Use base ten blocks to solve 53/4

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

4 years ago

0.4 times 0.59 sgaehags

ra1l [238]

Answer:

0.236

Step-by-step explanation:

Multiply 0.4 by 0.59

hopes this helps have a good day :) <3

brainlest???

5 0

3 years ago

Help with this question please?

Margaret [11]

The recipe makes 8 pancakes.
He wants to make 12 pancakes.

First, find out how many times what he needs is compared to the recipe.

He wants 12 pancakes; the recipe makes 8 pancakes.

12/8 = 1.5

He wants to make 1.5 times the recipe.

Now multiply every ingredient amount by 1.5 to find what he needs to make 12 pancakes.

240 g of plain flour.
240 g * 1.5 = 360 g of plain flour

2 egs
2 eggs * 1.5 = 3 eggs

600 ml milk
600 ml * 1.5 = 900 ml

Answer: 360; 3; 900

6 0

3 years ago

Instructions: Enter your responses as percentages. Include a minus (-) sign for all negative answers. a. The price of good X dec

zalisa [80]

Answer:

COMPLETE QUESTION:

Suppose the own price elasticity of demand for good X is -3, its income elasticity is 1, its advertising elasticity is 2, and the cross-price elasticity of demand between it and good Y is -4. Determine how much the consumption of this good will change if: Instructions: Enter your answers as percentages. Include a minus (-) sign for all negative answers.

a. The price of good X decreases by 5 percent.

b. The price of good Y increases by 8 percent.

c. Advertising decreases by 4 percent.

d. Income increases by 4 percent.

ANSWER

a) The quantity demanded of good X will change by 15 percent

b) The demand for X will change by -32 percent.

c) The demand for good X will change by -8 percent

d) The demand of good X will change by 4 percent

Step-by-step explanation:

Price elasticity of demand measures how responsive quantity demanded is to a change in the price of a commodity.

price elasticity = $\frac{\frac{dQ}{Q} }{\frac{dP}{P} }$ .

Note: Same applies to income,advertising and cross-price elasticity.

where, P is the price of the demanded good and Q is the quantity of the demanded good and dQ and dP are the changes in quantities of demanded goods and prices respectively.

a) Quantity demanded on goods X due to decrease by 5 percent in price is ;

-3 = $\frac{\frac{dQ}{Q} }{-5}$ , therefore percentage increase in quantity of goods demanded is (-3 x -5) = 15 percent

b) Cross- Price Elasticity; Quantity demanded on goods X due to increase by 8 percent in price in goods Y is;

-4 = $\frac{\frac{dQ}{Q} }{8}$ , therefore percentage decrease in quantity of goods demanded is (-4 x 8) = -32 percent

c) Advertising Elasticity ; Quantity demanded on goods X due to decrease by 4 percent in advertising is;

2 = $\frac{\frac{dQ}{Q} }{-4}$ , therefore percentage decrease in quantity of goods demanded is (2 x -4) = -8 percent

d) Income Elasticity ; Quantity demanded on goods X due to increase by 4 percent in income is;

1 = $\frac{\frac{dQ}{Q} }{4}$ , therefore percentage increase in quantity of goods demanded is (1 x 4) = 4 percent

3 0

3 years ago

Which angle is the included angle for JL and KL ? A) L B) K C) L

umka2103 [35]

angle for JL and KL is <L
answer is C. L

6 0

3 years ago

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