please helppppppppppppp ASAP. please ensure to use step by step explanation. thanks.
Answers
I'll do the first two parts to get you started.
=====================================================
Part (i)
We can show that the operation [tex]\nabla[/tex] is not commutative by picking two random and different real numbers for a,b. In other words, I'm using a counter-example.
Let's say we go for a = 1 and b = 2
[tex]a \nabla b = \frac{3a+b}{5} - 1\\\\1 \nabla 2 = \frac{3*1+2}{5} - 1\\\\1 \nabla 2 = \frac{5}{5} - 1\\\\1 \nabla 2 = 1 - 1\\\\1 \nabla 2 = 0\\\\[/tex]
Now let's swap the values. We'll try a = 2 and b = 1
[tex]a \nabla b = \frac{3a+b}{5} - 1\\\\2 \nabla 1 = \frac{3*2+1}{5} - 1\\\\2 \nabla 1 = \frac{7}{5} - 1\\\\2 \nabla 1 = 1.4 - 1\\\\2 \nabla 1 = 0.4\\\\[/tex]
We can see that [tex]1 \nabla 2[/tex] and [tex]2 \nabla 1[/tex] are not the same value. In general, [tex]a \nabla b \ne b \nabla a[/tex] Therefore, the operation [tex]\nabla[/tex] is not commutative.
The only time [tex]a \nabla b = b \nabla a\\\\[/tex] is true is when [tex]a = b[/tex], since,
[tex]\frac{3a+b}{5}-1 = \frac{3b+a}{5}-1\\\\\frac{3a+a}{5}-1 = \frac{3a+a}{5}-1\\\\\frac{4a}{5}-1 = \frac{4a}{5}-1\\\\[/tex]
It's when [tex]a \ne b[/tex] is where the operation becomes noncommutative.
Another way to arrive at the [tex]a = b[/tex] condition is to solve the original equation for either 'a' or b.
=====================================================
Part (ii)
Using the previous part as inspiration, we'll do a counter-example to show that the operation is not associative. Pick 3 random values for a,b,c. Here are the values I'll pick.
a = 1b = 2c = 3Then,
[tex]d = b \nabla c = \frac{3b+c}{5}-1 = \frac{3*2+3}{5}-1 = 0.8\\\\a \nabla (b \nabla c) = a \nabla d = \frac{3a+d}{5}-1 = \frac{3*1+0.8}{5}-1 = -0.24\\[/tex]
Next, we can say:
[tex]d = a \nabla b = \frac{3a+b}{5}-1 = \frac{3*1+2}{5}-1 = 0\\\\(a \nabla b) \nabla c = d \ \nabla c = \frac{3d+c}{5}-1 = \frac{3*0+3}{5}-1 = -0.4[/tex]
Let's compare the two outputs:
[tex]a \nabla (b \nabla c) = -0.24\\\\(a \nabla b) \nabla c = -0.4[/tex]
They don't match up, so [tex]a \nabla (b \nabla c) \ne (a \nabla b) \nabla c[/tex] when (a,b,c) = (1,2,3).
In general, the operation is not associative in R.
Related Questions
Helppp for a math exammm
Answers
Answer:
d.
Step-by-step explanation:
A permanent magnet d.c. motor has an armature resistance of 0.5 Ω and when a voltage of 120 V is applied to the motor it reaches a steady-state speed of rotation of 20 rev/s and draws 40 A. What will be (a) the power input to the motor, (b) the power loss in the armature, (c) the torque generated at that speed
Answers
Answer:
applied to the motor it reaches a steady-state speed of rotation of 20 rev/s and draws 40 A. What will be (a) the power input to the motor, (b) the power loss in the armature, (c) the torque generated at that speed
voltage of 120 V is applied to the motor it reaches a steady-state speed of rotation of 20 rev/s and draws 40 A. What will be (a) the power input to the motor, (b) the power
Solution A is 40% acid and solution B is 80% acid. How many
liters of each should be used in order to make 100 L of a solution
that is 64% acid?
Answers
Step-by-step explanation:
Solution A is 40% acid and solution B is 80% acid. How many
liters of each should be used in order to make 100 L of a solution
is 64% acid
There should be 40 L of solution A and 60 L of solution B should be added in order to make 100 L of a solution that is 64% acidic.
What is equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, solution A is 40% acidic and solution B is 80% acidic, they are mixed to get a 100 L solution which is 64% acidic.
Establishing the equations,
A+B = 100
A = 100-B.......(i)
40% of A + 80% of B = 64% of 100
0.4A + 0.8B = 64......(ii)
Solving the equations,
0.4(100-B) + 0.8B = 64
40 - 0.4B + 0.8B = 64
0.4B = 24
B = 24/0.4
B = 60
Putting, B = 60 in Eq(i)
A = 100-60
A = 40
Hence, The amount of solutions needed is A = 40 L and B = 60 L.
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A car traveled 133 miles in 4 3/4 hours. What was the cars average speed in miles per hour?
Answers
4 3/4 = 19/4
133/(19/4) = 133(4/19) = 1197/19 = 63 mph
Find the equation of the line l that is perpendicular to -3x + 6y = 11 and I passes
through the point (-2, 3)
Answers
Answer:
Step-by-step explanation:
-3x + 6y = 11
Put into slope-intercept form to find the slope
6y = 3x + 11
y = 3x/6 + 11/6
y = ½x + 11/6
so slope is ½
perpendicular lines have negative reciprocal slopes, so our perpendicular line has slope -2
the slope point form of the perpendicular line will be
(y - 3) = -2(x -(-2))
(y - 3) = -2(x +2)
the slope intercept form will be
y = -2x - 4 + 3
y = -2x - 1
Derivative help please
Please dont comment if you dont know,
Thank u
Answers
[tex]y = x^{\tfrac 1{\ln x}}\\\\\implies \ln y = \ln \left( x^{\tfrac 1{\ln x}} \right)\\\\\implies \ln y = \dfrac{1}{\ln x} \cdot \ln x\\\\\implies \ln y = 1\\\\\implies y =e\\\\\\\text{Now,}\\\\\ \lim \limits_{x \to \infty} x^{\tfrac 1{\ln x}}=\lim \limits_{x \to \infty} y = \lim \limits_{x \to \infty} e = e[/tex]
rotate point B about point F 288 degrees clockwise
Answers
When a shape is rotated, it must be rotated through a point
The new position of point B is point A
The angle of rotation is given as:
[tex]Angle = 288^o[/tex]
The shape is a regular pentagon (with 5 sides).
The smallest angle of rotation that maps the pentagon onto itself is calculated using:
[tex]\theta = \frac{360}n[/tex]
So, we have:
[tex]\theta = \frac{360}5[/tex]
[tex]\theta = 72[/tex]
Let the number of rotations be n.
So, we have:
[tex]\theta \times n= Angle[/tex]
This gives
[tex]72 \times n= 288[/tex]
Divide both sides by 72
[tex]n= 4[/tex]
This means that the new position of B is 4 points away from B.
Point A is 4 points away from B, in clockwise direction
Hence, the new position of point B is point A
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Find the volume of the prism. Round to the nearest tenth.
Answers
Answer:
A: 437.1 cm³
Step-by-step explanation:
You find the area of the prism by the base of the prism & height multiplied together.
Here, the base of the prism is a triangle.
All the triangles sides are given, so lets lave them: A:8, B:8, and C:10.
Using SSS, we can find the area, which is ≈ 31.1.
If we multiply that number by 14.
We get he area of the prism.
Depending on how your rounded, the area of the prism is:
≈437.2, which is close enough to know that the asswer is A: 737.1 cm³
Hope this helped <3
What is the distance, rounded to the nearest tenth, between the points (2, 1) and (6, 6)? Enter the answer in the box.
units
Answers
Answer:
6.4 should be the correct answer
Step-by-step explanation:
if im wrong and you wanted it in a different format im sorry
The ratio 5/8 to 10/9 has a unit rate of 9/16
True or false
Answers
Answer:
This is false.
Step-by-step explanation:
The easiest thing to do is notice that 8 goes into 16 whilst 9 doesn't so that shows 9/16 would not be the unit rate.
The ratio 5/8 to 10/9 has a unit rate of 9/16 is false.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given are two ratios 5/8 and 10/9.
The unit rate of (5/8) is (5/8)/(8/8) = 5/8 = 0.625 similary the unit rate of the ratio 10/9 is 1.11.
Now, the unit rate of 9/16 is 0.5625 which is not in the range of two ratio's unit rates.
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In an A.P. if Tₚ = q and Tq = p, then find the rth term.
Please solve this problem
Answers
Formula:
We know that
nth term of the AP is Tn = a+(n-1)d
Where, a = First term
d = Common difference
n = number of terms
Now,
Given that
pth term of the A.P. = Tp = q
⇛a + (p-1)d = q
⇛(p-1)d = q - a
⇛d = (q-a)/(p-1) →→→→(i)
and
qth term of the A.P. = Tq = p
⇛a + (q-1) d = p
⇛ (q-1)d = p-a
⇛ d = (p-a)/(q-1) →→→→(ii)
From Eqn(i) and Eqn(ii)
⇛(q-a)/(p-1) = (p-a)/(q-1)
On applying cross multiplication then
⇛(q-a)×(q-1) = (p-a)×(p-1)
⇛q²-q-aq+a = p²-p-ap+a
⇛q²-q-aq = p²-p-ap
⇛ap-aq = p²-p+q-q²
⇛a(p-q) = (p²-q²)-(p-q)
⇛a(p-q) = (p+q)(p-q)-(p-q)
⇛ a(p-q) = (p-q){(p+q)-1}
On cancelling (p-q) both sides then
⇛a = (p+q-1) →→→→Eqn(iii)
On Substituting the value of a in Eqn(ii) then
⇛ d = [p-(p+q-1)]/(q-1)
⇛d = (p-p-q+1)/(q-1)
⇛d = (-q+1)/(q-1)
⇛d = -(q-1)/(q-1)
⇛d = -1
We have,
a = p+q-1 and d = -1
Now, rth term of the AP
⇛ Tr = a + (r-1)d
⇛Tr = (p+q-1)+(r-1)(-1)
⇛ Tr = p+q-1+(-r+1)
⇛ Tr = p+q-1-r+1
⇛ Tr = p+q-r
Therefore, Tr = p+q-r
Answer: rth term of the given A.P. is p+q-r
Answer:
rth=q+p+qxp
Step-by-step explanation:
rth= 3 of the T and Tq added together and joined.
Need help asap please !!!
Answers
Slope = change in y / change in x
Slope = (2-1)/(3 - -1)
Slope = 1/4
Determine the slope from the given graph below:
A ➼ The slope is -7
B ➼ The slope is−16
C ➼ The slope is 6
D ➼ The slope is -6
(Please help me! I'll mark brainliest and give five stars.<3)
Answers
Step-by-step explanation:
again (I just answered the same question), the slope is the ratio "y coordinate change / x coordinate change".
I see e.g the points
(-1, -1) and (0, -7) on the line.
x changes by +1 (from -1 to 0).
y changes by -6 (from -1 to -7).
so, the slope is -6/1 = -6.
so, D is the right answer.
Ivy is graphing how much money she earns for each hour of babysitting. She finds that the data tends to be linear and draws a line that passes through the points (2, 17) and (5, 42.50). About how much does Ivy earn per hour? A. $42.50 B. $17 C. $25.50 D. $8.50
Answers
Answer: 8.5
Step-by-step explanation: (42.50 - 17) ÷ (5 - 2)
= 25.50 ÷ 3
= 8.5
Thank me later
42.50/5=8.5 and 17/2=8.5
A local flower shop sells a dozen roses for $15.48 if each rose cost the same price how much would It cost per rose
Answers
HURRY!
Given the function ƒ = {(1 , 2), (2 , 3), (3 , 4)} write the set of ordered pairs representing ƒ -1.
Select one:
a. {(1, 2), (3, 2), (4, 3)}
b. {(2,1), (3, 2), (4, 3)}
c. {(2, 1), (2, 3), (3, 4)}
Answers
The set of ordered pairs is {(2, 1), (2, 3), (3, 4)} which represents ƒ -1, which is the correct answer that would be an option (C).
What is an ordered pair?An ordered pair is made up of two components isolated by a comma and put inside parentheses. (x, y) indicates an ordered pair, where 'x' is the first component and 'y' is the second component in the ordered pair.
Given the function ƒ = {(1 , 2), (2 , 3), (3 , 4)}
According to option (A),
The set of ordered pairs is {(1, 2), (3, 2), (4, 3)}
This represents ƒ -3,
According to option (B),
The set of ordered pairs is {(2,1), (3, 2), (4, 3)}
This represents ƒ -2,
According to option (C),
The set of ordered pairs is {(2, 1), (2, 3), (3, 4)}
This represents ƒ -1,
Thus, the set of ordered pairs is {(2, 1), (2, 3), (3, 4)} which represents ƒ -1.
Hence, the correct answer would be option (C).
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Rewrite in simplest terms: (-8x– 6y) + (6x – 3y)
Answers
Answer:
-5x - 6y
Step-by-step explanation:
Firstly, you remove any uncessary parentheses and collect like terms.
So that becomes -8x - 6y + (3x)
Hence, the brackets can be removed, which means we can continue to collect like terms which gives the final answer of -5x - 6y
16,40 and 56 LCM
Solve please
Answers
Answer:
pic?
Step-by-step explanation:
send me the picture please
Factor Completely. 2a(x+y)+b(x+y)
Answers
Let's simplify step-by-step.
2a(x+y)+b(x+y)
Distribute:
=(2a)(x)+(2a)(y)+(b)(x)+(b)(y)
=2ax+2ay+bx+by
Answer:=2ax+2ay+bx+byThe simplification of the expression is 2ax+2ay+bx+by.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
An algebraic equation is a statement of the equality of two expressions formulated by applying algebraic operations to a set of variables.
Given expression is 2a(x+y)+b(x+y). The expression will be solved as below,
E = 2a(x+y)+b(x+y)
Multiply the values in the whole bracket and simplify,
E = (2a)(x)+(2a)(y)+(b)(x)+(b)(y)
E = 2ax+2ay+bx+by
The simplified expression is given as 2ax+2ay+bx+by.
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1 4 × √ 2 = 2 n Find N
Answers
Divide by 2 on both sides.
3plss help, it times;;;;;;;;;;;;;;;;;;;;;;;;;
Answers
Answer:
w=4
Step-by-step explanation:
72/48=6/w
3/2=6/w
12=3w
w=4
Jeremiah buys 6 tacos and 8 enchiladas for 60 dollars. Kennedy buys 3 tacos and 2 enchiladas for 18 dollars.
Answers
Answer:
What's the question lol
someone pease help me i really need it and giving brainlist to first answer
Answers
Answer:
I think this is what is wanted
Step-by-step explanation:
The volume (V) of a rectangular pyramid can be determined by using the following
formula.
Iwi
V
Where l= the length of the rectangle, w = the width of the rectangle, and h = the heigh
of the pyramid, what is the result of solving this equation for w?
Ow=3V-th
O2 - V +3 - th
V3
th
3V
O w=
Answers
Answer:
[tex]{ \rm{V = \frac{lwh}{3} }} \\ \\ { \rm{3V = lwh}} \\ \\ { \boxed{ \rm{ \: w = \frac{3V}{lh } \: }}}[/tex]
What is the constant of proportionality in this table?
XY
48
5 10
6 12
10 20
Answers
Answer:
2
Ok lets start off with your 3 numbers
First do 10 / 5 = 2
Then do 12 / 6 = 2
After that do 20 / 10 = 2
now you see you that its all equivalent to 2 that's your answer!
6. Gloria has 7 yellow pencils. She has 9 red pencils. Which strategy
would NOT help you find 9 -
- 7?
A Make 10
(B
Think Addition
Count to Subtract
My Way
Answers
The strategy that won't help her to calculate 9 - 7 is (a) Make 10
The given parameters are:
[tex]Yellow = 7[/tex]
[tex]Red = 9[/tex]
To determine 9 - 7,
She can use addition, as in 9 + (-7)She can subtract directly by countingHowever, she cannot make 10.
This is so, because 9 and 7 are not up to 10
Hence, the strategy that won't help her to calculate 9 - 7 is (a)
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Determine the slope from the given graph below:
A • The slope is 5
B • The slope is -1/5
C • The slope is 7
D • The slope is -7
(I’ll give brainliest <3)
Answers
Slope is the change in Y over the change in x.
Use 2 points on the graph(x,y) to use to solev6.
(2,3) and (0,-7)
Slope = (-7 -3) / (0-2)
Slope = -10/-2
Slope = 5
Answer: A the slope is 5
Determine the slope from the given graph below:
A ⇹ The slope is -7
B ⇹ The slope is−16
C ⇹ The slope is 6
D ⇹ The slope is -6
Answers
Step-by-step explanation:
although there is no graph visible here, I suspect this is the same question as I just answered twice already.
the slope is -6.
D is the right answer.
Factor x4 - y4 completely.
A) (x^2 + y^2)(x + y)(x - y)
B) (x^2 - y^2)(x + y)(x - y)
C) (x^2 + y^2)(x - y)(x - y)
D) (x^2 + y^2)(x + y)(x + y)
Answers
Option A
Rate as BRAINLIEST
if any doubt leave a comment
Find the equation of the line.
Answers
Answer:
y = 2x + -3
Step-by-step explanation:
Use the equation y=mx+b
m is the slope (2 in this case)
b is the y intercept (-3 in this case)
The equation of the line would be y = 2x + -3