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2 years ago

15

The formula uppercase S = StartFraction n (a Subscript 1 Baseline plus a Subscript n Baseline) Over 2 EndFraction gives the part

ial sum of an arithmetic sequence. What is the formula solved for an?
a Subscript n Baseline = StartFraction 2 uppercase S minus a Subscript 1 Baseline n Over n EndFraction
a Subscript n Baseline = StartFraction 2 uppercase S + a Subscript 1 Baseline n Over n EndFraction
a Subscript n Baseline = 2 uppercase S + a Subscript 1 Baseline n + n
a Subscript n Baseline = 2 uppercase S minus a Subscript 1 Baseline n + n

2 answers:

yanalaym [24]2 years ago

5 0

Answer:

Step-by-step explanation

hope this helps

zmey [24]2 years ago

5 0

Answer:

a.

Step-by-step explanation:

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Which is the solution of the quadratic equation (4y – 3)2 = 72?

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Step-by-step explanation:

(4y - 3)2 = 72

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1 year ago

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This background applies to the next several questions. Assume a 15 cm diameter wafer has a cost of 12, contains 84 dies, and has

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Answer:

1) $Yield_1= \frac{1}{(1+ 0.02 \frac{1}{2} 2.104)^2}=0.959$

$Yield_2= \frac{1}{(1+ 0.031 \frac{1}{2} 3.1415)^2}=0.909$

2) $Cost/die_1 = \frac{12}{84 x 0.959}=0.149$

$Cost/die_2 = \frac{15}{100 x 0.909}=0.165$

3) $Area_1 = \frac{1.1 \pi (7.5cm)^2}{84}=\frac{2.104 cm^2}{1.1}=1.913 cm^2$

$Area_2 = \frac{1.1 \pi (10cm)^2}{100}=\frac{3.1415 cm^2}{1.1}=2.856 cm^2$

And for the new yield we need to take in count the increase of 15% for the area and we got this:

$Yield_1= \frac{1}{(1+(1.15) 0.02 \frac{1}{2} 1.913)^2}=0.957$

$Yield_2= \frac{1}{(1+(1.15) 0.031 \frac{1}{2} 2.856)^2}=0.905$

4) $DR_{old}=\frac{1}{\sqrt{0.92}} -1$ =0.0426 defects/cm^2

$DR_{new}=\frac{1}{\sqrt{0.95}} -1$ =0.0260defects/cm^2

Step-by-step explanation:

Part 1

For this part first we need to find the die areas with the following formula:

$Area= \frac{W area}{Number count}$

$Area_1 = \frac{\pi (7.5cm)^2}{84}=2.104 cm^2$

$Area_2 = \frac{\pi (10cm)^2}{100}=3.1415 cm^2$

Now we can use the yield equation given by:

$Yield=\frac{1}{(1+ DR\frac{Area}{2})^2}$

And replacing we got:

$Yield_1= \frac{1}{(1+ 0.02 \frac{1}{2} 2.104)^2}=0.959$

$Yield_2= \frac{1}{(1+ 0.031 \frac{1}{2} 3.1415)^2}=0.909$

Part 2

For this part we can use the formula for cost per die like this:

$Cost/die = \frac{Cost per day_i}{Number count_i x Yield_i}$

And replacing we got:

$Cost/die_1 = \frac{12}{84 x 0.959}=0.149$

$Cost/die_2 = \frac{15}{100 x 0.909}=0.165$

Part 3

For this case we just need to calculate the new area and the new yield with the same formulas for part a, adn we got:

$Area_1 = \frac{1.1 \pi (7.5cm)^2}{84}=\frac{2.104 cm^2}{1.1}=1.913 cm^2$

$Area_2 = \frac{1.1 \pi (10cm)^2}{100}=\frac{3.1415 cm^2}{1.1}=2.856 cm^2$

And for the new yield we need to take in count the increase of 15% for the area and we got this:

$Yield_1= \frac{1}{(1+(1.15) 0.02 \frac{1}{2} 1.913)^2}=0.957$

$Yield_2= \frac{1}{(1+(1.15) 0.031 \frac{1}{2} 2.856)^2}=0.905$

Part 4

First we can convert the area to cm^2 and we got 2 cm^2 the yield would be on this case given by:

$Yield= \frac{1}{(1+DR\frac{2cm^2}{2})^2}=\frac{1}{1+(DR)^2}$

And if we solve for the Defect rate we got:

$DR= \frac{1}{\sqrt{Yield}}-1$

Now we can find the previous and new defect rate like this:

$DR_{old}=\frac{1}{\sqrt{0.92}} -1$ =0.0426 defects/cm^2

And for the new defect rate we got:

$DR_{new}=\frac{1}{\sqrt{0.95}} -1$ =0.0260defects/cm^2

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2 years ago

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djyliett [7]

Answer:

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Step-by-step explanation:

We want to solve the equation:

$\frac{1}{h-5}+\frac{2}{h+5}=\frac{16}{h^2-25}$

We multiply through by the LCM: $h^2-25=(h+5)(h-5)$

$(h^2-25*\frac{1}{h-5}+(h^2-25)*\frac{2}{h+5}=\frac{16}{h^2-25} \times(h^2-25)$

Simplify to get:

$h+5+2(h-5)=16$

We expand to get:

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2 years ago

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