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Ghella [55]
3 years ago
12

Can i get some help​

Mathematics
1 answer:
Step2247 [10]3 years ago
8 0

Answer:

for #11 the answer is 13

Step-by-step explanation:

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42 cm^2

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The straight line ℓ is perpendicular to the line y + 2x = 9 and passes through the point p(4, 3). find the x-intercept of ℓ.
evablogger [386]
The slope of the line l is the opposite reciprocal of y+2x=9. Rearranged the equation to y=9-2x and we get a slope of -2. The opposite reciprocal of -2 is 1/2.

y-y=m(x-x)
y-3=.5(x-4)
y=.5x+1

At the x-intercept, y=0, so
0=.5x+1
-1=.5x
x=-2
8 0
3 years ago
Find a compact form for generating functions of the sequence 1, 8,27,... , k^3
pantera1 [17]

This sequence has generating function

F(x)=\displaystyle\sum_{k\ge0}k^3x^k

(if we include k=0 for a moment)

Recall that for |x|, we have

\displaystyle\frac1{1-x}=\sum_{k\ge0}x^k

Take the derivative to get

\displaystyle\frac1{(1-x)^2}=\sum_{k\ge0}kx^{k-1}=\frac1x\sum_{k\ge0}kx^k

\implies\dfrac x{(1-x)^2}=\displaystyle\sum_{k\ge0}kx^k

Take the derivative again:

\displaystyle\frac{(1-x)^2+2x(1-x)}{(1-x)^4}=\sum_{k\ge0}k^2x^{k-1}=\frac1x\sum_{k\ge0}k^2x^k

\implies\displaystyle\frac{x+x^2}{(1-x)^3}=\sum_{k\ge0}k^2x^k

Take the derivative one more time:

\displaystyle\frac{(1+2x)(1-x)^3+3(x+x^2)(1-x)^2}{(1-x)^6}=\sum_{k\ge0}k^3x^{k-1}=\frac1x\sum_{k\ge0}k^3x^k

\implies\displaystyle\frac{x+4x^3+x^3}{(1-x)^4}=\sum_{k\ge0}k^3x^k

so we have

\boxed{F(x)=\dfrac{x+4x^3+x^3}{(1-x)^4}}

5 0
3 years ago
Find the Perimeter of the figure below, composed of a rectangle and two
larisa [96]

Answer:

Step-by-step explanation:

3 0
3 years ago
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