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### Wilmington, DE (19810)

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# Rajesh's Responses in WyzAnt Answers

#### My height is 147cm and my new height size is 30.5cm. I need to know how to set this up as a proportion and solve it.

Thanks for the help!

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Asked by David from Marcus Hook, PA
10

Ratio of height to new height = height:new height = 147/30.5 = 4.82

This is a ratio problem and not a proportion problem.

Ratio is the answer obtained by dividing two similar quantities (quantities with same units). We use symbol : to specify ratio.

Equality of two ratios is called proportion. We indicate that ratio of a/b is same as ratio of c/d as follows.

a/b=c/d or a:b = c:d

In a proportion problem, normally one of the 4 variables is unknown and we can solve for it as follows.

e.g.

3/4 = x/12, find x.

3/4 = x/12....multiply both sides by 12

3/4 * 12 = x/12 * 12 ....simplify

3 * 3 = x

x = 9

#### Limit questions

Evaluate the limit..

Lim x-->0    1-cos 5x / 1-cos 7x

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Asked by Aqib from Carrollton, TX
00

Let us first simplify the equation.

(1-cox5x)/(1-cos7x) .... multiply numerator and denominator by (1+cos5x)(1+cos7x)

=[(1-cos5x)(1+cos5x)(1+cos7x)]/[(1-cos7x)(1+cos7x)(1+cos5x)]......remember that (a+b)(a-b)=a2-b2

=[(1-cos25x)(1+cos7x)]/[(1-cos27x)(1+cos5x)]  ....1-cos2x = sin2x

=[sin25x(1+cos7x)]/[sin27x(1+cos5x)]....rearrange and multiply and divide by 25x2.49x2

=[25x2.sin25x/25x2][49x2/(49x2sin27x)][(1+cos7x)/(1+cos5x).....rearrange

=(sin5x/5x)2.(7x/sin7x)2.(25x2/49x2).(1+cos7x)/(1+cos5x)

now simplify and take limit. Remember that limit x->0 (sinx/x) = 1

=(25/49) . lim x->0 (sin5x/5x)2 . lim x->0 (7x/sin7x)2 . lim x->0 (1+cos7x)/(1+cos5x)

=(25/49).1.1.(1+cos0)/(1+cos0) = (25/49).(2/2)

=25/49

#### equation of a locus

Find the equation of a locus of moving point such that the slope of line joining the point to A(1,3) is three times that of the slope of the line joining the point to B(3,1)

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Asked by Aqib from Carrollton, TX
00

Let the moving point P be (x, y)

remember that slope m of line joining points (x1, y1) and (x2, y2) is m = (y1-y2)/(x1-x2)

slope of line joining point P(x, y) to A(1, 3) is (y-3)/(x-1)

slope of line joining point P(x, y) to B(3, 1) is (y-1)/(x-3)

We have been told that, slope of PA = 3 x slope of PB

(y-3)/(x-1) = 3 (y-1)/(x-3) ......multiply both sides by (x-1) (x-3)

(x-3)(y-3) = 3 (y-1)(x-1)

xy-3x-3y+9=3(xy-y-x+1)=3xy-3y-3x+3....subtract xy-3x-3y+9 from both sides

0 = 2xy -6 = 2(xy-3) = 0

xy -3 = 0 ...add 3 to both sides

xy = 3

y = 3/x is the equation of the locus

#### 2.4 mil libs price sold 5.50 per lb amd 4.8 mil libs 4.50 ld. what linear function 1(p) expresses the amount

of almonds sold as a function of the price per pound

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Asked by Dawn from Bellmore, NY
10

Let me restate this cryptic question.

2.4 million lb (pounds) of almonds are sold when the selling price is \$5.50 per lb.

4.8 million lb (pounds) of almonds are sold when the selling price is \$4.50 per lb.

What linear function expresses the amount of almonds sold as a function of the price per pound?

Here selling price is the independent variable (x-axis) and almond sales in pound is a function of price (y-axis).

We can see that as price of almonds goes up, its sales decrease. So we expect a negative slope for this linear equation line.

Here we need to find the equation of line that passes through two points (x1, y1)=(5.5, 2.4) and (x2, y2)=(4.5, 4.8).

Solution using equation of line in 2 points form

(y-y1)/(y1-y2) = (x-x1)/(x1-x2) substitute co-ordinates of above two points in this equation

(y - 2.4)/(2.4 - 4.8) = (x - 5.5)/(5.5 - 4.5)

(y-2.4)/(-2.4) = (x - 5.5)/1

(y-2.4)/(-2.4) * -2.4 = (x - 5.5)/1 * -2.4 multiply both sides by -2.4

y - 2.4 = -2.4 (x - 5.5)

y - 2.4 = -2.4x + 13.2 ...remember when you multiply 2 negative numbers, you get a positive number

y - 2.4 + 2.4 = -2.4x + 13.2 + 2.4

y = -2.4x + 15.6 (where x is price per pound of almonds and y is almonds sold in million pounds)

Alternative method by using slope-intercept form

Equation of line is given by

y = mx + c where m is the slope and c is the y-intercept

Slope of line passing through two points (x1, y1) and (x2, y2) is m = (y1-y2)/(x1-x2)

y = mx + c ....substitute above value of slope m.

y = (y1-y2)/(x1-x2)*x + c where c is the constant y-intercept

Substitute values of (x1, y1) and (x2, y2) in this equation

y= (2.4 - 4.8)/(5.5 - 4.5) *x +c

y=-2.4/1 *x +c y=-2.4x+c...................(1)

substitute (x1, y1) = (5.5, 2.4) in above equation to solve for c

2.4 = -2.4*5.5 +c

2.4 = -13.2 +c ....add 13.2 on both sides to get value of c

2.4 + 13.2 = -13.2 +c + 13.2

15.6 = c Substitute this value in equation (1) above to get

y = -2.4x + 15.6

Check:

We see that slope of the linear equation is negative. This is as expected.

substitute x = 5.5 in above equation and see if you get y = 2.4

substitute x = 4.5 in above equation and see if you get y = 4.8

#### Consider the following special types of polynomials.

difference of squares, perfect square, sum or difference of cubes in order to answer the question for each case

Which of the special types of polynomial models would you use to easily factor the following expressions? Explain and complete factor them.

1) 16y^2+ 24y + 9

2) 49x^2 – 100y^2

3) 27x^3 + 64y^3

4) x^3 - 125

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Asked by Jamal from Oregon, OH
00

1) use perfect square formula a2+2ab+b2=(a+b)2

16y2 + 24y + 9 = (4y)2 + 2.4y.3 + 32 = (4y+3)2

2) use difference of squares formula a2 - b2 = (a+b)(a-b)

49x2 - 100y2 = (7x)2 - (10y)2 = (7x-10y)(7x+10y)

3) use sum of cubes formula, a3 + b3 = (a+b)(a2-ab+b2)

27x3 + 64y3 = (3x)3 + (4y)3 = (3x+4y)(9x2-12xy+16y2)

4) use difference of cubes formula, a3 - b3 = (a-b)(a2+ab+b2)

x3 - 125 = x3 - 53 = (x-5)(x2+5x+25)

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