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A railroad tunnel is shaped like a semi-ellipse, as shown below. A semiellipse is shown on the coordinate plane with vertices on the x axis and one point of intersection with the positive y axis. The height of the tunnel at the center is 35 ft, and the vertical clearance must be 21 ft at a point 8 ft from the center. Find an equation for the ellipse.

Answer:

A rhino runs at a speed of about 28 miles per hour.

We need to determine the speed in feet per second.

Converting miles to feet:

The miles can be converted to feet by multiplying 5280 with 28 miles per hour.

Thus, we have;

28 x 5280 = 14784028 × 5280 = 147840

Thus, the speed of the rhino in feet per hour is 147840

Converting hours to seconds:

The hours can be converted into seconds by dividing 147840 by 3600 (Because an hour has 60 seconds in a minute and 60 minutes in an hour)

Thus, we get;

Speed=\frac{147840}{3600}Speed=

3600

147840

Speed = 41.066667Speed=41.066667

Rounding off to the nearest whole number, we get;

Speed = 41

Therefore, the speed of the rhino is 41 feet per second.

Answer:

D) 4.7

Step-by-step explanation:

this perpendicular connection with the circle center cuts this intersecting line in half, which is therefore on both sides of x 6.5 long.

I assume 16 is the diameter, so the radius is 8.

therefore, x is one side of the right-angled triangle of

radius

x

half of the intersecting line

Pythagoras

8² = x² + (6.5)²

64 = x² + 42.25

21.75 = x²

x = 4.7

Answer:

AB= A. (50)^1/2

BC= B. (65)^1/2

AC= D. (145)^1/2

<ABC≈ 105

Answer:

276in³

Step-by-step explanation:

First, we can separate this into two separate rectangular prisms. We can add their volumes to get the total volume. I have separated the prisms by the light green lines, as shown in the picture.

For the top one, we have a length of 5 in , width of 3 in, and height of x in. We know that the total height is 10 in, and the bottom height is 6. The top difference is the difference of those two heights, or 10-6= 4 = x. Therefore, the volume of the top prism is 5 in* 3 in* 4 in = 60 in³

For the bottom prism, we have a length of 12 in, height of 6 in, and width of 3 in (this is the same, as the 3in from the top prism matches with the width of the of the bottom prism), making our volume 12 in * 6 in * 3 in = 216 in ³.

We can then add 216 in ³ and 60 in³ to get 276in³ as our total volume

Answer:

I hope this helps. There is a link

b

So what is that distance well we know that to get to negative 4 pi over 3 we took negative pi and travelled pi over 3.. So this is just pi over 3.. So our reference angle would be pi over 3.

Step-by-step explanation:

Answer:

We need 1600 squares with a width of 6 feet to cover the entire field without any gaps nor overhangs.

Step-by-step explanation:

The number of squares required to cover the field is equal to the area of the field divided by the area of a square:

[tex]n = \frac{A}{l^{2}}[/tex] (1)

Where:

[tex]n[/tex] - Quantity of squares, in feet.

[tex]A[/tex] - Area of the field, in square feet.

[tex]l[/tex] - Length of each square, in feet.

If we know that [tex]A = 57600\,ft^{2}[/tex], then we have the following hyperbolic function:

[tex]n = \frac{57600}{l^{2}}[/tex]

Now we plot the function with the help of graphing tools, whose result is presented below. Please notice that quantity of squares must be an integer and we need 1600 squares with a width of 6 feet to cover the entire field without any gaps nor overhangs.

Answer:

2/9 ; 4/9

Step-by-step explanation:

______SPINNER A_____

_____ 2 ____ 4 _____ 6

1 ____ 2 _____4 _____6

3____ 6 _____12____ 18

5____10_____20____30

4 * 3 = 12 ; 5 * 2 = 10 ; 5 * 6 = 30

Probability of scoring a total of 6 :

From the sample space ; Number of 6's = 2

Total sample space = 9

Recall : probability = required outcome / Total possible outcomes

P(total of 6) = 2 / 9

P(total greater than 10) :

Required outcome ; > 10 = (12, 18, 20, 30) = 4

P(total > 10) = 4 / 9

Step-by-step explanation:

b) what is the probability of scoring a total of 6?

b) = 2/9

C) what is the probation scoring a total greater than 10

c)= 3/9

Answer:

check the picture below.

so the focus point is at 5, -1 and the directrix is above it, meaning is a vertical parabola, and is opening downwards, like in the picture.

keep in mind that the vertex is half-way between those two fellows, at a "p" distance from either, in this case 1 unit, since the parabola is opening downwards, "p" is negative then, or -1, and the vertex will be from 5, -1 up one unit, so 5,0.

Answer:

x=3

Step-by-step explanation:

Equation: 7x-8=3x+4

4x=12

x=3

Answer:

13 feet

Step-by-step explanation:

the width = 234/18 = 13 feet

Answer:

C. 14 RootIndex 3 StartRoot x EndRoot)

Step-by-step explanation:

To obtain the sum ; the a clear explanation has been attached in the picture below ;

Answer:

Reese's love peanut butter and chocolate

hope it helps u

plz mark it as brainliest

Answer: (a) P = 6W + 2

(b) L = 2W + 1

(c) Width = 13cm

Length = 27cm

Step-by-step explanation:

The formula for perimeter of a rectangle is 2(length + width). Since the length is 1 cm more than twice its width, then the length will be:

L = (2 × W) + 1

(b) L = 2W + 1

Therefore, P = 2(L + W)

P = 2( 2W + 1) + 2W

P = 4W + 2 + 2W

(a) P = 6W + 2

Since perimeter is given as 80cm. Therefore,

P = 6W + 2

6W + 2 = 80

6W = 80 - 2

6W = 78

W = 78/6

W = 13

Width is 13cm

Length = 2W + 1

Length = 2(13) + 1

Length = 27cm

The width of the rectangle is 13cm and the length is 27cm.

A rectangle is a quadrilateral. Opposite sides are equal. The four angles in a rectangle is equal to 90 degrees.

The formula for determining the perimeter of a rectangle = 2x (length + width)

P = 2(L + W)

80 = 2(1 + 2w + w)

80 = 2(1 + 3w)

40 = 1 + 3w

40 - 1 = 3w

39 = 3w

w = 13cm

Length = 1 + 2(13) = 27cm

To learn more about rectangles, please check: https://brainly.com/question/16595449

Answer:

A

Step-by-step explanation:

simplify equation A

then you will get same as the expression above

Answer:

x = 9/2     y = 0

Step-by-step explanation:

2/3x + 5y = 3            5y = -2/3x + 3                y = -2/15x + 3/5

4/3x - 2(-2/15x + 3/5) = 6

4/3x + 4/15x - 6/5 = 6

8/5x - 6/5 = 6

8/5x = 36/5

x = 9/2

2/3(9/2) + 5y = 3

3 + 5y = 3

5y = 0

y = 0

Answer:

Answer:

The values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001 is 0 < x < 0.3936.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001. f(x) = e^x ≈ 1 + x + x²/2! + x³/3!, x < 0

The explanation of the answer is now provided as follows:

Given:

f(x) = e^x ≈ 1 + x + x²/2! + x³/3!, x < 0 …………….. (1)

[tex]R_{3}[/tex] = (x) = (e^z /4!)x^4

Since the aim is [tex]R_{3}[/tex](x) < 0.001, this implies that:

(e^z /4!)x^4 < 0.0001 ………………………………….. (2)

Multiply both sided of equation (2) by (1), we have:

e^4x^4 < 0.024 ……………………….......……………. (4)

Taking 4th root of both sided of equation (4), we have:

|xe^(z/4) < 0.3936 ……………………..........…………(5)

Dividing both sides of equation (5) by e^(z/4) gives us:

|x| < 0.3936 / e^(z/4) ……………….................…… (6)

In equation (6), when z > 0, e^(z/4) > 1. Therefore, we have:

|x| < 0.3936 -----> 0 < x < 0.3936

Therefore, the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001 is 0 < x < 0.3936.

Hi!

[tex]3x^3-2y^3-6x^2y^2+xy=\\\\=3\cdot(\frac{2}{3})^3-2\cdot(\frac{1}{2})^3-6\cdot(\frac{2}{3})^2\cdot(\frac{1}{2})^2+\frac{2}{3}\cdot\frac{1}{2}=\\\\=3\cdot\frac{8}{27}-2\cdot\frac{1}{8}-6\cdot\frac{4}{9}\cdot\frac{1}{4}+\frac{1}{3}=\\\\=\frac{8}{9}-\frac{1}{4}-\frac{2}{3}+\frac{1}{3}=\frac{8}{9}-\frac{1}{4}-\frac{1}{3}=\frac{32}{36}-\frac{9}{36}-\frac{12}{36}=\boxed{\frac{11}{36}}[/tex]

Answer:

Fifty seven thousand nine hundred and eight

57908

Answer:

They are parallel so also -4/3

Hello,

Answer D

[tex]\begin{array}{|c|c|}x&y\\--&-------------\\-1&-3*\sqrt{-1+1} =-3*0=0\\0&-3*\sqrt{0+1} =-3*1=-3\\3&-3*\sqrt{3+1} =-3*2=-6\\8&-3*\sqrt{8+1} =-3*3=-9\\15&-3*\sqrt{15+1} =-3*4=-12\\--&-------------\\\end{array}[/tex]

9514 1404 393

Answer:

  B.

Step-by-step explanation:

The symmetric properties of equality and congruence let you swap sides of the equality/congruence symbol without changing the truth of the statement:

  A ≅ B   ⇔   B ≅ A

Explanation:

The blue rectangle has area of 4a^2*6a^2 = 24a^4

The red rectangle has area 4a^2*9a = 36a^3

The green rectangle has area 4a^2*3 = 12a^2

The total area is 24a^4 + 36a^3 + 12a^2

Answer:

Rupees 39,000 are

378.63 Pound sterling

The solution for x is x = (y + 49)/7.

Given that an equation 7x - 49 = y, we need to determine the equation in for of x,

To solve for x in the equation 7x - 49 = y, we'll isolate x on one side of the equation.

Here's the step-by-step process:

Start with the given equation: 7x - 49 = y.

Add 49 to both sides of the equation to isolate the term with x:

7x = y + 49.

Divide both sides of the equation by 7 to solve for x:

(7x)/7 = (y + 49)/7.

Simplify:

x = (y + 49)/7.

Therefore, the solution for x is x = (y + 49)/7.

Learn more about equation click;

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Answer:

X=39.3

Step-by-step explanation:

Cos=adjacent/hypotenuse

Cosx=6.5/8.4

X=arccos(6.5/8.4)

X=39.3° rounded from 39.302°

Answer:

Step-by-step explanation:

The Midpoint formula is

[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex] where all of those x's and y's come from the coordinates of points L and M. Filling in:

[tex]M=(\frac{8+10}{2},\frac{4+14}{2}) =(\frac{18}{2}, \frac{18}{2})=(9,9)[/tex]

Answer:

x = 7

Step-by-step explanation:

First we find out what we are using sin,cos, or tan then we plug in the numbers

Sin 26 x 16 = 7