice D

Step-by-step explanation:

After writing the data down seperate the values according to the x-axis on the graphs. You will find that 6 people chose between 0 to 3, 4 people chose between 4 to 7, 3 people chose between 8 to 11 and 2 people chose between 12 to 15.

What is the value of x?

Answers

Answer: 98 is your answer

Step-by-step explanation:

Math help asap!
[Function Inverses]​

Answers

Answer:

It's (B) [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Hope this helped you!

Answer:

f^-1(8) = 3/2

Step-by-step explanation:

f(x) = 2x + 5

y = 2x + 5

x = 2y + 5

2y = x - 5

y = (x - 5)/2

f^-1(x) = (x - 5)/2

f^-1(8) = (8 - 5)/2

f^-1(8) = 3/2

Find the sum of the first 16 terms in an arithmetic series where a1 = 2, and the common difference is d=2. Question 4 options: A) 272 B) 240 C) 360 D) 306

Answers

Answer:

A) 272

Step-by-step explanation:

[tex]S_{n}=\frac{n}{2}*[2a + (n-1)d]\\\\s_{16}=\frac{16}{2}[2*2+15*2]\\\\ =8*[4+30]\\\\=8*34\\=272[/tex]

Answer:

272

Step-by-step explanation:

In one city, customers must pay 6% on all items purchased. The video game controllers cost $18.50 each. If a customer purchases 2 controllers, how much tax will she pay? A. $1.11 B. $2.22 C. $19.61 D. $39.22

Answers

Answer: B $2.22

Step-by-step explanation:

2 controllers will cost

= 2 x 18.50 = 37

6% tax = 37 x 0.06 = 2.22

Answer:

B

Step-by-step explanation:

i took the test

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