If "n is the positive integer, then n is even if and only if 7n + 4 will be even" is true.
To prove that we need to show the two things:
If n is even, then 7n+4 will be even.
If 7n + 4 is even, then n will be even.
Proof: Suppose that n is even. Then they exists an integer k such that n =2k. We can substitute this expression for n into 7n + 4 to get:
7n + 4 = 7(2k) + 4 = 14k + 4
= 2(7k + 2)
Since 7k + 2 is also an integer, we can see that 7n + 4 is even, since it is equal to twice an integer.
Now suppose that 7n + 4 is even. Then there exists an integer m such that 7n + 4 = 2m. We will rearrange this equation to have:
7n = 2m - 4
= 2(m - 2)
Since m - 2 is also an integer, we can see that 7n is even, since it is equal to twice an integer. Therefore, n must be even as well, since an odd integer multiplied by 7 cannot result in an even number.
Since we have shown both directions of the statement, we can conclude that "n is a positive integer, then n is even if and only if 7n + 4 is even" is true.
To know more about positive integer here
https://brainly.com/question/26051073
#SPJ4
On its own 2c is a product with
We deduced the following from the given phrase:
1) The supplied expression is a sum with the four terms a, b, l, and c.
2) 2c is the result of the factors 2 and c on its own.
Describe a function?A function is a relationship between a number of inputs and outputs. Simply described, a function is an association between inputs in which each input is coupled to exactly one output. For each function, there is a corresponding range, codomain, and domain.
What follows is:
A + (b+1) + 2c is the function that has been discovered and written in the question.
As we can see, three distinct terms—a, b+1, and 2c—have been demonstrated to be a part of this function.
As a result, we deduced the following from the above formula:
1) With the four terms a, b, 1 and 2c, the complete equation is a sum.
2) 2c is the result of the factors 2 and c on its own.
To learn more about function, visit:
https://brainly.com/question/22340031
#SPJ1
The complete question is:
On its own 2c is a product with
Write
tanz
in terms of
secz
using the Pythagorean Identity for: Part: 0 / 2 Part 1 of 2 (a)
z
in Quadrant II.
tanz=
Part:
1/2
Part 2 of 2 (b)
z
in Quadrant IV.
We can write tanz in terms of secz using the Pythagorean Identity as:
tanz = -sqrt(sec^2z - 1)
Part 1 of 2:
The Pythagorean Identity states that sin^2z + cos^2z = 1. We can use this identity to write tan^2z in terms of sec^2z.
First, let's rearrange the Pythagorean Identity to isolate cos^2z:
cos^2z = 1 - sin^2z
Next, we can divide both sides of the equation by cos^2z to get:
1 = sec^2z - (sin^2z)/(cos^2z)
Since tan^2z = (sin^2z)/(cos^2z), we can substitute this into the equation:
1 = sec^2z - tan^2z
Finally, we can rearrange the equation to isolate tan^2z:
tan^2z = sec^2z - 1
Now, let's consider the case when z is in Quadrant II. In this quadrant, tanz is negative and secz is negative. Therefore, we can write:
tanz = -sqrt(sec^2z - 1)
Part 2 of 2:
In the case when z is in Quadrant IV, tanz is negative and secz is positive. Therefore, we can write:
tanz = -sqrt(sec^2z - 1)
So, in both cases, we can write tanz in terms of secz using the Pythagorean Identity as:
tanz = -sqrt(sec^2z - 1)
Learn more about Pythagorean
brainly.com/question/24252852
#SPJ11
y = f(x) if f”(x) = 6x-2. f’(0) =3, f(0) 7
a) f(x) = x^3 -x^2 + 3x +7
b) f(x) = x^3 - x^2
c) f(x) = 0
d) f(x) = x^3 - x^2 + 3x
a) f(x) = x^3 -x^2 + 3x +7 is the correct answer
the perimeter of a rectangular window is 654 inches if the length of the window is 205 inches what is the width of the window?
Answer:
The width of the window is 122 inches
Step-by-step explanation:
654- known two sides(410) =244
divide 244/2, to get both unknown sides of the rectangular window, 122 inches
A loaf of bread weighs about 1 pound. Choose all of the metric measures that are less than 1 pound
As one loaf of bread weighs about 1 pound, the metric measures that are less than 1 pound are:
450g100gIn which system is pound is the unit of weight?The pound means the unit of measurement used in the U. S. customary system and the British imperial system to measure weight. One familiar use of pounds is measuring how much a person weighs.
A pound is approximately 0.4535 kilogrammes, so 453.5 grammes. With this information, we can determine that answers 450 grammes and 100 grammes are the only correct ones because they are lesser than 453.5 grammes.
Full question "A loaf of bread weighs about 1pound. Chose all of the metric measures that are less than 1pound. 1kg 0.5kg 500g 450g 100g"
Read more about Pounds
brainly.com/question/28571689
#SPJ1
What is the slope of the line shown below? slope =
sloperise/run
Answer:
m= 3/4
Step-by-step explanation:
hope this helps
I need help with this question! I'll give 20 points!
Answer:
Step-by-step explanation:multiply x by y to the power of 67000 and then you will get 730000000.
A circle has 36 pi square meters what is the circumference of this circle
Answer: 18cm
Step-by-step explanation:
The length of the radius of the circle with center O has a circumference of 36π is 18cm.
A toymaker is creating a toy that has different gears. He needs to determine how far the center of each gear is from the knob, so he can connect wire to those points inside the toy. Here's what he knows: The distance between the center of a metal gear and a plastic gear is 14 inches. The distance between the center of the metal gear and a wooden gear is 10 inches. All radii are even whole numbers, and all are greater than 2 inches. No two gears are the same size. He has labeled distances between the knob & points of tangency to the gears in his diagram. You can help him decide which gear is made of which material. ● ● ● 1. Now help him find the distance from the knob to the center of each gear! Show all of your work. Use the page below for workspace as needed. Distance from knob to... Metal gear: Plastic gear: Wooden gear:
The use of gears enables the exchange of torque for angular velocity (i.e., if the gears are of unequal size, the larger gear will experience higher torque but lower angular velocity than the smaller gear).
What is system?Any organized assembly of resources and procedures united and regulated by interaction or interdependence to accomplish a set of specific functions.
here, we have,
Two gears or pulleys must rotate at the same angular velocity if they are attached to the same axle.
Since the angle doesn't change the unit in any way, the work unit is also in ft-lbs. The rotating equivalent of a formula you might remember from physics is "Work = Force * Distance."
Energy is preserved in a gear train if friction-related heat losses are disregarded.
A gear ratio is the comparison of the number of rotations made by the driving gear system and the driven gear.
Learn more about system here-
brainly.com/question/27162243
#SPJ1
11. The distance round a circular hut is 17.6 m. What is the area of its floor?
12.A string measures 220 cm. Its two ends are joined to form a circle. What area
does the string enclose?
13. The area of a circular mat is 1.54 m². What is its circumference?
11. The area of the floor is 24. 62 m²
12. The area of the enclosed string is 3, 853. 09cm²
13. The circumference of the circular mat is 4.39m
How to determine the areaThe formula for the area of a circle is expressed with the equation;
A = πr²
Where;
A is the area.π takes the value 3.14r is the radius of the circle.Also, circumference of a circle is 2πr
For a circumference of 17. 6m, we have
17. 6 = 2×3.14r
r = 2. 80
Substitute the value
Area = 3.14 × (2. 80)²
Area = 24. 62 m²
For the string, circumference = 220cm
220 = 2× 31.4r
r = 35. 03 cm
Area of the enclosed string = 3.14 × (35. 03)²
Area = 3, 853. 09cm²
For the circular mat
1.54 = 3.14r²
r² = 0. 49
Take the square root
r = 0. 7m
Circumference = 2× 3.14 × 0. 7 = 4.39m
Learn about circles at: https://brainly.com/question/14283575
#SPJ1
Sarah was explaining her first step factoring, but made an error in her explanation.
Factor: 5x^2-4x-9
Sarah said, “I know that a=5, b=-4, and c=-9. Now, I need to find factors of -9 that add to -4.”
Explain the error in Sarah’s thought process.
The expression cannot be factored over integers since the roots are not integers.
The error in Sarah's thought process is that she is assuming that the factoring of a quadratic equation can always be done by finding two numbers that add up to the coefficient of the middle term (in this case, -4) and multiply to the coefficient of the quadratic term (in this case, 5). However, this method only works when the quadratic expression is factorable over the integers, which is not always the case.
In fact, the expression [tex]5x^2-4x-9[/tex] cannot be factored over the integers, which means that there are no two integers whose product is [tex]5*(-9)=-45[/tex] and whose sum is -4. To confirm this, we can use the quadratic formula (-b ± \sqrt{(b^2-4ac)} )/2a, which gives the roots of the quadratic equation [tex]ax^2+bx+c=0[/tex]. For this expression, [tex]a=5, b=-4[/tex], and c=-9, so the roots are:
[tex]x=[-(-4)±sqrt{(-4)^2-45(-9)}]/(2*5\leq)[/tex]
[tex]x=(4±sqrt(196))/10\\x=(4±14)/10\\x=1 or x=-9/5[/tex]
Since the roots are not integers, the expression cannot be factored over the integers.
To learn more about factors visit;
https://brainly.com/question/14549998
#SPJ1
A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large boxes. Each small box has 10 granola bars and each large box has 30 granola bars. The camp bought a total of 6 boxes that have 100 granola bars altogether. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
There will be 4 small boxes and 2 large boxes of granola bars.
What are variables?A variable is an attribute or a phenomenon that can be measured and has a changing value over time.
Given,
Number of granola bars in the small box = 10
Number of granola bars in the large box = 30
The number of small boxes = three times the number of a large boxes
To Find,
The number of small boxes purchased =?
The number of large boxed purchased =?
Let the number of large boxes be y
The number of small boxes be x
Total number of boxes, x + y = 6 ..... equation i
Total number of granola bars in small box = 10x
Total number of granola bars in large box = 30x
So, 10x + 30x = 100
After dividing by 10 we get
x + 3y = 10 ..... equation ii
Subtracting equation ii from equation i
We get, 2y = 4
y = 2
Putting the value of y in equation i we get x = 4
So, there will be 4 small boxes and 2 large boxes of granola bars.
Learn more about variables on:
https://brainly.com/question/2466865
#SPJ1
-3y=2x-7
graphing linear equations in 2 variables
By solving the given equation, we can plot these two points on a coordinate plane, and then connect the points with a line. The formed line is the graph of the linear equation 3y=2x-7.
What is a coordinate plane?The coordinate plane is made up of two perpendicular lines called the x-axis and the y-axis. The x-axis, which is horizontal, is used to measure the distance of a point from the left and right side of the plane. The y-axis, which is vertical, is used to measure the distance of a point from the top and bottom of the plane.
To graph the equation 3y=2x-7, we first need to identify two points that satisfy the equation. We can do this by plugging in different values for x and solving for y. For example, when x=0, the equation becomes 3y=-7. Thus, one point that satisfies the equation is (0,-7). We can find a second point by plugging in a different value for x. For example, when x=2, the equation becomes 3y=-3. Thus, the second point that satisfies the equation is (2,-3).
Now, we can plot these two points on a coordinate plane, and then connect the points with a line. The formed line is the graph of the linear equation 3y=2x-7.
For more questions related to linear equation,
https://brainly.com/question/11897796
#SPJ1
Create a number sequence with 5 terms involving fractions with a common difference of 1/3 from one term to the next starting from 1/3
Answer:This free number sequence calculator can determine the terms (as well as the sum of all terms) of the arithmetic, geometric, or Fibonacci sequence.
Step-by-step explanation:
1. Show that the seriesn=1∑[infinity](−1)n−1(3n+5)3ln(n+2)+31is convergent, and determine how many terms of the series we need to add to find the sum within0.05. Is this series absolutely convergent? Justify your answer. 2. Determine whether the seriesn=1∑[infinity](−1)n−13n+4ln(5n+2)is absolutely convergent, conditionally convergent or divergent.
The series converges.
1. This is an alternating series, and therefore, the series converges by the Alternating Series Test. This is because the sequence of the absolute value of the terms, {|3n+5|}^(1/3), is a monotonically decreasing sequence, and it is bounded. To determine how many terms are necessary to get within 0.05 of the sum, we use the formula:
Sn≈s[infinity]+a1r1/1−r
where a1 is the first term, and r is the common ratio. In this case, we have a1 = (3+5)^(1/3) = 2, and r = (-1)^(1/3) = -1. Thus, Sn ≈ 2 + (2)(-1)/1 - (-1) = 4.
Since the series is alternating, it is absolutely convergent.
2. This series is also an alternating series, so it is absolutely convergent by the Alternating Series Test. The sequence of the absolute value of the terms, {|3n+4|}^(1/ln(5n+2)), is a monotonically decreasing sequence, and it is bounded. Therefore, the series converges.
Learn more about absolute value
brainly.com/question/1301718
#SPJ11
PLEASE HURRY IM FAILING
Answer:
A. 3/2
Step-by-step explanation:
what is a dilation? a dilation can make objects bigger or smaller.
10 times [tex]\frac{3}{2}[/tex] is 15
4 times [tex]\frac{3}{2}[/tex] is 6
8 times [tex]\frac{3}{2}[/tex] is 12
therefore the answer is A.. [tex]\frac{3}{2}[/tex]
Answer:
A. 3/2
Step-by-step explanation:
What is dilation?
The original image is DEFG. It is called the pre-image
The dilated image is D'E'F'G' and is called image
A transformed image has the coordinates labeled with a '
In this case the transformed image is a dilation of the original pre-image. A dilated image is a cop.y of the pre-image but with either an expansion or a compression
If the image is larger than the pre-image it is an expansion, if smaller than the pre-image then it is a compression
With dilation, comes a scale factor which indicates how much a pre-image has been expanded or compressed
Solution
If you look at the two images, take any side in the pre-image and compare its length with the corresponding side you can find the scale factor
Here if you take a side, say DE = 4 and look at the corresponding side D'E' = 6you see that the DE side has been expanded with a scale factor of 6/4 = 3/2
This scale factor applies to all sides, so you need to take only one side to find the scale factor
Answer: Scale Factor of dilation = 3/2
This is option A
McKenzie and Lindy work on a landscaping crew. They can complete the landscaping job in 4 hours if they work together. McKenzie generally takes 6 hours less Lindy. How long would it take McKenzie to complete the landscaping job if Lindy calls in sick?
McKenzie would take 6 hours to complete the landscaping job alone if Lindy calls in sick.
If McKenzie and Lindy can complete the landscaping job in 4 hours working together, it means their combined work rate is 1/4 of the job per hour. Let x be the number of hours it takes Lindy to complete the job alone, then McKenzie can complete the job in x-6 hours.
Using the formula for their individual work rates, we have:
[tex]1/x + 1/(x-6) = 1/4[/tex]
Multiplying both sides by [tex]4x(x-6)[/tex], we get:
[tex]4(x-6) + 4x = x(x-6)[/tex]
Expanding and simplifying, we get:
[tex]2x^2 - 12x - 48 = 0[/tex]
Dividing both sides by 2 and using the quadratic formula, we get:
[tex]x = (12 ± \sqrt{12^2 + 4248}) / (2*2)[/tex]
x = (12 ± 18) / 4
x = 7.5 or -1.5
Since we cannot have a negative time, the answer is that it would take Lindy 7.5 hours to complete the job alone, and McKenzie would take 1.5 hours less, or 6 hours, to complete the job alone if Lindy calls in sick.
Therefore, McKenzie would take 6 hours to complete the landscaping job alone if Lindy calls in sick.
For more questions like Functions visit the link below:
https://brainly.com/question/26535687
#SPJ11
The volume of a cylinder is 180 pi cubic inches and the radius of the cylinder is 3 inches. what is the height of the cylinder 
Using the formula of the cylinder we know that the height of the given cylinder is 6.36 inches.
What is a cylinder?One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid.
It is regarded as a prism with a circle as its base in basic geometry.
In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.
So, the cylinder formula for the volume is:
V = πr²h
Now, substitute the values as follows:
V = πr²h
180 = 3.14*3²h
180 = 28.26h
180/28.26 = h
6.36 = h
Therefore, using the formula of the cylinder we know that the height of the given cylinder is 6.36 inches.
Know more about cylinders here:
https://brainly.com/question/23935577
#SPJ9
Find the equation of the line through the point (3,-7) that is parallel to the line 4x + 7y - 10 = 0. Write the answer in the point-slope form y - y1 = m(x – x1).
The equation of the line through the point (3, -7) that is parallel to the line 4x + 7y - 10 = 0 is y = (-4/7)x - (37/7) in the point-slope form
To find the equation of the line through the point (3, -7) that is parallel to the line 4x + 7y - 10 = 0, we first need to find the slope of the given line. We can do this by rearranging the equation to the slope-intercept form, y = mx + b, where m is the slope.
4x + 7y - 10 = 0
7y = -4x + 10
y = (-4/7)x + (10/7)
The slope of the given line is -4/7. Since we want a line that is parallel to this one, the slope of our new line will also be -4/7.
Now we can use the point-slope form of a line, y - y1 = m(x - x1), to write the equation of the new line. We plug in the given point (3, -7) for (x1, y1) and the slope -4/7 for m.
y - (-7) = (-4/7)(x - 3)
y + 7 = (-4/7)x + (12/7)
y = (-4/7)x + (12/7) - 7
y = (-4/7)x - (37/7)
So the equation of the line through the point (3, -7) that is parallel to the line 4x + 7y - 10 = 0 is y = (-4/7)x - (37/7) in the point-slope form.
Know more about slope-intercept here:
https://brainly.com/question/4015585
#SPJ11
Write the slope-intercept equation of the function f whose graph satisifies the given conditions.
The graph of f passes through (-9,-3) and is perpendicular to the line whose equation is x=-3
This is a horizontal line passing through the point (-9, -3).
What is Slope?Slope is a measure of how steep a line is. It is defined as the ratio of the change in the y-coordinates of two points on a line to the change in the x-coordinates of those same points. In other words, slope is the amount by which the y-coordinate changes when the x-coordinate changes by 1 unit.
Since the given line is vertical, its slope is undefined. The slope of a line perpendicular to it is zero. Therefore, the slope of the graph of f is zero.
We can use the point-slope form of a linear equation to write the equation of the line passing through the point (-9, -3) with a slope of zero:
y - (-3) = 0(x - (-9))
Simplifying, we get:
y + 3 = 0
Subtracting 3 from both sides, we get:
y = -3
So the equation of the function f is:
f(x) = -3
Therefore, this is a horizontal line passing through the point (-9, -3).
To know more about Slope visit:
https://brainly.com/question/16949303
#SPJ1
Which equation best represents the relationship between x and y in the graph?
Ay = 3x - 2
- ¹x +3
-8-7-6-5
9
8
-7
6
S
-1
-2
-3
4
-5
-6
-7
-8
-9
4 5 6 7 8
X
An equation that best represents the relationship between x and y in the graph is: A. y = -3x/4 - 3.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At point (-4, 0), an equation of this line can be calculated by using the point-slope form:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 0 = (-3 - 0)/(0 + 4)(x + 4)
y - 0 = -3/4(x + 4)
y = -3x/4 - 3.
Read more on equation here: https://brainly.com/question/14774311
#SPJ1
Linier ALgebra : Let W E R^nxn, s E R, and λ an eigenvalue of W. Prove that λ – s is an eigenvalue of W – sλ. (As usual, I = Inxn denotes the n x n identity matrix.)
$\lambda - s$ is an eigenvalue of W – s$\lambda$ and $\mathbf{v}$ is the corresponding eigenvector.
Linear Algebra: Let W $\in$ $\mathbb{R}^{n \times n}$, s $\in$ $\mathbb{R}$, and $\lambda$ an eigenvalue of W. To prove that $\lambda$ – s is an eigenvalue of W – s$\lambda$, we will use the definition of eigenvalues and eigenvectors:
An eigenvalue $\lambda$ of a square matrix A $\in$ $\mathbb{R}^{n \times n}$ is a scalar such that there exists a nonzero vector $\mathbf{v} \in \mathbb{R}^n$ for which the following equation holds:
A$\mathbf{v}$ = $\lambda \mathbf{v}$
Therefore, we can rearrange the equation to show that W – s$\lambda$ $\mathbf{v}$ = $(\lambda -s) \mathbf{v}$, which implies that $\lambda - s$ is an eigenvalue of W – s$\lambda$ and $\mathbf{v}$ is the corresponding eigenvector.
Learn more about eigenvalues and eigenvectors:
brainly.com/question/29658558
#SPJ11
The cafeteria needs 815 onions. There are 8 onions in each bag. How many bags should the cafeteria buy?
815 ÷ 8 = 101.875 ≈ 102
∴ The cafeteria should buy 102 bags.
Answer:
102 bags.
Step-by-step explanation:
You divided 815 by 8. The answer is 101.875 and you can't have half a bag so you round it up to the nearest whole number.
There are 6 people in a group. Their names are selected randomly and they act independently. a) Calculate probability that the first person arriving has the same name as 1 or more people. b) Calculate probability that there are people in the group with a same name.
There are 6 people in a group. Their names are selected randomly and they act independently. The probability that the first person arriving has the same name as 1 or more people is 0. The probability that there are people in the group with the same name is 98.46%.
The probability that the initial arrival shares a name with one or more others is 0 percent. This is because the first person arriving has no one to compare their name with, so there is no chance that they will have the same name as someone else.
The probability that there are people in the group with the same name can be calculated using the formula
P(same name) = 1 - P(different names).
The probability of everyone having different names is calculated by multiplying the probabilities of each person having a different name from the previous person. This can be represented as
(6/6) * (5/6) * (4/6) * (3/6) * (2/6) * (1/6) = 0.0154.
Therefore, the probability of there being people in the group with the same name is 1 - 0.0154 = 0.9846 or 98.46%.
Learn more about probability at https://brainly.com/question/15584918
#SPJ11
3x+4y=36 find y and x
Answer:
y = 36
x = 12
Hope it helps!
List in order from least to greatest.
Answer:
56%, 4/5, 1.07, 5/4
Step-by-step explanation:
5/4=1.25
56%=0.56
1.07
4/5=0.8
so the order is
56%, 4/5, 1.07, 5/4
What is the true solution to the equation below? ln e^lnx + on e ^lnx2 = 2 on 8
After solving the given equation In [tex]e^{lnx} +[/tex] in [tex]e ^{lnx2}[/tex] = 2 in 8, we know that the value of x is (B) 4.
What are equations?The equals sign is a mathematical symbol that indicates that two expressions in a formula are equal.
A mathematical statement known as an equation is one that uses the word "equal to" between two expressions with the same value.
As in 3x + 5 = 15, for example.
Equations can be of many different types, such as linear, quadratic, cubic, and others.
So, we have the equation:
[tex]Ine^{inx} + Ine^{Inx2}[/tex] [tex]= 2In8,[/tex]
Now, solve the following equation as follows:
[tex]Inx * Ine +Inx^2 * Ine = 2In8[/tex]
[tex]e^{Inx}+Ine^{Inx2} = 2in8[/tex]
[tex]Inx+Inx^2 = In8^2[/tex]
[tex]In* (x*x^2) In64[/tex]
[tex]x^2 = 64 =4^3[/tex]
[tex]x=4[/tex]
Therefore, after solving the given equation In [tex]e^{lnx }[/tex] + in[tex]e ^{lnx2}[/tex] = 2in8, we know that the value of x is (B) 4.
Know more about equations here:
brainly.com/question/22688504
#SPJ1
Correct question:
What is the true solution to the equation below? In [tex]e^{lnx}[/tex]+ in [tex]e ^{lnx2}[/tex] = 2 in 8
a x = 2
b x = 4
c x = 8
d x = 64
Train wheels are designed to slope inward toward the track to keep the train stable as it goes around curves. However, as the slope of the wheels increases, it becomes less efficient at producing speed. How might making changes in the slope of a train's wheels affect the train overall?
There is a trade-off between stability and speed when it comes to the slope of a train's wheels.
What is slope ?
Slope is a measure of the steepness of a line or a surface. In mathematics, slope is often represented by the letter "m" and is calculated as the change in the vertical direction (y-axis) divided by the change in the horizontal direction (x-axis) between two points on the line or surface.
Changing the slope of a train's wheels can have both positive and negative effects on the train's overall performance.
On the positive side, increasing the slope of the wheels can improve the train's stability and safety as it goes around curves. This is because the inward slope of the wheels helps to counteract the centrifugal force that pushes the train outward as it goes around curves. By increasing the slope of the wheels, this counteracting force can be increased, which can help prevent derailments and improve the overall safety of the train.
On the negative side, increasing the slope of the wheels can decrease the train's efficiency at producing speed. This is because the slope of the wheels creates additional friction between the wheels and the track, which can slow the train down and require more energy to maintain speed. As the slope of the wheels increases, this friction also increases, which can make the train less efficient at producing speed and more costly to operate.
Therefore, there is a trade-off between stability and speed when it comes to the slope of a train's wheels. Train designers must find the optimal balance between these two factors to ensure that the train is both stable and efficient.
To learn more about Slope from given link.
https://brainly.com/question/3605446
#SPJ1
When given a problem such as (5 + 3i)(7 – 4i), what are 2 important processes to remember to simplify your answer?
To simplify the expression (5 + 3i)(7 – 4i), two important processes to remember are to use the distributive property to multiply the real parts and imaginary parts separately and simplify the resulting expression by combining any like terms.
Use the distributive property:
For the expression (5 + 3i)(7 – 4i),
(5 + 3i)(7 – 4i) = 5(7) + 5(-4i) + 3i(7) + 3i(-4i)
= 35 - 20i + 21i - 12i^2
Note that i^2 = -1,
35 + i(21 - 20) - 12(-1) = 47 + i(41)
Simplify the resulting expression:
After using the distributive property to expand the expression, we can simplify the resulting expression by combining any like terms. In this case, there are no like terms to combine, so our final answer is:
(5 + 3i)(7 – 4i) = 47 + 41i
To learn more about distributive property follow the link: brainly.com/question/5637942
#SPJ4
There are 5 yellow, 4 green and 3 black balls in a bag. All the 12 balls are drawn one by one and arranged in
a row. Find out the number of different arrangements possible.
There are 27720 different arrangements possible.
The number of different arrangements possible can be found using the formula for permutations with repetition:
n! / ([tex]p{1}[/tex]! * [tex]p{2}[/tex]! * ... *[tex]p_{k}[/tex]!)
where n is the total number of items, and [tex]p{1}[/tex], p2, ..., pk are the number of times each item is repeated.
In this case, n = 12 (the total number of balls), [tex]p{1}[/tex] = 5 (the number of yellow balls), [tex]p{2}[/tex] = 4 (the number of green balls), and [tex]p{3}[/tex] = 3 (the number of black balls).
So the number of different arrangements possible is:
12! / (5! * 4! * 3!)
= 479001600 / (120 * 24 * 6)
= 27720
Therefore, number of different arrangements possibleis 27720.
You can learn more about different arrangements possible at
https://brainly.com/question/2396043
#SPJ11