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-5yx^{4}
−
5
y
x
4
Diferenciar w.r.t. x
-20yx^{3}
−
2
0
y
x
3
Cuestionario
Algebra
5 problemas similares a:
- 5 x ^ { 4 } y
−
5
x
4
y
Problemas similares de búsqueda web
What is the coefficient of the term x^4 y^5 in (x+y+2)^{12}?
What is the coefficient of the term
x
4
y
5
in
(
x
+
y
+
2
)
1
2
?
https://math.stackexchange.com/questions/693371/what-is-the-coefficient-of-the-term-x4-y5-in-xy212
You could use the binomial theorem twice. Let [x^{k}] denote the coefficient of x^k from the polynomial P(x)=\sum_{j=0}^{n}a_jx^j, i.e. [x^{k}]P(x)=a_{k}. Now, \begin{eqnarray}[x^4y^5](x+y+2)^{12}&=&[x^4y^5](x+(y+2))^{12}\\&=&[x^4y^5]\sum_{j=0}^{12}\binom{12}{j}x^j(y+2)^{12-j}\\&=&[y^5]\binom{12}{4}(y+2)^{12-4}\\&=&\binom{12}{4}[y^5](y+2)^8\\&=&\binom{12}{4}[y^5]\sum_{j=0}^{8}\binom{8}{j}y^j2^{8-j}\\&=&\binom{12}{4}\binom{8}{5}2^{8-5}\\&=&\frac{12!}{4!8!}\frac{8!}{5!3!}2^3=\frac{12!2^3}{3!4!5!}\end{eqnarray}
You could use the binomial theorem twice. Let
[
x
k
]
denote the coefficient of
x
k
from the polynomial
P
(
x
)
=
∑
j
=
0
n
a
j
x
j
, i.e.
[
x
k
]
P
(
x
)
=
a
k
. Now,
How do you find the coefficient of \displaystyle{a} of the term \displaystyle{a}{x}^{{4}}{y}^{{5}} in the expansion of the binomial \displaystyle{\left({3}{x}-{2}{y}\right)}^{{9}} ?
How do you find the coefficient of
a
of the term
a
x
4
y
5
in the expansion of the binomial
(
3
x
−
2
y
)
9
?
https://socratic.org/questions/how-do-you-find-the-coefficient-of-a-of-the-term-ax-4y-5-in-the-expansion-of-the
\displaystyle{a}={\left(-{326592}\right)} Explanation: Pattern for power 9 as per Pascal's Triangle 1 9 36 84 126 126 84 36 9 1 \displaystyle{a}{x}^{{4}}{y}^{{5}} is the \displaystyle{6}_{{t}}{h} ...
a
=
(
−
3
2
6
5
9
2
)
Explanation: Pattern for power 9 as per Pascal's Triangle 1 9 36 84 126 126 84 36 9 1
a
x
4
y
5
is the
6
t
h
...
x^4y^4
x
4
y
4
http://www.tiger-algebra.com/drill/x~4y~4/
x4y4 Final result : x4y4 Step by step solution : Step 1 :Final result : x4y4 Processing ends successfully
x4y4 Final result : x4y4 Step by step solution : Step 1 :Final result : x4y4 Processing ends successfully
Can both x^2 + y+2 and y^2+4x be squares?
Can both
x
2
+
y
+
2
and
y
2
+
4
x
be squares?
https://math.stackexchange.com/questions/384100/can-both-x2-y2-and-y24x-be-squares
Thanks to Erick Wong for setting me on the right track. Assume for sake of contradiction that x^2+y+2 and y^2+4x are both perfect squares. Then as y is a positive integer, x^2+y+2 \geq (x+1)^2=x^2 +2x+1 ...
Thanks to Erick Wong for setting me on the right track. Assume for sake of contradiction that
x
2
+
y
+
2
and
y
2
+
4
x
are both perfect squares. Then as
y
is a positive integer,
x
2
+
y
+
2
≥
(
x
+
1
)
2
=
x
2
+
2
x
+
1
...
How do you sketch the graph of \displaystyle{y}=-{5}{x}^{{2}} and describe the transformation?
How do you sketch the graph of
y
=
−
5
x
2
and describe the transformation?
https://socratic.org/questions/how-do-you-sketch-the-graph-of-y-5x-2-and-describe-the-transformation
See below :) Explanation: The standard \displaystyle{y}={x}^{{2}} is drawn in blue, the graph of \displaystyle{y}=-{5}{x}^{{2}} is drawn in red. The tranformations, in order are as follows; - ...
See below :) Explanation: The standard
y
=
x
2
is drawn in blue, the graph of
y
=
−
5
x
2
is drawn in red. The tranformations, in order are as follows; - ...
What is the end behaviour of \displaystyle{y}=-{x}^{{4}} ?
What is the end behaviour of
y
=
−
x
4
?
https://socratic.org/questions/58e54adeb72cff279f0d5371
graph{y = -x^4 [-10, 10, -5, 5]} Explanation: The polynomial is of even degree, so the end behaviour will be in the same direction. The leading coefficient is negative, so \displaystyle\lim_{{{x}\to-\infty}}=-\infty ...
graph{y = -x^4 [-10, 10, -5, 5]} Explanation: The polynomial is of even degree, so the end behaviour will be in the same direction. The leading coefficient is negative, so
x
→
−
∞
lim
=
−
∞
...
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{ x } ^ { 2 } - 4 x - 5 = 0
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Aritmética
699 * 533
6
9
9
∗
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3
3
Matriz
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
[
2
5
3
4
]
[
2
−
1
0
1
3
5
]
Ecuación simultánea
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
{
8
x
+
2
y
=
4
6
7
x
+
3
y
=
4
7
Diferenciación
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
d
x
d
(
x
−
5
)
(
3
x
2
−
2
)
Integración
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
∫
0
1
x
e
−
x
2
d
x
Límites
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}
x
→
−
3
lim
x
2
+
2
x
−
3
x
2
−
9
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