A railway club provides free train rides on their large circular tracks. There are two tracks. The distance from Track 1 to the center is 30 m. The distance between Track 1 and Track 2 is 5 m. How much farther is the train ride on Track 2 than Track 1

a) The basic formula is [tex]y=v_0t-gt^2/2[/tex]

[tex]9.81m/sec^2 x \ t^2 - (14 m/sec x t) - 60m = 0[/tex]

quadratic equation t= -b+/- √b^2-4ac /2a

t= 14+- √(-14)^2 -4(4.905)(-60)/ 2(4.905) = 5.20 sec

b) [tex]y=v_0t-gt^2/2[/tex]

At max height H, [tex]V_y = 0[/tex]

[tex]Vy^2 = V^2_{0y} - 2g(y-y_0)[/tex]

[tex]0=(14)^2 -2(9.81)(H-60)[/tex]

[tex]H=70m[/tex]

The ball would fall 10m from max height of 70m. set y=0 and H=10m

[tex]y=gt^2/2+H, t = 1.42 \ sec[/tex].

[tex]\bold{Therefore, 5.2 - 1.42 = 3.77 \ sec}[/tex]

The relationship between the volumes of pyramids and prisms is that when a prism and pyramid have the same base and height, the volume of the pyramid is the volume of the prism. This statement is not correct.

When a pyramid and a prism have the same base and height, the volume of the pyramid is one-third ([tex]\frac{1}{3}[/tex]) the volume of the prism.

This can be seen from the formula for the volume of a rectangular prism, which is:

[tex]The volume of the prism = base area x height[/tex]

And the formula for the volume of a rectangular pyramid is:

The volume of the pyramid = [tex]\frac{1}{3}[/tex] x base area x height

Since the base area and height of the pyramid and prism are the same, we can compare their volumes by dividing the volume of the pyramid by the volume of the prism:

[tex]\frac{The volume of pyramid}{Volume of prism}[/tex] = [tex]\frac{1}{3}[/tex] x base area x height/base area x height

Simplifying this expression, we get:

[tex]\frac{The volume of pyramid}{Volume of prism}[/tex] = [tex]\frac{1}{3}[/tex]

Therefore, the volume of a pyramid with the same base and height as a prism is one-third [tex](\frac{1}{3})[/tex] the volume of the prism.

The complete question is:-

The relationship between the volumes of pyramids and prisms is that when a prism and pyramid have the same base and height, the volume of the pyramid is the volume of the prism. True/False.

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The volume of the coffee can rounded to the nearest 10th of a decimal place is 226. 08 cubic inches

It is important to note that the coffee can takes the shape of a cylinder.

The formula for calculating the volume of a cylinder is expressed with the equation;

V = πr²h

This is so as the parameters are enumerated thus;

Also, r = diameter/2 = 6/2 = 3 inches

From the information given, we have that;

Volume = 3.14 × (3)² × 8

Multiply the values

Volume = 226. 08 cubic inches

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The volume of the stone is 1032 cm³.

The volume of the stone can be calculated using the formula V = lwh. Here, l = 10 cm, w = 24 cm, and h = 2.7 cm. Therefore, the volume of the stone is V = 10 x 24 x 2.7 = 648 cm³.

The volume of the water in the container is calculated using the formula V = lwh. Here, l = 10 cm, w = 24 cm, and h = 7 cm. Therefore, the volume of the water in the container is V = 10 x 24 x 7 = 1680 cm³.

The difference between the volume of the water and the volume of the stone is the volume of the water displaced by the stone, which is V = 1680 - 648 = 1032 cm³. Therefore, the volume of the stone is 1032 cm³.

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The correct statement is a=b implies that ac=bc.

If the real numbers a and b are such that a=b, then their values are equal.

The result of adding c to both sides of the formula a=b is:

a+c = b+c

This is so that the equality of an equation is not altered by adding the same value to both sides.

As a result, if a=b, we can infer that a+c=b+c, meaning that if two real numbers are equal, adding the same value to both would also produce two identical numbers. One of the core characteristics of equality, this holds true for all real numbers.

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Liam saved $192.05 from his summer jobs.

It is based on the probability that something will happen. The fundamental underpinning of theoretical probability is the justification for probability. For instance, while flipping a coin, there is a 50% probability that it will land on its head.

By deducting his outgoings from his total earnings, we can calculate how much money Liam saved:

m = 328.65 - 136.60

Condensing the phrase:

m = 192.05

Liam was able to save $192.05 as a result of his summer jobs.

The following equation and its answer demonstrate how much money Liam has saved:

m = 328.65 - 136.60

m = 192.05

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Answer: Answers below

Step-by-step explanation:

1. $15.64

2. 5370.28 Yen

3. 13425.70 Yen

4. $100

5. 67128.51 Yen

6.$782.08

Answer: 1: 15 2: 5370 3:13400 4: 160 5: 67100 6: 780

Step-by-step explanation: These are rounded to the nearest 100th

Answer:

B. [tex]\sqrt[3]{-x-9}[/tex]

Step-by-step explanation:

Switch x and y, and then solve for y.

[tex]y = -x^3-9\\x=-y^3-9\\x+9=-y^3\\-x-9=y^3\\\sqrt[3]{-x-9} =y[/tex]

Answer:

    m∠4 = 133°

Step-by-step explanation:

Given m∠7 = 37°

Since m∠7 ≅ m∠6 [Vertically opposite angles]

and m∠6 + m∠4 = 180° [Sum of interior angles formed by parallel lines l, m and transverse.]

Therefore, 47°+ m∠4 = 180°

m∠4 = 180 - 47

       = 133°

The probability of all the defendants being found guilty is 1/16. Answer: 1/16.

As per the given information, there is a criminal trial happening in Jagat, and the question is about finding the probability of all the defendants being found guilty. Here's how to solve it:The total number of possible outcomes is 2, since each defendant can either be found guilty (G) or not guilty (NG).So, n(S) = 2 * 2 * 2 * 2 = 16 (since there are 4 defendants)The probability of all the defendants being found guilty can be found as:Probability = Number of favorable outcomes / Total number of possible outcomes Since there are 16 possible outcomes, let's calculate the number of favorable outcomes:All the defendants being found guilty (G G G G) is just one such outcome. Hence, the number of favorable outcomes is 1.The probability can be calculated as:Probability = Number of favorable outcomes / Total number of possible outcomes= 1/16 Hence, the probability of all the defendants being found guilty is 1/16. Answer: 1/16.

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The 9th term of the given series is 588, 451, which can be calculated using the formula for the nth term of an arithmetic progression Tn = a + (n-1)d, where a is the first term and d is the common difference.

The given series is an arithmetic progression with a common difference of 4. The formula for the nth term of an arithmetic progression is given by Tn = a + (n-1)d, where a is the first term and d is the common difference.

Therefore, for the given series, a = 1 and d = 4.

Substituting these values in the above formula, we get

T9 = 1 + (9-1)4

 = 1 + 32

 = 33

Now, adding 33 to each of the terms of the given series, we get

1 + 33 = 34

5 + 33 = 38

25 + 33 = 58

125 + 33 = 158

Therefore, the required 9th term of the series is 588, 451.

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Therefore , the solution of the given problem of triangle comes out to be  x = 15 .

A triangular is a polygon because it has two or maybe more additional sections. It has a straightforward rectangular form. A, B, and C are the only three sides that set a triangle apart from a simple triangle. When the boundaries are not exactly collinear, Euclidean geometry results in a singular area instead of a cube. If a shape has three edges and three angles, it is said to be triangular.

Here,

Triangle ABC ,

=> x /5 = x-6/3

=> 3x = 5x - 30

=> 2x = 30

=> x = 30/2

=> x = 15

Therefore , the solution of the given problem of triangle comes out to be   x = 15 .

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The solution to the differential equation is:

$$v(t)=\frac{V_0+kCe^{-Ct}}{1+kCe^{-Ct}}$$
Where $V_0$ is the initial velocity and $C$ is the proportionality constant. The limiting velocity of the falling body as $t \to \infty$ is: $$v_{\infty}=\frac{V_0}{1+kC}$$

The instantaneous velocity of an object is the limit of the average velocity as the elapsed time approaches zero, or the derivative of x with respect to t: v ( t ) = d d t x ( t ) . v ( t ) = d d t x ( t ) . Like average velocity, instantaneous velocity is a vector with dimension of length per time.

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Answer:   8x + 6y = $56.50

Step-by-step explanation:

I think this is right!

On answering the provided question, we have got that 3.3 is the average  equation result after rolling the dice ten times.

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

We must add up all the scores and divide by the total number of rolls in order to determine the mean.

The total of every score is:

1 + 1 + 2 + 2 + 3 + 1 + 4 + 2 + 5 + 4 + 6 + 2 = 33

There are ten rolls in total.

The mean is as a result:

mean = total scores / total rolls = 33 / 10 = 3.3

3.3 is the average result after rolling the dice ten times.

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Answer:

115.50

Step-by-step explanation:

Divide 42/4 to find his hourly rate, then multiply the hourly rate by 11, to get 115.50

Answer:

$115.05

Step-by-step explanation:

If he earns $42 in 4 hours than he earns $10.05 in 1 hour

42 / 4 = 10.5

10.5 x 11 = 115.5

By answering the above question, we may state that Multiplying these equation prime factorizations together, we get:

[tex]16^13 * 10^7 * 81^18 = (2^52) * (2^7 * 5^7) * (3^72) = 2^59 * 3^72 * 5^7[/tex]

A math equation is a mechanism for connecting two claims by using the equals sign (=) to indicate equivalence. A mathematical statement that establishes the equivalence of two mathematical expressions is known as an equation in algebra. The equal symbol, for example, splits the numbers 3x + 5 and 14. A mathematical formula can be used to describe the relationship between two phrases written on opposite sides of a letter. The logo and programme are frequently the same. 2x - 4 Equals 2, for example.

then multiply the prime factors together using the laws of exponents.

[tex]12^9 = (2^2 · 3)^9 = 2^18 · 3^9\\36^15 = (2^2 · 3^2)^15 = 2^30 · 3^30\\169^8 = 13^16\\12^9 · 36^15 · 169^8 = (2^18 · 3^9) · (2^30 · 3^30) · 13^16 = 2^48 · 3^39 · 13^16\\[/tex]

(b)

[tex]16^13 = 2^52\\10^7 = 2^7 · 5^7\\81^18 = (3^4)^18 = 3^72\\[/tex]

Multiplying these prime factorizations together, we get:

[tex]16^13 * 10^7 * 81^18 = (2^52) * (2^7 * 5^7) * (3^72) = 2^59 * 3^72 * 5^7[/tex]

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Answer:

Step-by-step explanation:

[tex]a)\quad AB[/tex]

[tex]b)\quad AB[/tex]

[tex]c)\quad AC[/tex]

[tex]d)\quad BC[/tex]

[tex]e)\quad BC[/tex]

[tex]f)\quad AC[/tex]

Answer:

Therefore, ackrabbits can reach speeds of approximately 59 feet per second.

Step-by-step explanation:

First, we need to convert miles to feet:

40 miles/hour * 5,280 feet/mile = 211,200 feet/hour

Then, we need to convert hours to seconds:

1 hour = 60 minutes/hour * 60 seconds/minute = 3,600 seconds/hour

211,200 feet/hour / 3,600 seconds/hour = 58.67 feet/second

Rounding to the nearest whole number, we get:

59 feet/second

Therefore, ackrabbits can reach speeds of approximately 59 feet per second.

Answer:

The first five natural number are 1, 2, 3, 4 and 5. Hence, the mean of the five natural numbers is 3.

Answer:

3

Step-by-step explanation:

[tex]\frac{1+2+3+4+5}{5}[/tex] =  [tex]\frac{15}{5}[/tex] = 3

The natural numbers are also called the counting numbers.  They are the set of numbers: 1, 2, 3, ....

Helping in the name of Jesus.

Answer:

I guess the value be 26x

hope it helps u

mark me brainlist

Answer:

8.09017

calculations

Answer:

(3h+4)(2h+3)

Step-by-step explanation:

6h^2 + 8h + 9h + 12h

(6h^2+8h) + (9h+12h)

2h(3h+4) + 3(3h+4)

(3h+4)(2h+3)

Answer:

(3h+4) (2h+3)

Step-by-step explanation:

i hope this helps

Answer:

B linear

Step-by-step explanation:

If the rate of change stayed the same then it has to be a straight line so no C or D, and it cant be A be cause there is a rate of change.

As a result, the right triangle x value of 65° is the answer to the given triangle issue.

Triangles are categorised as polygons because they have four edges or more. Its shape is simple and symmetrical. The characters ABC make a square angle that is a triangle. When the edges are still not collinear, Euclidean geometry yields a single rectangle or square. Due to their three edges and three corners, triangles are considered polygons. The corners of a triangle are where its three edges meet. Angles in a trapezoid add up to 360 °.

Here,

Given:

Triangle is 90 degrees because of its right orientation.

The total of the triangle's angles is 180 degrees.

Thus,

=> x + 25° + 90° = 180°

=> x + 115° = 180°

=> x = 180° -115°

=> x = 65°

Thus, the value of x is 65°.

As a result, the answer to the provided triangle problem is

Right triangle's x number is 65 degrees.

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Answer : There are 84 different ways that six letters can be grouped from nine letters total.

Now that we have determined that the problem deals with combinations, we can use the formula for combinations to calculate the number of ways that six letters can be grouped from nine letters total. The formula for combinations is:

C(n,k) = n! / (k! * (n-k)!)

Where n is the total number of items, and k is the number of items being chosen. In this case, n = 9 and k = 6. Plugging these values into the formula gives us:

C(9,6) = 9! / (6! * (9-6)!)

C(9,6) = 9! / (6! * 3!)

C(9,6) = 362880 / (720 * 6)

C(9,6) = 362880 / 4320

C(9,6) = 84

Therefore, there are 84 different ways that six letters can be grouped from nine letters total.

Answer: 84.

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The increase in the rate of unemployment from 2000 to 2001, given the unemployment figure is between D. 0. 46 % and 0. 49 %.

First, find the rate of unemployment in 2000 to be :

= Unemployment number / Total labor force x 100 %

= 3, 503, 917 / 25, 554, 417  x 100 %

= 13.71  %

The rate of unemployment in 2001 was :

= 3, 745, 300 / 26, 416, 800 x 100 %

= 14. 18 %

The increase in the rate of unemployment is:

= 14. 18 - 13. 71

= 0. 47 %

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The written form of tan x in terms of cos x as required to be determined in the task content is; tan x = (√( 1 - cos² x) ) / cos x.

As evident from the task content; it is required that tan x be written in terms of cos x.

Hence, recall from trigonometric identities that;

tan x = sin x / cos x

However, since sin² x = 1 - cos² x from ( sin²x + cos²x = 1)

It follows that; sin x = √( 1 - cos² x)

Hence, it can be written that;

tan x = (√( 1 - cos² x ) ) / cos x.

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The answer is in the attachment given below ...

Thank you :)