dV/dt = -1.4t³ is differential equation that describe the relationship.
The differential equation dV/dt = kV³ where k is the constant will forecast the rate of change of volume.
We know that a tank's water leak causes its volume to fluctuate at a pace that is proportional to its cube as time passes.
The tank is leaking the volume. Therefore, the rate might be expressed negatively.
The rate of change of volume can be expressed as follows: dV/dt is proportional to V³ that is dV/dt = kV³ for the specified conditions.
The proportionality constant in this case is k. By employing the boundary conditions, its value can be determined.
Therefore, dV/dt=kV³ where k is the constant will be the differential equation predicting the rate of change of volume.
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Let F be a differentiable function such that f(-1)= -6 and f'(x)=4x-1. What is the approximation for f(-1.2) found by using the line tangent to the graph of f at x= -1?
The tangent line approximation for f(-1.2) is defined as follows:
f(-1.2) = -5.
How to obtain the equation of the tangent line?The point-slope format for the equation of the tangent line is given as follows:
y - y* = m(x - x*).
In which the parameters are given as follows:
(x*, y*) are the coordinates of the point.m is the slope of the linear function, representing the numeric value of the derivative at point (x*, y*).The derivative for this problem is given as follows:
f'(x) = 4x - 1.
f(-1)= -6, hence the coordinates of the point are given as follows:
x* = -1, y* = -6.
Hence the slope is given as follows:
m = f'(-1).
m = 4(-1) - 1
m = -5.
Thus the tangent line is defined as follows:
y + 6 = -5(x + 1).
y = -5(x + 1) - 6.
At x = -1.2, the approximation is calculated as follows:
y = -5(-1.2 + 1) - 6
y = -5.
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Vanessa purchased a used car on a payment plan. Four months after purchasing the car, the balance was $1,200. Seven months after purchasing the car, the balance was $975.
Write an equation that models the balance y after t months.
y=___t+___
The linear function that models the balance after t months is given as follows:
y = -75t + 1500.
How to define the linear function?The linear function for this problem is defined in slope-intercept format, as follows:
y = mx + b.
In which the coefficients of the function are given as follows:
m is the slope, representing the rate of change in the balance each month.b is the y-intercept, representing the initial balance.Four months after purchasing the car, the balance was $1,200. Seven months after purchasing the car, the balance was $975, hence two points of the function are given as follows:
(4, 1200) and (7, 975).
Given two points, the slope is calculated as the change in the output divided by the change in the input, hence:
m = (975 - 1200)/(7 - 4)
m = -75.
Hence:
y = -75t + b.
When t = 4, y = 1200, hence the intercept b is calculated as follows:
1200 = -75(4) + b
b = 1200 + 75 x 4
b = 1500.
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2 - 1 x 99 - 5 + 2 - 4 -5 x 5 divided by 3 x 8
Answer:
1,160
Step-by-step explanation:
Okay im learning algebra right now and this question hit my head here, its asked which expression was equivalent to this 2v+6v+3c. here are the answer 2v + 9c / 8v + 3c / 11vc / 11+ v+ c
Answer:
8v+3c
Step-by-step explanation:
Given 2v+6v+3c
1) Add all like terms
-Since both 2 and 6 have "v" and the two together
2) 8v+3c
Answer: 8v+3c
Hope this helps :)
Leon's annual premium is x
dollars. If he pays his
premium semi-annually,
there is a y-dollar surcharge
on each semi-annual
payment. Express the
amount of his semi-annual
payment algebraically.
The algebraic expression for the payment of the plan with y dollar surge is A = x/2 + y.
What are algebraic expressions?The concept of algebraic expressions is the use of letters or alphabets to represent numerical values without stating their exact meanings. The fundamentals of algebra taught us how to express an unknown value using letters like x, y, and z. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
Given that the annual premium plan is x dollars.
The payment is made semi-annually this is represented as follows:
x/2
There is a surplus charge of y, this is written as:
A = x/2 + y
Hence, the algebraic expression for the payment is A = x/2 + y.
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What are the three credit reporting agencies you would possibly need to contact to report an error on your credit report?
Answer:
Experian, Equifax, and/or Transunion
Step-by-step explanation:
None
Triangle 1 has vertices at (A, B), (C, D), and (E, F).
Triangle 2 has vertices at (-A, B), (-C, D), and (-E, F).
What can you conclude about triangle 2?
A) Triangle 2 is congruent to
triangle 1 because a translation
is a rigid motion.
B) You cannot tell because you do
not know where the points are in
the plane.
C)Triangle 2 is not congruent to
triangle 1 because a dilation is
not a rigid motion.
D)Triangle 2 is congruent to
triangle 1 because a reflection is
a rigid motion.
Triangle 1 and triangle 2 are concurrent if, Triangle 1 has vertices at (A, B), (C, D), and (E, F), Triangle 2 has vertices at (-A, B), (-C, D), and (-E, F) and are reflected so, option D is correct.
What is triangle?Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol and consists of three connected vertices.
Given:
Triangle 1 has vertices at (A, B), (C, D), and (E, F),
Triangle 2 has vertices at (-A, B), (-C, D), and (-E, F).
Triangle 1 is reflected on the y-axis and we get triangle 2,
Both, triangle 1 have the same magnitude of dimension as triangle 2,
Thus, both are concurrent also.
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Answer: D is the correct answer
Step-by-step explanation:
imagine math
600 people attended a concert. 20% are men , 35% are women , and the rest are children. find the number of men, women and children.
Answer: men: 120 men, 310 women, and 170 children
600*0.2=120
600*0.35=310
600-120-310=170
find the general solution of the homogeneous differential equation (x^2-y^2)dx+(3xy)dy=0
The equation for a homogeneous differential in its general solution.
= (x² + 4y²)³x² = c.
What does the phrase "homogeneous differential equation" mean?When both f(x,y) and g(x,y) have the same degree, a differential equation of the form f(x,y)dy = g(x,y)dx is referred to as a homogeneous differential equation. For k 0, a function of the type F(x,y) that can be expressed in the form kn F(x,y) is referred to as a homogeneous function with degree n.
The name "homogeneous differential equation" is for what?If M(x,y) and N(x,y) are both homogeneous functions that have the same degree, then a first-order differential equation is said to be homogeneous. is homogeneous since it contains homogeneous functions that have the same degree, M(x,y) = x 2 - y 2, and N(x,y) = xy (namely, 2).
According to the given information:[tex]$\mathrm{v}+\mathrm{x} \frac{\mathrm{dv}}{\mathrm{dx}}=-\left(\frac{\mathrm{x}^2+\mathrm{v}^2 \mathrm{x}^2}{3 \mathrm{xv} \mathrm{x}}\right)=-\left(\frac{\mathrm{x}^2\left(1+\mathrm{v}^2\right)}{3 \mathrm{x}^2 \mathrm{v}}\right)$[/tex]
[tex]$v+x \frac{d v}{d x}=-\left(\frac{1+v^2}{3 v}\right)$[/tex]
[tex]$x \frac{d v}{d x}=\frac{-1-v^2}{3 v}-v=\frac{-1-v^2-3 v^2}{3 v}=\frac{-1-4 v^2}{3 v}$[/tex]
[tex]$\frac{3}{8} \int \frac{8 v}{1+4 v^2} d v=-\int \frac{d x}{x}$[/tex]
Integrating we have [tex]$\frac{3}{8} \log \left(1+4 v^2\right)=-\log x+\log c$[/tex]
= 3log(1 + 4v²) + 8 log x = log c
= (1 + 4v²)³.x⁸ = c
= [tex]$\left(1+4 \frac{y^2}{x^2}\right)^3 \cdot x^8=c$[/tex]
= (x² + 4y²)³x² = c.
the general solution of the homogeneous differential equation.
= (x² + 4y²)³x² = c.
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Consider the following equation. − 16 p + 37 = 49 − 21 p Select the equation that has the same solution as the given equation. A. − 14 + 6 p = − 9 − 6 p B. 2 + 1.25 p = − 3.75 p + 10 C. 3 2 p − 5 + 9 4 p = 7 − 5 4 p D. − 55 + 12 p = 5 p + 16
The equation that has the same solution as the given equation include the following: C. 3/2p − 5 + 9/4p = 7 − 5/4p.
How to determine the equation that has the same solution?From the information provided, we have the following equation:
-16p + 37 = 49 - 21p
Next, we would rearrange the equation by collecting like terms as follows;
-16p + 21p = 49 - 37
5p = 12
p = 12/5
Furthermore, we would evaluate and determine the solution for each of the given equation as follows;
-14 + 6p = -9 - 6p
Collecting like terms, we have:
6p + 6p = -9 + 14
12p = 5
p = 5/12 (Different solution).
2 + 1.25p = -3.75p + 10
Collecting like terms, we have:
1.25p + 3.75p = 10 - 2
5p = 8
p = 8/5 (Different solution).
3/2p − 5 + 9/4p = 7 − 5/4p
Collecting like terms, we have:
3/2p + 9/4p + 5/4p = 7 + 5
5p = 12
p = 12/5 (Same solution).
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How do you find the area of a regular hexagon with only the radius?
The Area Of Regular hexagon that has the radius of 5 units is 65 square units .
The formula to calculate the area of regular hexagon is = [tex]\frac{1}{2} \times a\times P[/tex] ;
where "a" is apothem and "P" is Perimeter .
the number of sides in the hexagon (n) = 6 ;
let the side length of hexagon be (s) = 2x ;
the perimeter is = [tex]n\times s[/tex] = 12x ;
So , the area is = [tex]\frac{1}{2} \times a\times (12x)[/tex] = 6 × a × x ;
the central angle of one triangle in the hexagon is(2θ) = 60 degree ;
So , θ = 30 degree .
we use the trigonometric ratio to find the value of "a" and "x" by using "r" and "θ" ,
⇒ [tex]\frac{Sin30}{1} =\frac{x}{r}[/tex] ⇒ [tex]\frac{Sin30}{1} =\frac{x}{5}[/tex]
⇒ [tex]x=5Sin(30) = \frac{5}{2}[/tex] ;
and ⇒ [tex]\frac{Cos30}{1} =\frac{a}{r}[/tex] ⇒ [tex]\frac{Cos30}{1} =\frac{a}{5}[/tex]
⇒ [tex]a=5Cos(30) = \frac{5\sqrt{3} }{2}[/tex] ;
substituting the values of "a" and "x" in the Area ,
we get ;
Area = 6 × a × x = [tex]6\times (\frac{5\sqrt{3} }{2} )\times(\frac{5}{2} )[/tex] ;
= [tex]\frac{75\sqrt{3} }{2}[/tex] = 64.95 ≈ 65 square units .
Therefore , Area of regular hexagon is ⇒ 65 square units .
The given question is incomplete , the complete question is
How do you find the area of a regular hexagon with only the radius as 5 units ?
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if f(x)=3x+5 and g(x)=x-2 , what is ( f - g)(x)
Answer:
(f - g)(x) = 2x + 7
Step-by-step explanation:
(f - g)(x)
= f(x) - g(x)
= 3x + 5 - (x - 2) ← distribute parenthesis by - 1
= 3x + 5 - x + 2 ← collect like terms
= 2x + 7
What is the degree of 6 in polynomial?
The degree of 6 in polynomials is 0. The degree of a polynomial is defined as the highest power of the variable that appears in the equation.
When a numerical coefficient is present, as in example 6, the power is considered to be 0. This means that the degree of the polynomial is 0. To find the degree of a polynomial, we need to first identify the variables and their corresponding powers.
For example, if the polynomial is 4x^3 + 6x^2 - 3x + 6, we can identify that the variable is x and the powers are 3, 2, and 1 respectively. The highest power among the three is 3, so the degree of the polynomial is 3.
In example 6, there is no variable present, only a numerical coefficient. Therefore, the power of the coefficient is 0 and the degree of the polynomial is 0.
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A new pizza joint just opened up that is advertising over 150,000 different pizza choices. They offer 3 types of crust, 3 different meats, 4 types of cheese, 8 different veggies and 2 types of sauce. Based on these values, exactly how many pizza types is that? Are they falsely advertising their choices or just wicked-good at math?
The total available number of pizza is 576 and yes, they are falsely advertising their choices
How to determine how many pizza types is that?From the question, we have the following parameters that can be used in our computation:
3 types of crust3 different meats4 types of cheese8 different veggies 2 types of sauce.The number of pizza is the products of the individual numbers above
So, we have the following representation
Pizza = 3 * 3 * 4 * 8 * 2
Evaluate the products
This gives
Pizza = 576
The number 576 is less than 150,000 (the number of different pizza advertised)
Since this is incorrect, then they are they falsely advertising their choices
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Are 3xy and 5yx like terms?
The terms 3xy and 5yx are like terms because they contain the same variable and also have the same degree .
The Like terms are defined as the terms that contain the same variable and also the variables are raised to the same power .
For Example : the terms 3x² and 7x² are like terms as they have the same variable and that variable has same power "2" .
The terms are given as 3xy and 5yx ,
both the terms have variables x and y ,
the power of x and y in first term "3xy" is "1" , and
the power of x and y in the second term "5yx" is also "1" .
So , we can conclude that the terms 3xy and 5yx are like terms .
Therefore , 3xy and 5yx are like terms .
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The expression 3x + 2y - 5z can be expanded as 3x + 2y - 5z = 3x + 2y - 5z + 0 = 3x + 2y - 5z + 0 + 0 = 3x + 2y - 5z + 0 + 0 + 0.
The expression 3x + 2y - 5z can be calculated as follows:
3x + 2y - 5z = 3x + 2y - 5z
= 3x + 2y - (5z + 0)
= 3x + 2y - (5z + 0 + 0)
= 3x + 2y - (5z + 0 + 0 + 0)
= 3x + 2y - 5z - 0 - 0 - 0
= (3x + 0) + (2y - 0) - (5z - 0 - 0 - 0)
= 3x + 2y - 5z
The expression 3x + 2y - 5z can be expanded by first adding 0 to each side: 3x + 2y - 5z + 0 = 3x + 2y - 5z + 0. Then, we can add 0 to each side again: 3x + 2y - 5z + 0 + 0 = 3x + 2y - 5z + 0 + 0. This can be done for a third time: 3x + 2y - 5z + 0 + 0 + 0 = 3x + 2y - 5z + 0 + 0 + 0. This expansion can be simplified by replacing the like terms: 3x + 0 + 2y - 0 - 5z - 0 - 0 - 0 = 3x + 2y - 5z. This simplification shows that the expression 3x + 2y - 5z is equal to itself and can be used to calculate the value of the expression.
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Which graph shows the solution to the inequality?
The graph that shows the solution to the inequality, would be Graph A.
How to find the graph?The inequality is :
x - 4 ≤ - 1
What this means is that all values of x should be able to deduct 4 such that the result would be less than or equal to - 1.
This means that the largest number that x can take is :
x - 4 = - 1
x = -1 + 4
x = 3
x can be a maximum of 3 and then all other x values have to be less than 3. This is shown as a solution in the first graph.
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Subtract 5x - 2 from -3x + 4.
(A) -8x + 2
(B) 2x + 2
(C) 8x - 6
(D) -8x + 6
Answer: D
Step-by-step explanation:
-3x + 4 - (5x - 2)
= -3x + 4 - 5x + 2
= -8x + 6
= D
A parallelogram has a base of 5 centimeters (cm) and a height of 12 cm and is stacked on top of a square with a side length of 5 cm. Hannah calculates the area of the parallelogram by multiplying the base and height to get 60 cm2, then dividing by 2 to get 30 cm2. She then multiplies the side length of the square by itself to find the area of the square, 25 cm2. Finally, she adds the areas together to find the area of the figure.
Is Hannah's answer correct? Why or why not?
Select the option that correctly answers both questions.
Responses
No, she incorrectly calculated the area of the parallelogram.
Yes, she correctly added the areas of the two figures to find the area of the composite figure.
No, she mistakenly added the area of the square and triangle when she should have multiplied them.
The correct response to Hannah's method is: No, she incorrectly calculated the area of the parallelogram.
Area of a composite shape.
A composite shape is one formed by more than one plane shape.
A given shape that has its two opposite sides to be equal and parallel is called a parallelogram. The area of a parallelogram can be determined by;
Area of a parallelogram = base x height
Also, a square has the measure of its sides to be equal. The area of a square can be determined by:
Area of a square = length x length
Considering the given question, we have;
i. Area of the parallelogram = base x height
= 5 x 12
Area of the parallelogram = 60 cm^2
ii. Area of the square = length x length
= 5 x 5
Area of the square = 25 cm^2
Total area of the given shape = 60 + 25
= 85 cm^2
Hannah's answer is incorrect. Thus the correct response is No, she incorrectly calculated the area of the parallelogram.
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a train travel 112KM in 1 hr 30 min with a certain speed . how many KM it will travel in 4hr 45 min with same speed
The train will travel 354.6km in 4hr 45 min.
Step-by-step solution:
GIVEN-
Distance=112km in 1hr and 30min(3/2h)
TO FIND-
Distance in 4hr and 45 min
Let the required distance be x km.
More distance → more time
Therefore the two quantities are directly proportional.
∴Distance=x
Time (in hours)=4hr 45min= 19/4h
[tex]\frac{x1}{y1}[/tex]=[tex]\frac{x2}{y2}[/tex]
⇒
[tex]\frac{112}{x}[/tex]=[tex]\frac{1.5}{19/4}[/tex]
⇒3/2 x= 112×19/4
∴x=354.6km
Hence, the required distance =354.6 km.
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Graph the linear inequality shown below on the provided graph.
y ≤ 1/3x-6
On solving the provided question, we can say that - here it the given inequality equation [tex]36x - 72 > 24x + 36 = > 12x > 108 = > x > 9[/tex]
What is inequality?
A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.
[tex]4(9x - 18) > > 3(8x + 12)\\36x - 72 > 24x + 36\\12x > 108\\x > 9[/tex]
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A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Select two options. The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill. The equation StartFraction 1 over 8 EndFraction (x + 16) = 76 represents the situation, where x is the food bill. The solution x = 60 represents the total food bill. The solution x = 60 represents each friend’s share of the food bill and tip. The equation 8 (x + 16) = 76 represents the situation, where x is the food bill.
The equation 8x = 60 represents the situation and x represent each friend’s share of the food bill.
The equation x = 76/8 represents the situation and x represent each friend’s share of the food bill and tip.
How to solve an equationAn equation is an expression that shows the relationship between two or more numbers and variables.
Let x each friend’s share of the food bill.
A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. Hence:
8x + 16 = 76
subtracting 16 from both sides of the equation:
8x = 60
Also, let x represent each friend’s share of the food bill and tip.
8x = 76
x = 76/8
The contribution of each friend for food bill is given by 8x = 60
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You can rent a car via two options. Option A charges $35 per day plus $0.15 per mile. Option B charges $0 per day, but $1.00 per mile. How many miles must you drive in one day for option A to be cheaper?
The number of miles that miles must be driven in one day for option A to be cheaper is 41 miles or lesser
How to illustrate the equation?The equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
Option A charges $35 per day plus $0.15 per mile. This will be:
35 + 0.15m
Option B charges $0 per day, but $1.00 per mile. This will be m.
Equating them will be:
35 + 0.15m < m
Collect the like terms
m - 0.15m < 35
0.85m < 35
Divide
m < 41
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What is the measure of m?
Give your answer in simplest form.
The value of m in the given triangle will be 10.39.
What is the Pythagorean theorem?According to the Pythagorean Theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs of a right triangle. In other words, a² + b² = c² for the triangle depicted below. The right triangle's legs, a, and b, are perpendicular sides, and the hypotenuse, c, is the side that faces away from the right angle.
where a, b, and c are the base, height, and hypotenuse of the triangle.
Given in the figure there is one big triangle whose height is m and whose hypotenuse is 24 or (18 + 6). let x be the base of the triangle.
From the Pythagorean theorem
x² + m² = 24²
x² = 576 - m²
For another triangle whose base is n and height is 18.
From the Pythagorean theorem
n² + 18² = x².......(1)
from equation (1)
n² + 18² = 576 - m²
n² + m² = 576 - 324
n² + m² = 252........(2)
For another triangle whose base is 5 and height is n.
From the Pythagorean theorem
n² + 6² = m²
n² - m² = 36.....(3)
From comparing equations 2 and 3
n² + m² - (n² - m²) = 252-36
2m² = 216
m² = 108
m = ± 10.39
since the length can not be n negative.
m = 10.39
therefore the value of m in the given triangle is 10.39.
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a trader made a loss of 15% when an article was sold.find the ratio of the selling price to the cost price
Ratio of selling price to the cost price =17/20
what is selling and cost price?
Cost price is the amount paid while purchasing an assets or manufacturing product. On the other hand, selling price is the amount that is earned by the seller when products or assets are sold.
What is the ratio of the selling price to the cost price?
given, a trader made a loss of 15% when an article was sold.
let, the purchasing price of article = $ Y
as he made a loss of 15%
so the amount of loss = Y 15/ 100
Now, the selling price will be Y - Y15/100
selling price = (100Y -15Y) /100 = 85Y/100
selling price = 17Y/20
ratio of the selling price to the cost price = 17Y/100/Y = 17/20
ratio = 17/20
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Solve the system of equations y = x2 + 2x − 1 and y − 3x = 5
Answer:
[tex](x, y)=\{(-2,-1), (3,14)\}[/tex]
Step-by-step explanation:
[tex]y=x^2+2x-1, y=3x+5 \\ \\ \implies x^2+2x-1=3x+5 \\ \\ x^2-x-6=0 \\ \\ (x-3)(x+2)=0 \\ \\ x=-2, 3 \\ \\ x=-2 \implies y=-1 \\ \\ x=3 \implies y=14 \\ \\ \therefore (x, y)=\{(-2,-1), (3,14)\}[/tex]
Practice Questions: Using Fractions and Decimals
Answer:
-0.5
-1/2
Let's see how to turn a fraction into a decimal!Let's do... 8/16
First, divide 8 by 16
8/16 = -0.5
so the answer should be: -0.5
What about turning a decimal into a fraction?Well, let's see how to do it:
Remove the decimal point and put -5 over 10→ -5/10 (add as many zeros as necessary after the 1)
Now simplify to the lowest terms: -5/10 simplifies to -1/2
To remove any confusion, 1/2 is the same as 8/16, 8 is half of 16, and 1 is half of 2.
Hope this helped!
Find the greatest common factor.
2ax2 + 2ax + 2a
The greatest common factor of the expression 2ax² + 2ax + 2a is 2a.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
2ax² + 2ax + 2a
There are three terms.
The greatest common factor in each term is 2a
Now,
2a (x² + x + 1)
Thus,
The expression with the greatest common factor is 2a (x² + x + 1).
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Which is not a solution of the inequality
9 -3x > -36
A) 0
B) -22
C) 50
D) 11
SHOW WORK PLS!
50 is not a solution of the inequality -3x > -36
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
-3x > -36
Now let us check which are all the solutions of the inequality
0>-36 is possible.
Hence 0 is a solution
-3(-22)>-36
66>-36
Hence -22 is a solution
-3(50)>-36
-150<-36
50 is not solution of the inequality.
-33>-36
11 is also solution of the inequality
Hence, 50 is not a solution of the inequality -3x > -36
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A popular kid's game has 15 tiles and 1 open space. The goal of the game is to rearrange the tiles to put them in order (from least to greatest, starting at the upper left-hand corner and going across each row). Use the figure to write the transformation(s) that describe the path of where the 8 tile is currently, and where it must be by the end of the game. Can this same translation be used to describe the path of all the tiles?
The translation that describe the path of the 8 tile to reach it's final position is given as follows:
(x,y) -> (x + 3, y - 1).
This same translation cannot be used to describe the path of all tiles, as some will move up, some down, some left and some right, but the movement is not the same for all tiles.
What are the translations?There are four translations that are standard, and their rules are defined as follows:
Translation left a units: (x,y) -> (x - a, y).Translation right a units: (x,y) -> (x + a, y).Translation up a units: (x, y) -> (x, y + a).Translation down a units: (x,y) -> (x, y - a).The tiles will be placed in order, meaning that the tile number eight should be the second row and fourth column.
As the tile with the number eight is at the first row and the first column, the movements are given as follows:
3 units right: x -> x + 3.1 unit down: y -> y - 1.Hence the compound translation is given as follows:
(x,y) -> (x + 3, y - 1).
This, however, cannot be used for all the points, as some of them, for example 5 and 6, are already in their final position, while the movement for tile 1 is 2 units up.
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GEOMETRY FIND LENGTH OF THIRD SIDE
Answer:
2.65
Step-by-step explanation:
a^2 + b^2 = c^2 (Pythagorean theorem)
square root of 3 = 1.73205080757
2 x square root of 3 = 3.4
2^2 + 3.4^2 = C^2
4+ 11.6= C^2
