<span>We can determine, a 30/25/15 series trade discount would be calculated as follows:
let X = retail price.
X - 0.30 </span>× X = Y ⇒ first discounted price.
<span>
Y - 0.25 </span>× Y = Z ⇒ second discounted price.
<span>
Z - 0.15*Z = T </span>⇒ total discounted price.
<span>
X - 0.30 </span>× X = (1 - 0.30) × X = 0.70 × X = Y
<span>
Y - 0.25 </span>× Y = (1 - 0.25) × Y = 0.75 × Y = Z
<span>
Z - 0.15 </span>× Z = (1 - 0.15) × Z = 0.85 × Z = T
<span>
since Z = 0.85 </span>× Y, then 0.85 × Z = 0.85 × 0.75 × Y
<span>
since Y = 0.70 </span>× X, then 0.85 × Z = 0.85 × 0.75 × 0.70 × X
<span>
based on the above, then T = total discount
= 0.85 </span>× 0.75 × 0.70 × X
= 0.44625X<span>
30/25/15 series discount is equivalent to a total discount of 44.625%
</span>
1. Multiply
2. Divide
1. Multiply by 4 on both sides
2. Divide by 7 on each side
Y = 8
The given above is an arithmetic sequence with first term equal to 3 and the common difference equal to 4. That is from 7 - 3 = 11 - 7 = 15 - 11. The nth term of an arithmetic sequence is given by the equation,
an = a1 + (n - 1) x d
Substituting the given,
an = 3 + 4(n - 1)
thus, the answer is the fourth choice.
Problem 10
<h3>Answer: (x+5)^2+(y-3)^2=25</h3>
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Work Shown:
All we're doing really is replacing the original 'y' with 'y-3' to shift the center up 3 units. This shifts every point on the circle the same as well.
This new circle has center (-5,3) and radius 5. The old center was (-5,0). The radius stayed the same.
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Problem 11
<h3>Answer: (x-8)^2+(y-15)^2 = 9</h3>
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Work Shown:
x^2+y^2-16x-30y+280 = 0
(x^2-16x)+(y^2-30y)+280 = 0
(x^2-16x+64)-64+(y^2-30y+225)-225+280 = 0
(x-8)^2+(y-15)^2-9 = 0
(x-8)^2+(y-15)^2 = 9
This circle has center (8,15) and radius 3.
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Problem 12
<h3>Answer: (x+6)^2+(y-11)^2 = 20</h3>
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Work Shown:
x^2+y^2+12x-22y+137 = 0
(x^2+12x)+(y^2-22y)+137 = 0
(x^2+12x+36)-36+(y^2-22y+121)-121+137 = 0
(x+6)^2+(y-11)^2-20 = 0
(x+6)^2+(y-11)^2 = 20
This circle has center (-6,11) and radius sqrt(20) = 2*sqrt(5).
2⁽ˣ⁺¹⁾ = 3ˣ
ln[2⁽ˣ⁺¹⁾] = ln(3ˣ)
(x+1).ln(2) = x.ln(3)
Expand:
x.ln(2) + ln(2) = x.ln(3)
x.ln(2) - x.ln(3) = - ln(2)
x[ln(2) - ln(3)] = - ln(2)
x = [ - ln(2)] / [ln2) - ln(3)
And x = 1.7095
