A train leaves New York for Boston, 200 miles away, at 5:00 P.M. and averages 75 mph. Another train leaves Boston for New York on an adjacent set of tracks at 4:00 P.M. and averages 65 mph. At
what time will the trains meet? (Round to the nearest minute.)

We have used spherical coordinates to show that the triple integral from negative infinity to infinity of the [tex]\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z=2 \pi$$[/tex]

Triple integrals, as their name suggests, are three sequential integrations that can be used to determine a volume or to integrate in a fourth dimension over three other independent dimensions.

The total amount of heat in the three-dimensional room can be calculated using this triple integral.

We understand that triple integrals have several uses if "dimension" can refer to something other than a spatial dimension. We could determine a 3-D object's overall inertia or the gravitational attraction on a basketball.

The sum of an infinite number of rectangular prisms across a bounded region in three-space is a double integral, which represents the volume beneath the surface above the xy-plane.

[tex]$$To show that $\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z=2 \pi$, begin by converting the integral into spherical coordinates. Recall that $\rho^2=x^2+y^2+z^2$ and $d V=\rho^2 \sin \phi d \rho d \phi d \theta$. To convert the bounds, notice that as $x, y$, and $z$ expand infinitely in both directions, this can be modeled to a sphere of an infinite radius.\\$$[/tex]

[tex]$$This means that the new bounds become $0 \leq \rho \leq \infty, 0 \leq \phi \leq \pi$, and $0 \leq \theta \leq 2 \pi$. Because the integral is infinite, let the upper limit of $\rho$ be $R$ and take the limit as $R$ goes to infinity. To evaluate with respect to $\rho$, first use $u$ substitution by letting $u=\rho^2$ and then integrating by parts$$[/tex]

[tex]$\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z$[/tex]

[tex]& =\lim _{R \rightarrow \infty} \int_0^{2 \pi} \int_0 \int_0^R \sqrt{\rho^2} e^{-\left(\rho^2\right)} \rho^2 \sin \phi d \rho d \phi d \theta \\& =\lim _{R \rightarrow \infty} \int_0^{2 \pi} \int_0^\pi \int_0^R e^{-\rho^2} \rho^3 \sin \phi d \rho d \phi d \theta \\[/tex]

[tex]& =\lim _{R \rightarrow \infty} \int_0^{2 \pi} \int_0^2 \sin \phi\left[\frac{1}{2}\left(-e^{-\rho^2}\left(1+\rho^2\right)\right)\right]_{\rho=0}^{\rho-R} d \phi d \theta \\& =\frac{1}{2} \lim _{R \rightarrow \infty} \int_0^{2 \pi \pi} \int_0^\pi \sin \phi\left[-e^{-R^2}\left(1+R^2\right)+e^{-0^2}\left(1+0^2\right)\right] d \phi d \theta\end{aligned}$$[/tex]

[tex]$$\\\text{Use L' Hospital's Rule to simplify the limit}$$\begin{aligned}& \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z \\& =2 \pi(1)-2 \pi \lim _{R \rightarrow \infty}\left(\frac{2 R}{2 R e^{R^2}}\right) \\& =2 \pi-\lim _{R \rightarrow \infty} \frac{1}{e^{R^2}} \\& =2 \pi-0 \quad \text { As } \lim _{x \rightarrow \infty} \frac{1}{e^x}=0 . \\& =2 \pi\end{aligned}$$[/tex]

[tex]$$Therefore,$$\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2} e^{-\left(x^2+y^2+z^2\right)} d x d y d z=2 \pi$$[/tex]

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The correct option for the given question is an option (C) which is Segments A and C only.

The goal of image segmentation techniques is to separate the image's various components according to the region of interest. Videos are collections of images, therefore motion segmentation separates them into moving foreground and background by separating the elements that exhibit various motion patterns.

We can extract visual information by classifying visual elements from the scenes into different groups and analyzing these spatial and temporal changes that take place in the image sequence. Each group represents an object's motion in the dynamic sequence.

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The complete question is:

This plot shows an object being moved by a series of forces. Which segments of the motion could have been caused by fixed springs?

A) None of the segments could represent work being done by springs.

B) Any of the segments could represent work being done by springs.

C) Segments A and C only.

D) Segments B and D only.

E) Segment A only.

The line touches -x axis at 3 and touches y axis at 3

P(x,y) = (-3,3)

α+ β = -3

α β = 3

Extreme values are present in a set of data in business. which of the following descriptive summary measures are most appropriate interquartile range and median.

Range is the maximum easy and normally comprehensible measures of dispersion. Range is described because the distinction among the highest (or largest) and lowest (or smallest) determined fee in a series. Therefore, it's miles the maximum affected measures of dispersion via way of means of the acute values of the series.

The median offers the best weight to factors withinside the center of the ordered records. When there are intense numbers withinside the records set (very low or very excessive numbers), the median is a great data preference for a degree of principal tendency.

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Answer:

67

Step-by-step explanation:

The given arithmetic sequence is,

203, 199, 195,......

In the sequence, the first time a = 203,

And common difference of the sequence d = -4

Formula for nth term of the sequence,

aₙ = a + (n-1) . d

To find 35th term of the sequence, substitute n= 35,

a₃₅ = 203 + (35-1).(-4)

= 203 + 34x-4

= 203 - 136

= 67

©Thank You

Answered By Solution 49

The answer is the tall are the group predicted the snowman will 800/9 or  alternative form was 88.8.

What is meant by predicted?

Based on the given conditions, formulate :: 80 ÷ (1 - 10%)

Calculate the sum or difference:

= 80 / 1 - 0.1

= 80 / 0.9

Multiply both the numerator and denominator with the same integer : 800 / 9 or alternative form was 88.8

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Camille can buy maximum of 3 shirts with the amount with him and left with $24 after buying 3 shirts .

Price of each shirt is $32 and the maximum she can buy is 5 shirts

suppose he buys x shirts from the money he initially have

so 32*x<=120

=> x<=3.75

solving the inequality we get:

so x=3 so maximum he can buy is 3 shirts.

Cost of each shirts is $32 so  the cost of 3 shirts is given by:

=>3*32

=> $96

so the amount of money left with him = 120 -96

=> 24

so total $24 she can save after buying 3 shirts.

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Complete question:

camille have $120 with him he can buy upto 5 shirts and cost of each shirt is $32 .how much money could she have and how manu shirts he buys? enter the correct answers in the boxes in dollars and cents.

The function:

f(x) = 1/x

Does not has 0 on its domain, then the domain is not R, that is why the function is not from R to R.

A function from R to R is a function where the domain is the set of all real numbers and the range is also the set of all real numbers.

Here the given function is rational, and it is:

f(x) = 1/x

Remember that we can't divide by zero, so the input x = 0 can't be on the domain of function f(x).

Thus, the domain is not the set of all real numbers.

That is why the function f is not from R to R, because the domain is not R.

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Intuitively speaking two events are independents when the occurrence of one event (A) does not exert influence over the event (B)

Symbolic speaking in terms of sets

P(A∩B)= P(A) * P(B)

Examining each alternative

A. Flipping two coins and having one show a head and the other show a head

Independent. Each flipping coin does not exert any influence on the other

B. Being sneezed on and catching a cold

Dependent. This sequence of events expresses cause consequences effects.

C. When rolling a pair of dice, getting a total of 6 and having one die show a 3

Dependent

Under these conditions, the second event is dependent since all we need is a sum of six, having the first dice showing three. The second one has to show three. So it does exert influence under the result.

D. Rolling a 4 on one die and rolling a 2 on another die

Independent. To get a 4 does not exert any influence on getting a 2 on another dice.

E. Seeing clouds and winning the lottery

Independent.

There is no influence seeing clouds and winning the lottery.

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Answer:

4.5:87

Step-by-step explanation:

First, we can set up an equation because 1.5:29 is equal to 4.5:x

[tex]\frac{1.5}{29} = \frac{4.5}{x}[/tex]

Now, we can solve for x by:

1.5x = 4.5 * 29

1.5x = 130.5

x = 87

The ratio will be 4.5:87

Answer:

2.25.50

Step-by-step explanation:

it is simplified since 25 is not divisible by 2

Answer:

I believe the answer may be 31.5cm.

Step-by-step explanation:

I first found the area of the total region which was 70cm. From there I found the area of the triangle to the left of the region by doing 6x7 which is 42, and multiplied by 1/2 because it is a triangle. I did the same to the triangle on the right, doing 5x7 which is 35, and multiplied by 1/2 since this is also a triangle. Finally, I subtracted both totals of 21, and 17.5 from the 70, getting a grand total of 31.5cm.

Answer:

31.5 cm²

Step-by-step explanation:

To find the area of the crossed region, subtract the areas of the two triangles from the area of the rectangle.

Formulae:

Area of the rectangle

⇒ A = (4 + 6) × 7

⇒ A = 10 × 7

⇒ A = 70 cm²

Area of triangle 1

⇒ A = ¹/₂ × 6 × 7

⇒ A = 3 × 7

⇒ A = 21 cm²

Area of triangle 2

⇒ A = ¹/₂ × 5 × 7

⇒ A = 2.5 × 7

⇒ A = 17.5 cm²

Area of the crossed region

⇒ A = 70 - 21 - 17.5

⇒ A = 49 - 17.5

⇒ A = 31.5 cm²

Answer: 53

Step-by-step explanation: We know that the a triangle has three sides.

We also know that all of the sides are equal. And all the sides equal 159. So do 159/3 which equals 53.

sint= [tex]y=\frac{\sqrt{5} }{5}[/tex], cost= [tex]x=\frac{2\sqrt{5} }{5}[/tex], tant=2.

If the terminal point P(X, Y) is determined as a real number, t lies on the unit circle then:

sint=y cost=x tant=y/x

we are given a terminal point of P [tex](\frac{\sqrt{5} }{5} ,\frac{2\sqrt{5} }{5} )[/tex] but not given that t lies on the unit circle. we must then first verify that P lies on the unit circle:

The equation of the unit circle is:

x²+y²=1

After substituting the given points in the above equation:

[tex](\frac{\sqrt{5} }{5} )^{2} +(\frac{2\sqrt{5} }{5} )^2=1[/tex]

Now evaluate the powers we get:

[tex]\frac{5}{25} +\frac{20}{25} =1[/tex]

Adding the equation we get:

1=1

Since P [tex](\frac{\sqrt{5} }{5} ,\frac{2\sqrt{5} }{5} )[/tex] lies on the unit circle, then:

[tex]sint=y=\frac{\sqrt{5} }{5}\\\\cost=x=\frac{2\sqrt{5} }{5} \\\\tant=\frac{y}{x}=\frac{\frac{2\sqrt{5} }{5} }{\frac{\sqrt{5} }{5} }[/tex]

By solving the tant we get:

tant=2.

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the value of the function at t = 7 is 1723.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given the function: x(t) = 6T³ - 7t²- 6t + 50.

the value of x at t = 7

Substitute the value of t in the given function

x(7) = 6 * 7³ - 7*7² - 6 * 7 +50

x(7) = 1723

Therefore, the value of the function at t = 7 is 1723.

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Question

Answered step-by-step

"Match the key aspect of a function's graph with its meaning. f(x) > 0 intervals of the domain where the graph is above the x-axis f(x) < 0 location on graph where input is zero x-intercept location on graph where output is zero y-intercept intervals of the domain where the graph is below the x-axis Common Core Algebra 'httpsinIscorekam edgenuftycomPlayer Common Core Algebra /- MAJIO9 / AcR 7haijliy Giapiij Instruction Active of a Graph the Meaning of Key Features Matching of a function $ graph with its meaning Match the key aspect intervals of Ihe domain where the graph. IS above the x-axis flx) > E Iocation on graph where input IS zero fix) < 0 Iocation on graph where output IS x-Intercepi zero Intervals Of the domain where the y-intercept graph Is below the x-axis Untto Done PrevousAaml Type here i0 search"

The span of the two vectors is the set of all linear combinations of the two vectors. This means that any point on the line through u and the origin, as well as any point on the line through v and the origin, can be written as a linear combination of u and v.

1. Start by taking two non-zero vectors u and v.

2. The span of the two vectors is the set of all linear combinations of the two vectors, which means that any point on the line through u and the origin, as well as any point on the line through v and the origin, can be written as a linear combination of u and v.

3. Therefore, span{u, v} contains the line through u and the origin, as well as the line through v and the origin.

The span of two non-zero vectors u and v contains the line through u and the origin, as well as the line through v and the origin. Any point on these two lines can be written as a linear combination of u and v.

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The set of inequality that most closely resembles the graph below is called y<4 , [tex]$y \geq 4 x-4$[/tex].

Two or more inequalities in one or more variables make up a system of inequalities. When a problem has a variety of possible solutions and those solutions are subject to several constraints, systems of inequalities are used. Inequality in income, gender, health care, and social class are some of the most prominent examples of social inequality.

At position five, there is an open circle with a right arrow. As a result, the compound inequality can be solved, for instance, by the numbers 0 and 6, but not by the number 4. An expression that doesn't contain the equals sign (=) is called an inequality. ,, >, and are the most widely used inequality symbols. Addition, subtraction, multiplication, and division are the four operations kinds that are performed on linear inequalities.

Therefore the correct answer is option A ) y<4 , [tex]$y \geq 4 x-4$[/tex]

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Tony walked 7/10 km which in decimal will be 0.7 km

Volet spent 0.5 hrs reading a pocket which in Fraction will be 5/10 = 1/2

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.

The three main sorts of fractions are as follows. Proper fractions, improper fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorize its kinds based on these two parameters.

Tony walked 7/10 km which in decimal will be 0.7 km

Volet spent 0.5 hrs reading a pocket which in Fraction will be 5/10 = 1/2

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The value of x in the given inequality is x ≥ 4

A relationship between two expressions or values that are not equal to each other is called inequality.

Given is an inequality, 3x−3 ≥ 9​

Solving for x,

3x−3 ≥ 9​

Adding 3 both the side,

3x -3 + 3 ≥ 9 + 3

3x ≥ 12

Diving both sides by 3,

3x / 3 ≥ 12 / 3

x ≥ 4

Hence, the value of x in the given inequality is x ≥ 4

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The three-dimensional object formed when the shape is rotated about the axis is a hollow cylinder.

This object is generated by taking a vertical rectangle and rotating it around the vertical axis. Mathematically, this can be described as a revolution of the rectangle about the y-axis in which the points of the rectangle are shifted a certain distance away from the axis. The three-dimensional object formed when the shape is rotated about the axis is a hollow cylinder.The formula used to calculate the volume of a hollow cylinder is V = π(r^2)h, where r is the radius of the cylinder, and h is the height. For example, if we have a cylinder with radius 4 and height 8, the volume would be V = π(4^2)8 = 128π cubic units.

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Answer:

36 chocolate bars and 25 yogurt cups were sold

Step-by-step explanation:

c= # of choc. bars sold = y + 11

y = # of yogurt cups sold

3(y + 11) + 5y = $233

3y + 33 + 5y = 233

8y = 200

y = 200/8 = 26

c = y + 11 = 25 + 11 = 36

The steel container meet the standard for stainless steel because it contains 12.5% of chromium.

An equation is an expression showing the relationship between numbers and variables.

Stainless steel contains at least 10.5% chromium.

We need to determine if a steel container  that weighs 40 grams contains 5 grams of chromium is stainless steel.

Therefore:

Percentage of chromium in the steel container = (5 grams / 40 grams) * 100% = 12.5%

12.5% > 10.5%, hence the steel container meet the standard for stainless steel

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Step-by-step explanation:

The vertical extent of the graph is all range values 3 and -2, so the range is (−2,3]

The value of (hg)(x) would be  4x.

What is the function?

A function is a mathematical relationship between a set of inputs (also known as domain) and a set of possible outputs (also known as range). The inputs are usually represented by variables, such as 'x' in the examples you provided. The outputs are usually represented by expressions, such as 'x² - 8x + 4' in the example f(x) = x² - 8x + 4.

(hg)(x) is the composition of two functions h(x) and g(x). In this case, it would be equivalent to h(g(x)), which means to first apply the function g(x) to the input x, then apply the function h(x) to the output of g(x).

(hg)(x) = h(g(x)) = h(4x - 3) = (4x - 3) + 2 = 4x.

Hence, the value of (hg)(x) would be  4x.

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Schools, churches, and corporations are examples of Secondary Groups.

What does a secondary formal group mean?

A secondary group is a comparatively larger group made up of impersonal, purpose-driven, and frequently transient interactions.

                                  These groups typically involve significantly less emotional engagement and are built around reaching a goal that is unrelated to the relationship itself.

What do main and secondary social institutions entail?

Small and distinguished by long-lasting, close-knit ties, primary groups are common. Non-personal, ad hoc, and goal-driven interactions are examples of secondary groupings.

                             An exchange of implicit goods, such as love, care, concern, support, etc., is what constitutes a primary group. Family units, romantic partnerships, crisis support networks, and religious organizations are a few examples of these.

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Answer:

  (x, y) = (1120, 700)

Step-by-step explanation:

You want the number of discount (x) and premium (y) tickets to be sold so that a total of 1820 tickets are sold for $40 and $45, respectively, and they generate revenue of $76,300.

The equations reflect the relationships stated in the problem:

  x + y = 1820 . . . . . . the total number of tickets sold is 1820

  40x +45y = 76,300 . . . . . total sales must be $76,300

It usually works well to substitute for the variable representing the lower-price tickets:

  40(1820 -y) +45y = 76300 . . . . . . substitute for x using the first equation

  5y = 3500 . . . . . . . . . . . . . . subtract 72800, simplify

  y = 700 . . . . . . . . . . . . divide by 5

  x = 1820 -700 = 1120

The numbers of tickets of each type sold are (x, y) = (1120, 700).

According to the given statement,  The value of x = -5 / 36.

The x variable is ubiquitous in math and stands for an unknown. It doesn't always have to be an x - any letter of our alphabet can represent an unknown. To work with variables, the first step is to identify the unknown and label it. Next is writing an equation you can solve to find the unknown.

Given: f(x) = x-1 /5

g(x) = 2x + 7

Solving for g(x) = ƒ(x),

2x + 7 = x-1 /5

10x + 35 = 5x - 1

5x = -36

x = -36 / 5

Hence, the value of x for g(x) = ƒ−¹(x) is x = -5 / 36.

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