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ki77a [65]
4 years ago
9

I’ll mark brainlest:( i need help!

Mathematics
1 answer:
enyata [817]4 years ago
7 0

Answer: Choice A)  3 \sqrt{26}

==================================================

Work Shown:

\text{The two points are } (x_1,y_1) = (6,7) \text{ and }  (x_2,y_2) = (3,-8)\\\\d = \text{Distance between } (x_1,y_1) \text{ and } (x_2,y_2)\\\\d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} = \text{Distance Formula}\\\\d = \sqrt{(6-3)^2+(7-(-8))^2}\\\\d = \sqrt{(6-3)^2+(7+8)^2}\\\\

d = \sqrt{(3)^2+(15)^2}\\\\d = \sqrt{9+225}\\\\d = \sqrt{234}\\\\d = \sqrt{9*26}\\\\d = \sqrt{9}*\sqrt{26}\\\\d = 3\sqrt{26}\\\\

When going from 234 to 9*26, the idea here is to factor where one factor is the largest perfect square possible. That way we can use the rule \sqrt{x*y} = \sqrt{x}*\sqrt{y} to break up the root and simplify.

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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

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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
On Sunday Sheldon bought 4 1/2 kg of plant food. he used 1 2/3 kg on his strawberry plants and used 1/6 kg for his tomato plants
sweet-ann [11.9K]

Answer:

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Step-by-step explanation:

6 0
3 years ago
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Which statement is true? Question 2 options: All parallelograms are rectangles. All rectangles are squares. All quadrilaterals a
alekssr [168]

For this case, we have that:

  • By definition, a rectangle is a parallelogram. So, we discard the first option.
  • On the other hand, we have that all rectangles can not be squares, since a square has all its sides equal, while the rectangle, poir definition, no.So, we discard the second option.
  • All quadrilaterals are not rectangles because there are other figures with four sides that are not necessarily rectangular. We discard the third option.
  • Finally, we have that all squares are rectangles. This statement is true since squares can be rectangles with pairs of equal sides.

Answer:

Option D

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3 years ago
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3 years ago
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Answer:

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Step-by-step explanation:

dont think i  dont see u tryna cheat

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25 x 5 = 125

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