Answer:
1 7 21 35 35 21 7 1
Step-by-step explanation:
Pascal triangle is a mathematical expression that can be used to expand questions involving bracket, especially of high degree/ power. Example: [tex](a + b)^{9}[/tex] etc
For the given question, the Pascal triangle for the expansion is: 1 7 21 35 35 21 7 1
So that,
[tex](2x^{3}+3y^{2}) ^{7}[/tex] = 1.[tex](2x^{3}) ^{7}[/tex] + 7.[tex](2x^{3}) ^{6}[/tex].[tex]3y^{2}[/tex] + 21. [tex](2x^{3}) ^{5}[/tex].[tex](3y^{2}) ^{2}[/tex] + 35.[tex](2x^{3}) ^{4}[/tex].[tex](3y^{2}) ^{3}[/tex] + 35. [tex](2x^{3}) ^{3}[/tex].[tex](3y^{2}) ^{4}[/tex] + 21. [tex](2x^{3}) ^{2}[/tex].[tex](3y^{2})^{5}[/tex] + 7.[tex](2x^{3} )^{1}[/tex].[tex](3y^{2} )^{6}[/tex] + 1.[tex](3y^{2}) ^{7}[/tex]
= 128[tex]x^{21}[/tex] + 1344[tex]x^{18}[/tex][tex]y^{2}[/tex] + 6048[tex]x^{15}[/tex][tex]y^{4}[/tex] + 15120[tex]x^{12}[/tex][tex]y^{6}[/tex] + 22680[tex]x^{9}[/tex][tex]y^{8}[/tex] + 20412[tex]x^{6}[/tex][tex]y^{10}[/tex] + 10206[tex]x^{3}[/tex][tex]y^{12}[/tex] + 2187[tex]y^{14}[/tex]
Therefore;
[tex](2x^{3}+3y^{2}) ^{7}[/tex] = 128[tex]x^{21}[/tex] + 1344[tex]x^{18}[/tex][tex]y^{2}[/tex] + 6048[tex]x^{15}[/tex][tex]y^{4}[/tex] + 15120[tex]x^{12}[/tex][tex]y^{6}[/tex] + 22680[tex]x^{9}[/tex][tex]y^{8}[/tex] + 20412[tex]x^{6}[/tex][tex]y^{10}[/tex] + 10206[tex]x^{3}[/tex][tex]y^{12}[/tex] + 2187[tex]y^{14}[/tex]
Answer:
1, 8, 28, 56, 70, 56, 28, 8, 1
Step-by-step explanation:
Solve the system
u=2x-y v= 3 x+2y, for x and y in terms of u and v then find the value of Jacobian σ(x,y)/σ(u,v). Find the image under the transformation of the triangular region with the vertices (0,0) ,(2,4), and (2, -3) in the x,y plane. Sketch the transformed region in uv plane.The function for x in terms of u and v is x=?
Answer:
x = [tex]\frac{2u+v}{7}[/tex]
y = [tex]\frac{2v - 3u }{7}[/tex]
Jacobian value = 1/7
Step-by-step explanation:
Given data:
u = 2x -y
v = 3x + 2y
solving the system for x and y in terms of u and v
x = [tex]\frac{2u+v}{7}[/tex]
y = [tex]\frac{2v - 3u }{7}[/tex]
The value of the Jacobian = 1/7 ( solution attached below )
Image under the transformation of the triangular region with vertices ( 0,0) , (2,4) and (2,-3) in the x-y plane is attached below
In this exercise we have to use system and Jacobian knowledge to calculate the requested values, thus we find that:
[tex]X= \frac{2u+v}{7} \\\\Y= \frac{2v-3u}{7}\\\\J= \frac{1}{7}[/tex]
Given data as:
[tex]u = 2x -y[/tex] [tex]v = 3x + 2y[/tex]
Solving the system for x:
[tex]2u=4x-2y\\v= 3x-2y\\= 2u+v/7[/tex]
Solving the system for v:
[tex]u = 2(2u+v/7)-y\\y= 1/7(2v-3u)[/tex]
Find the value of the Jacobian:
[tex]\frac{dx}{du}= \frac{d(2u+v/7)}{du}= 2/7\\\\\frac{dv}{du}= \frac{d(2u+v/7)}{du}= 2/7[/tex]
[tex]\frac{dx}{du}= \frac{d(2v+3u/7)}{du}= -3/7\\\\\frac{dv}{du}= \frac{d(2v+3u/7)}{du}= 2/7[/tex]
Substitute the given value in equation will become:
[tex]J= 1/7[/tex]
See more about system at brainly.com/question/7589753
Make q the subject of the formula 2(q+p) = 1 + 5 q
Please help and show work
Answer:
175 is the answer
Step-by-step explanation:
5x5=25
25x7=175
If 2 and 6 are congruent, then line j is to parallel to lind k because
Mr. duc asked perry to set up 450 chairs in a large hall. Perry puts 20 chairs in each
Row. He has already set up 15 rows of chairs. How many more chairs must he set up
Answer:
150 more chairs
Step-by-step explanation:
20 chairs x 15 rows = 300
450 - 300 = 150
find the discrimnate of -x^2+2x-8=0
Answer:
-28
Step-by-step explanation:
(8 - h)(jh + jh) use h=-1 and j=5
I would do this but im kind of confused please help
Answer:
-90
Step-by-step explanation:
(8-h)(jh+jh)
Since the values of h and j are given, we use substitution to replace the variables with their number values
(8-(-1))(j(-1)+j(-1) replaced all the h with -1
(8-(-1))((5)(-1) + (5)(-1)) replaced all the j with 5
Then we solve inside the parenthesis first
(8+1)(-5+(-5))
(9)(-10)
Then, multiply
-90
14,779 107,033 123,737 round to the nearest hundred?
Step-by-step explanation:
14,800
107
123,700
hope this helps have a great day
Ok this is a number line problem
Can someone help me please
Answer:
A.) slope: -3
B.) y-intercept: 9
C.) equation: y= -3x+9
Step-by-step explanation:
I'm in Geometry In the 8th grade.
What is the slope between the point (3,5) and (7,6)
Answer:
1/4
Step-by-step explanation:
y2-y1 (6-5) / x2-x1 (7-3)
Amber had $45.00. She spent
of it and saved the rest. How much money did she save?
Answer:
$22.50
Step-by-step explanation:
(7p+3) - (2p+2)
the assignment is (add and subtract polynomials)
Answer:
5p + 1
Step-by-step explanation:
(7p + 3) - (2p + 2)
7p + 3 - 2p - 2
5p + 1
Karly is choosing between two health clubs. Yoga Studio A charges a membership fee of $22.00 and $24.50 per month. Yoga Studio B charges a membership fee of $47.00 and $18.25 per month. At how many months will they cost the same? *
Answer:
4 months
Step-by-step explanation:
Given
Studio A
[tex]Membership = \$22.00[/tex]
[tex]Monthly = \$24.50[/tex]
Studio B
[tex]Membership = \$47.00[/tex]
[tex]Monthly = \$18.25[/tex]
Required
Determine when the cost will be the same
For both, we have the total cost to be:
[tex]Cost = Membership + Monthly\ Cost * m[/tex]
Where m represents the number of month
For Studio A:
[tex]Cost = 22 + 24.5 * m[/tex]
For Studio B:
[tex]Cost = 47 + 18.25 * m[/tex]
Equate both expressions to get the required month
[tex]47 + 18.25 * m = 22 + 24.5 * m[/tex]
[tex]47 + 18.25 m = 22 + 24.5m[/tex]
Collect Like Terms
[tex]47 - 22 = 24.5m - 18.25 m[/tex]
[tex]25= 6.25m[/tex]
Reorder
[tex]6.25m = 25[/tex]
Solve for m
[tex]m = 25/6.25[/tex]
[tex]m = 4[/tex]
Hence, it'll take 4 months
If AB is rotated 180 clockwise about a point not on the line AB then which of the following statements
about its image, ''
AB , is true?
Answer:
yes
Step-by-step explanation:
Please hurry!!!! The quotient of 56 and n is multiplied by 3.
Create an equivalent expression using n to represent the unknown number.
Answer: n8→ I used n as the unknown number. Explanation: The quotient is the result of division between two numbers. The quotient of a number (I used n ) and 8 would be n8.
Step-by-step explanation:
I think it's 56/n=3n.
Mr. Gates went to the mall with $20. He bought a bra for $7.98, an adult diaper for $5.99, and a Barbie Doll for $1.50. How much money did he have left when he headed back to his crib?
BoldItalicUnderline
Answer:
$20 - $7.98 - $5.99 - $1.50 = $4.53
Step-by-step explanation:
Write as a mixed number 1 5/6 times 1 1/3=
Answer:
The answer is 2 4/9
Step-by-step explanation:
hope this helps
1 5/6 × 1 1/3= 22/9
22/9 as mixed number is 2 4/9
Answer: the answer is 11/6*4/3
Step-by-step explanation:
PLEASE HELP PLEASE!!!!!!!!!!!!!!!!
Answer:
-1 5/36
Step-by-step explanation:
Hope this helps!!
The large rectangle below represents one whole.
What percent is represented by the shaded area?
Answer: the percent of 6 of 20 is 30%
I just need the answer :)
Answer:
See belowStep-by-step explanation:
Equation of (y - k)^2 = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - pGiven is the parabola:
(y + 1)^2 = (x + 2)It has a vertex at (-2, -1)
New vertex (-1, -1) requires translation to the right by 1 unit. Which changes the function to:
(y + 1)^2 = (x + 2 - 1) ⇒ (y + 1)^2 = (x + 1)For this function the focus and directrix is:
(y + 1)^2 = (x + 1)k = -1, p = 1/4, h = -1Focus is
(h +p, k) = (- 0.75, -1)Directrix is:
x = -1 - 1/4 = - 1.25plsss help meeeeeeeeeeee
Answer:
a
Step-by-step explanation:
the 2 exponents cancel each other out because one is positive and the other is negative, so you are left with 17/16
f(x) = 4x + 5; {-2, - 1,0,1,2}
Answer:
Step-by-step explanation:
F(x) = 4x+5
F(-2) = -3
F(-1) = 1
F(0) = 5
F(1) = 9
F(2) =13
Determine whether the set W is a subspace of R3 with the standard operations. If not, state why.
W = {(0, x2, x3): x2 and x3 are real numbers}
W is a subspace of R3.
W is not a subspace of R3 because it is not closed under addition.
W is not a subspace of R3 because it is not closed under scalar multiplication.
Answer:
Step-by-step explanation:
From the given information.
R3 is a vector space over the field R, where R is the set of real numbers.
Where;
The set W = {(0, x2, x3): x2 and x3 are real numbers} is the subspace of [tex]\Re[/tex]³
To proof:
(0,0,0) ∈ W ⇒ W ≠ ∅
Suppose u and v is an element of W;
i.e.
u,v ∈ W (which implies that) ⇒ u (0,x2,x3) and v = (0,y2,y3) are real numbers.
Then
u+v = (0,x2,x3) +(0, y2, y3)
u+v = (0,x2+y2, x2+y3) ∈ W
⇒ u+v ∈ W ----- (1)
Now, if we take any integer to be an element of the real number [tex]\Re[/tex]
i.e
∝ ∈ [tex]\Re[/tex]
∝*[tex]\Re[/tex] = ∝(0,x2,x3)
∝*[tex]\Re[/tex] = (0,x2,x3) ∈ W
⇒ ∝*u ∈ W ------(2)
Thus from (1) and (2), W is a subspace of [tex]\Re[/tex]³
Solve for x: x-5=3x+7
Answer:
-11/3 = x
Step-by-step explanation:
What is 2+2 pls i really need the answer it would mean a lot to me
Answer:
ummm its 4
Step-by-step explanation:
How do you simplify 6 to the power of 2 plus 15
A. 21
B. 27
C.46
D.51
Correct answer gets brainlest!
Answer:
D
Step-by-step explanation:
6 to the power of 2 just means 6 squared. To solve this, just multiply 6 by itself. 6x6 is 36. Now, we have to add that to 15. 36+15 is 51.
Therefore, the correct answer is D!
Hope I helped!!!!!!!!!
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP FASTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT
Answer:
10 11/15
Step-by-step explanation:
Rewriting our equation with parts separated
=4+13+6+25
Solving the whole number parts
4+6=10
Solving the fraction parts
1/3 + 2/5 =
5/15+6/15=11/15
Combining the whole and fraction parts
10+11/15=10 11/15
Answer:
Step-by-step explanation:
-10 11/15
Lin has a small rectangular baking pan. She lines the bottom of the pan with aluminum foil. The piece of foil has an area of 11 1/4 square inches and a length of 4 1/2 what is the width of the piece of foil?
Please help ASAP!!!
Answer:
2 1/2
Step-by-step explanation:
( 11 1/4 ) / ( 4 1/2 ) = 2 1/2
( 2 1/2 ) = 5/2
-19/5 / -38/5 help please
Answer:
0.5
Step-by-step explanation:
