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ddd [48]
3 years ago
14

Use Pascal’s Triangle to expand the binomial. (8v+s)^5

Mathematics
1 answer:
il63 [147K]3 years ago
8 0
<span>Pascal 's triangle is 
</span>

1<span>
</span><span><span>1,1</span><span>
</span></span><span><span>1,2,1</span><span>
</span></span><span><span>1,3,3,1</span><span>
</span></span><span><span>1,4,6,4,1</span><span>
</span></span><span>1,5,10,10,5,1</span>

the row <span>1,5,10,10,5,1</span> is the one we need to expand <span><span><span>(8</span>v+s)</span></span>⁵.

Given <span><span>(a+b)</span></span>⁵ each term of the row is the coefficient of akbt

with k goes form 5 to 0 and t goes from 0 to 5.

so <span><span><span><span>(a+b)</span></span></span></span>⁵=1a⁵b⁰+5a⁴b¹+10a³b²+10a²b³+5a¹b⁵+1a⁰b⁵

<span><span>=<span>a</span></span></span>⁵+5a⁴b+10a³b²+10a²b³+5ab⁵+b⁵.

In the case of <span><span><span>(8</span>v+s)</span></span>⁵:

<span><span>a<span>=8</span>v</span><span>
</span></span><span>b=s</span>

<span><span>1<span><span>(8</span>v)</span></span></span>⁵s⁰+5(8v)⁴s¹+10(8v)³s²+10(8v)²s³+5(8v)¹s⁵+1(8v)⁰s⁵

<span> <span><span><span>=<span><span> (8</span>v)</span></span></span></span>⁵+5(8v)⁴s+10(8v)³s²+10(8v)²s³+5(8v)s⁵+s⁵=</span>

<span><span><span>= 8</span></span></span>⁵v⁵+5⋅8⁴v⁴s+10⋅8³v³s²+10⋅8²v²s³+40vs⁵+s⁵=

<span><span><span>= 32768</span><span><span>v</span></span></span></span>⁵<span><span><span>+20480</span><span><span>v</span></span></span></span>⁴<span><span><span>s</span><span>+5120</span><span><span>v</span></span></span></span>³<span><span><span><span>s</span></span></span></span>²<span><span><span>+640</span><span><span>v</span></span></span></span>²<span><span><span><span>s</span></span></span></span>³<span><span><span>+40</span><span>v<span>s</span></span></span></span>⁵<span><span><span>+</span><span>s</span></span></span>⁵<span>.</span>
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AB = 10 in; AD = 6 in <br><br> A= <br><br> 30sqrt3 in2<br> 30 in2<br> 60 in2
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Answer: 30

Step-by-step explanation:

If we were to draw diagonal BD, then we would create two congruent triangles, and we could find the area of each using the formula A=\frac{1}{2} ab \sin C.

However, since there are two triangles, we can double this, giving us A=ab \sin C.

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1 year ago
The alternating current (AC) breakdown voltage of an insulating liquid indicates its dielectric strength. An article gave the ac
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Answer:

Attached as image png.

Step-by-step explanation:

The alternating current (AC) breakdown voltage of an insulating liquid indicates its dielectric strength. An article gave the accompanying sample observations on breakdown voltage (kV) of a particular circuit under certain conditions. 62 51 53 58 42 54 56 61 59 64 51 53 64 62 50 68 54 55 57 50 55 50 56 55 46 56 54 55 53 47 48 56 58 48 63 58 57 56 54 59 54 52 50 55 60 51 56 59 Construct a boxplot of the data.

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4 0
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Find UV (Pic Stated Below)
natta225 [31]

Answer:

UV=29

Step-by-step explanation:

In right triangles AQB and AVB,

∠AQB = ∠AVB ...(i)  {Right angles}

∠QBA = ∠VBA ...(ii)  {Given that they are equal}

We know that sum of all three angles in a triangle is equal to 180 degree. So wee can write sum equation for each triangle


∠AQB+∠QBA+∠BAQ=180 ...(iii)

∠AVB+∠VBA+∠BAV=180 ...(iv)


using (iii) and (iv)

∠AQB+∠QBA+∠BAQ=∠AVB+∠VBA+∠BAV

∠AVB+∠VBA+∠BAQ=∠AVB+∠VBA+∠BAV  (using (i) and (ii))

∠BAQ=∠BAV...(v)


Now consider triangles AQB and AVB;

∠BAQ=∠BAV  {from (v)}

∠QBA = ∠VBA {from (ii)}

AB=AB  {common side}

So using ASA, triangles AQB and AVB are congruent.

We know that corresponding sides of congruent triangles are equal.

Hence

AQ=AV

5x+9=7x+1

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8=2x

divide both sides by 2

4=x

Now plug value of x=4 into UV=7x+1

UV=7*4+1=28+1=29

<u>Hence UV=29 is final answer.</u>

7 0
3 years ago
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