Thursday

October 2, 2014

October 2, 2014

Total # Posts: 27,219

**Calc Help Please Again!**

can't tell if your equation is y = e^(x+4) or y = e^x + 4 , why is there a 1 in front of the x ?
*May 16, 2014*

**Calc Help Please**

I got (1/4) (ln(x-2) - ln(x+2) ) + c how did your x-2 from the original denominator turn into 2-x) I used partial fractions
*May 16, 2014*

**Geometry**

make a sketch to see that height/36 = tan 25° height = 36tan25 = appr 16.8 ft
*May 16, 2014*

**Algebra**

yes
*May 16, 2014*

**alegbra**

my equation, (very close to yours) 225500 = PV e^(8.4246575(.0855)) 225500 = PV e^(.720308219) , now press 2nd ln 225500 = PV (2.055066524) PV = 109,728.81 I let the calculator carry all the decimal places and only rounded off my final answer to the nearest cent. You were off ...
*May 16, 2014*

**math**

distance = √( (-3-8)^2 + (-10+10)^2) = √(121 +0) = √121 = 11 We can see this without any calculation. Since the x values are the same for both points, the line is a vertical one. So all we have to do is take the difference between -3 and 8 , which is 11
*May 16, 2014*

**math**

number of $5 tickets --- x number of $10 tickets --- y number of $15 tickets ---- 180-x-y x + (180-x-y) = 2y x + 180 - x - y = 2y 180=3y y = 60 income equation: 5x + 10y + 15(180-x-y) = 1900 5x + 600 + 15(120-x) = 1900 5x - 15x + 600 + 1800 = 1900 -10x = -500 x = 50 x=50 y=60 ...
*May 16, 2014*

**math(compound interest )**

What you wanted as an equation is ... [ x( 1 + .1/360)^20 - 600 ](1+.1/360)^108 = 8900 x(1+.1/360)^20(1+.1/360)^108 - 600(1+.1/360)^108 = 8900 x((1.00557024)((1.03045024) - 618.2701442 = 8900 x(1.036190095 = 9518.270144 x = 9185.83
*May 16, 2014*

**math trigonometry**

I don't understand your question. Are we looking at two different equations ? Are we solving 10 sec Ø + 13sinØ = 0 and 5tan Ø - 12 = 0 ???? or .... ? is (0,90°) the domain?
*May 15, 2014*

**Algebra 1**

first equation: -2x - 2y = 4 ----> x+y = -2 2nd equation: 2y = -2x - 4 2x + 2y = -4 x + y = -2 looks like they are the same line, so you have one line any ordered pair that works in one of them, will work in the other. There will be an infinite number of solutions.
*May 15, 2014*

**Math-- Ms. Sue??**

#1 , wrong. If you plot your points you will see that it is (8,5) notice that now two pairs of points have the same x , making the lines vertical, and 2 pairs of points have the same y, making the horizontal. #2, ok #3, ok #4, your answer: (5,-4) and (-2,1) -- slope = (1-(-4...
*May 15, 2014*

**Math**

prob(brown, then violet) = (8/16)(1/16) = 1/32
*May 15, 2014*

**Math - Int Trig**

y = √x shift up 4 units -----> y = √x + 4 reflect about the y-axis ---> y = √-x + 4 , for x ≤ 0 shift right 2 units -----> y = √(-(x-2)) + 4 , x≤2 again, Wolfram verifies this http://www.wolframalpha.com/input/?i=y+%3D+√%28-%...
*May 15, 2014*

**Math - Int Trig**

start: y = |x| shifted right : y = |x-3) stretched by factor of 3 : y = 3|x-3| vertically down 2: y = 3|x-3| - 2 reflected about x-axis y = -3|x-3| + 2 behold the wonders of Wolfram http://www.wolframalpha.com/input/?i=y+%3D+%7Cx%7C+%2C+y+%3D+%7Cx-3%7C+%2C+y+%3D+3%7Cx-3%7C+%2C...
*May 15, 2014*

**math**

multiply each of the prob. answers I just gave you by 100
*May 15, 2014*

**math**

Four possible outcomes: HH HT TH TT prob(HH) = 1/4 prob(TT) = 1/4 prob (TH or HT) = 2/4 = 1/2 notice the 3 answers add up to 1, since one of those possibilities must happen
*May 15, 2014*

**Geometry**

(-3,-1) ---- dilation factor of 2 ----> (-6, -2) show it by plotting the two points how does the distance to the origin change ?
*May 15, 2014*

**Algebra 1**

looks like f(3) = 2 then g( f(3) ) = g(2) = -3
*May 15, 2014*

**Trig 3**

sloppy way of writing the trig expressions ( when you write tan2, you are asking for the tan(2 radians. What you meant was something like tan^2 Ø It has to be the sine of something, the cosine of something, or the tangent of something. anyway ..... (1 - cos^2 Ø)/...
*May 15, 2014*

**Geometry**

Any regular n-gon can be changed to n isosceles congruent triangles by drawing all radii to the vertices of the polygon. the area of a triangle = (1/2)(base)(height) the area of one of these = (1/2)(side)(apothem) where the apothem is the distance from the centre of the ...
*May 15, 2014*

**math(compund interest )**

Major Hint: Did you notice that from 16 April to 16 Oct is 6 months? So your time can be very easily expressed in half-years, and quarter-years. From all the knowledge you have gained by having received many answers for similar questions to the above, you should now be able to...
*May 15, 2014*

**mathematics for management**

NO you used the concept of continuous compounding but it said it was compounded monthly Even with the above in consideration your expression of 8888(e^0.06(0.25)) makes absolutely no sense. i = .06/12 = .005 n = 3(12) = 36 months PV = 8888(1.005)^-36 = $7427.21 For a single ...
*May 15, 2014*

**math**

How do you expect us to know what table you are working from. With today's excellent scientific calculators, the use of "tables" that were found in the back of most textbooks in the past is no longer common practise. Your question is simply PV = 100000(1.05)^-50...
*May 15, 2014*

**math**

what is 20000(1.06)^15 ?
*May 15, 2014*

**math(urgent)**

Just use the formula. Amount = payment( (1+i)^n -1)/i Amount = 1000(1.08)^3 -1)/.08 = 3246.40
*May 15, 2014*

**Trig**

3x^2 + 4y^2 = 12 divide by 12 x^2/4 + y^2/3 = 1 we know sin^2 t + cos^2 t = 1 so sin^2 t = x^2/4 = (x/2)^2 ---> sin t x/s ----> x = 2sin t and cos^2 t = y^2/3 = (y/√3)^2 cos t = y/√3 ----> y = √3cos t x = 2sint y = √4cost confirmation: http://...
*May 14, 2014*

**Calculus**

dy/dx = 2tan (x^4) * sec^2 (x^4) * 4x^3
*May 14, 2014*

**ALGEBRA**

using the ratios, let the width be 8x and the length be 15x led d be the diagonal d^2 = (8x)^2 + (15x)^2 = 64x^2 + 225x^2 = 289x^2 d = 17x or x = d/17 width = 8x = 8d/17 length = 15x = 15d/17
*May 14, 2014*

**geometry**

volume of similar solids is proportional to the cube of their corresponding sides so ratio of volume = 3^3 :^3 = 27 : 125
*May 14, 2014*

**Math**

so you want 9(2)(t/9) = 1000000 2^(t/9) = 111,111.111.. t/9 log2 = log111111.11 t/9 = log111111.11../log 2 = 16.7616.. t = 150.8548 years so 1909 + 150.8548 yrs = appr 2060 just what Ms Sue got by continuing her chart.
*May 14, 2014*

**math**

1.75 years = 21 months monthly rate = .18/12 = .015 PV = 900(1.015)^-21 = $658.35
*May 14, 2014*

**math**

100% of something = the whole thing or 1 50% of something = .5 or 1/2 of the whole thing = .5 145% of something = 1.45 yes, C is the right choice.
*May 14, 2014*

**math (urgent )**

my answer confirmed by Wolfram http://www.wolframalpha.com/input/?i=13.875-0.1875%2856.375%29%2F8-2+%281%2F8%2B27.125%2F300.875%29+
*May 14, 2014*

**math (urgent )**

This is what you typed: 13.875-0.1875(56.375)/8-2 (1/8+27.125/300.875 I added a bracket at the end, or else they are mismatched. Followed the order of operation, and got 12.1234035... The way you wrote it, there is now way to get 1.1908 check how you placed your brackets.
*May 14, 2014*

**Geometry Help & Proofs**

based on : ratio of volumes is proportional to the cube of their corresponding sides. so ratio of volumes: A : B = 1 : 5 A : C = 1^3 : 2^3 = 1 : 8 B : D = 1^3 : 3^3 = 1 : 27 A/B = 1/5 B = 5A A/C = 1/8 C = 8A B/D = 1/27 D = 27B ratio of volume of C :D = 8A : 27B = (8/27)(A/B...
*May 14, 2014*

**Math**

9/9 = 1 = 12/12 2/3 = 8/12 5/6 = 10/12 4/12 = 4/12 0/2 = 0 , obviously the smallest now can you tell ?
*May 12, 2014*

**Algebra**

(x - y) (3x + xy - 4y) + xy^2 - x^2y = (x-y)(3x + xy - 4y) - xy(x - y) = (x-y)(3x + xy - 4y - xy) = (x-y)(3x - 4y)
*May 12, 2014*

**Math**

The total of the first 16 students' marks was 16x66 or 1056 the total of the new students' marks was 6x74 or 444 so the total of the 22 students was 1500 giving an average of 1500/22 or appr 68.2
*May 12, 2014*

**finance**

WoW! I recognize the formula Future Value = Present Value (1 + i/n)^(cn) where n is the frequency of compounding per year and c is the number of years from your (1.089/12)12*5 I gather that the interest rate was 8.9 % per annum compounded monthly , for a time of 5 years and ...
*May 12, 2014*

**Algebra 1 Answer Evaluation**

anything squared cannot be negative in the real number set, so your first one has no real number solution 2. correct
*May 12, 2014*

**math**

distance (d) ∝ time (t) d = kt case 1: when t = 2 , d = 90 90 = k(2) k = 45 so d = 45t , the constant of proportionality is 45 the unit rate is 45 mph check on the others t = 3 --> d = 45(3) = 135 ✔ t = 5 --> d = 45(5) = 225 ✔ t = 6 --> d = 45(6...
*May 12, 2014*

**Algebra 1 (Reiny)**

x^2 + 3x - 18 = 0 (x+6)(x-3) = 0 x = -6 or x = 3
*May 12, 2014*

**MATH: TRIG**

you should recognize the 3-4-5 right angled triangle. so if cosx = 3/5 then sinx = 4/5 sin 2x = 2sinxcosx = 2(4/5)(3/5) = 24/25 you can always check your result with a calculator.
*May 12, 2014*

**Maths**

use substitution x^2 + 3x - 5 = x-2 x^2 + 2x - 3 = 0 (x+3)(x-1) = 0 x = -3 or x = 1 check with Wolfram http://www.wolframalpha.com/input/?i=Y%3Dx-2+%2C+Y%3Dx%5E2%2B3x-5 if x = -3, y = -3-2 = -5 if x = 1 , y = 1-2 = -1 x=-3, y=-5 ---> point (-3,-5) x = 1 , y = -1 --->...
*May 12, 2014*

**Algebra II**

quick way: for any linear equation written in the form Ax + By + C = 0 the slope is -A/B so here, the slope is -6/5
*May 12, 2014*

**math**

Don't post the same question using different names please.
*May 12, 2014*

**math**

3+x/7+x= 3/7 + 3/7 I would multiply each term by 7 , the LCD 21 + x + 7x = 3+3 8x = -15 x = -18/8 I seriously suspect a typo
*May 12, 2014*

**math**

3(40+x) = (2+3)(3+4)(4+5) 120 + 3x = 5(7)(9) = 315 3x = 195 x = 65
*May 12, 2014*

**geometry**

He has not seen 5 of the comedies and 7 of the dramas Since you want the non-seens from one OR the other there are 12 movies he has not seen prob(nonseen) = 12/18 = 2/3
*May 12, 2014*

**Algebra 1--Please, help me!**

1. 4x^2 + 8x = 32 4x^2 + 8x - 32 = 0 x^2 + 2x - 8 = 0 let y = x^2 + 2x - 8 now graph this, and look at where it crosses the x-axis. From Wolfram's graph http://www.wolframalpha.com/input/?i=y+%3D+x%5E2+%2B+2x+-+8 we can see x = -4 or x = 2 2. x(x + 3) = 32 x^2 + 3x - 32 = ...
*May 12, 2014*

**oops - MATH**

just noticed an arithmetic error.. in my evaluation of y, should be 60 - 2x = 60-2(20) = 20 so ..... max profit is 30(20) + 50(20) or 1600 , when 20 of the first product and 20 of the second product are made
*May 12, 2014*

**MATH**

let the number of the first product be x let the number of the 2nd product by y So we need to look at the regions 2x+y ≤60 and x+y≤30 and x+3y≤80 The profit function is 30x+50y which has a slope of -3/5 move that profit line to the right, parallel to itself, ...
*May 12, 2014*

**Math**

I tried a slightly different approach I looked at the trapezoid, and drew two verticals upwards from the base, creating a rectangle of 25 by 50 cm and two right-angled triangles , each of height 50 and base 75/2 I drew a water line, of height h and width of r in each of the ...
*May 12, 2014*

**Math**

You don't have an equation, so "solving" is the wrong instruction. are you expanding 2a(a^2 + 4a) ? then... = 2a^3 + 8a^2
*May 11, 2014*

**algebra**

I don't know what h=−16t<E> 6<E>+s is supposed to say, but I know that h = -16t^2 is the relation between t seconds and the distance fallen in feet Since we just want to find the distance, let's use h = 16t^2 when t = 3 h = 16(9) = 144 feet If this is...
*May 11, 2014*

**Math**

slope for the first 2 points = (0-1)/(4-2) = -1/2 y = -1/2 x + b , but (2,1) lies on it 1 = -(1/2)(2) + b b = 2 y = -(1/2)x + 2 check if third point is on it LS = -1 RS = (-1/2)(6) + 2 = -1 yes, all is good y = (-1/2)x + 2
*May 11, 2014*

**Math**

nothing to "solve", you don't have an equation. did you mean: evaluate 5(3^n) for n = 1,2,3, ... then you would get 5(3) , 5(9), 5(27), 5(81) .. = 15, 45, 135, 405, looks like that is what you are doing, if so, you are correct.
*May 11, 2014*

**Math**

First of all you have not defined x and y Secondly, 2(x+y) does not look like an area, it looks like the perimeter of the original rectangle. I will attempt it anyway: I drew a rectangle of length x and width y I then drew two lines, one parallel to the length, the other ...
*May 11, 2014*

**MATHHH**

case1: no defence in 1st row - we can choose any 6 of the 8 players = C(8,6) = 28 case2: 1 defence - four ways to choose the defenseman, choose 5 from the remaining 8 = 4 x C( 8,5) = = 224 Case3 : 2 defense = C(4,2) x C(8,4) = 420 total = 28+224+420 = 672 for choosing the 6 ...
*May 11, 2014*

**Math**

first do this: 4√6/√30 = 4/√5 now multiply top and bottom by √5 4/√5 * √5/√5 = 4√5/5
*May 11, 2014*

**alegbra**

first of all your "equation" makes no sense. LS = 25 RS = 1/25 25 ≠ 1/25 secondly , equations tend you have a variable in there somewhere, else it simply becomes a mathematical statement which is either true or false e.g. 2+3 = 4 --- false 1+1 = 2 ---- true ...
*May 11, 2014*

**alegbra**

amount = initial (.5)^(t/5730) .75 = 1 (.5)^(t/5730) log .75 = (t/5730) log .5 t/5730 = log .75/log .5 = .415... t = 2378.16 age is about 2400 years to the nearest century
*May 11, 2014*

**math**

The way the question stands, the "bottom" of the kite could be any length along the missing part of the diagonal. The angle at the shorter diagonal's end wasn't a right-angle ?
*May 11, 2014*

**math**

I think we are missing information Was there an angle given?
*May 11, 2014*

**ALGEBRA**

13.29 = 14.7 e^(.21a) .90408.. = e^(.21a) by rules of logs .21a = ln .90408... .21a = -.0100835.. a = -.48016 miles or - 2535 ft below sealevel !!!!!!! Wow, since the lowest point in North America, Death Valley is only about 260 ft below sea level, you city is a mystery. ... ...
*May 11, 2014*

**Math**

The surface area is proportional to the square of their radii (1.5r)^2/r^2 = x/36π 2.25/1 = x/36π x = 2.2(36π) = 81π
*May 11, 2014*

**Math**

From 1 to 10, isn't 6 the only number divisible by both 3 and 2 ? so prob = 1/10
*May 11, 2014*

**math 7Probability help**

mmmmmhhhhh possible sums of 2 dice is 2 , 3, 4, .... 11, 12, there are 11 of those the evens are: 2 4 6 8 10 12 or 6 of them so prob(even sum) = 6/11
*May 10, 2014*

**Finance**

I will do the last one, you do the other two in the same way c) PV = 5000(1.09)^-4 = $3542.13
*May 10, 2014*

**Math**

suppose we just look at 1/3^x (1/3^x - 2) = 15 3^-x(3^-x - 2) = 15 let 3^-x = a for easier typing then we have a(a-2) = 15 a^2 - 2a - 15 = 0 (a-5)(a+3) = 0 a = 5 or a = -3 3^-x = 5 log 3^-x = log5 -x log3 = log5 -x = log5/log3 x = -log5/log3 the other part of 3^-x = -3 has no ...
*May 10, 2014*

**MATHHH**

success if you draw 2 granolas or 2 fruits or 2 cheese prob(success) = (12/30)(12/30) + (10/30)(10/30) + (8/30)(8/30 = 4/25 + 1/9 + 16/225 = 77/225
*May 10, 2014*

**maths**

I will use a for alpha and b for beta then from the properties of zeros of a quadratic a+b = -1 ab = 1 then 1/a + 1/b = (b+a)/(ab) = -1/1 = -1 a^2 + b^2 = (a+b)^2 - 2ab = (-1)^2 - 2(1) = 1 - 2 = -1
*May 10, 2014*

**Math**

You could do the tedious task of expanding and then collecting powers of y^3. I let Wolfram do this for me http://www.wolframalpha.com/input/?i=expand+%281%2By%2Bky%5E2%29%5E7 It might be easier to read the expansion in reverse order 1 + 7y + 21y^2 + ... Notice that y^3 ...
*May 10, 2014*

**Calculus Please Help**

What a mess! http://integrals.wolfram.com/index.jsp?expr=sqrt%28100x%5E2-400%29%2Fx&random=false add C to the result
*May 9, 2014*

**Alegbra**

I suspect that this is a log question and your IN is actually ln ( the natural logarithm) so let's try: t = -62.5 ln(1 - N/80) or is it t = -62.5 ln( (1-N)/80) look at the first of the Related Questions below. It is the same question and Steve had his doubts about the same...
*May 9, 2014*

**Math**

1^2-(2-x)^2=2^2-x^2 1 - (4 - 4x + x^2) = 4 - x^2 1 - 4 + 4x - x^2 = 4 - x^2 4x = 7 x = 7/4 I don't understand why a textbook would write a term as 1^2 and 2^2 in an equation. That is just silly.
*May 9, 2014*

**Algebra (proportions)**

let the number of bears be x 50/x = 2/100 2x = 5000 x = 2500
*May 9, 2014*

**Calculus**

y = u^3 + u^2 - 1 dy/du = 3u^2 + 2u u = 1/(1-x) = (1-x)^-1 du/dx = -1(1-x)^-2 (-1) = 1/(1-x)^2 when x = 2, u = 1/(1-2) = -1 du/dx = 1/(1-2)^2 = +1 dy/du = 3(-1)^2 + 2(-1) = 1 dy/dx = dy/du * du/dx = 1(1) = 1 check my arithmetic, I made several arithmetic errors tonight.
*May 9, 2014*

**Math**

It didn't, n = 0 became a solution. Are you not familiar that if you have a factored form = 0, such as (A)(B) = 0 , then A = 0 or B = 0 ???
*May 9, 2014*

**Math**

I took out a common factor of n expand n(1-2n) What do you get ?
*May 9, 2014*

**Math**

n(1 - 2n) = 0 n = 0 or 1 - 2n = 0 n = 0 or n = 1/2
*May 9, 2014*

**Calculus**

y= sqrt[(3x^2+2)^3] = (3x^2 + 2)^(3/2) dy/dx = (3/2)(3x^2 + 2)^(1/2) (6x) = 9x(3x^2+2)^(1/2) or = 9√(3x^2 + 2) , which is valid for all values of x since (3x^2 + 2) is always positive.
*May 9, 2014*

**oops - Algebra**

looks like I can't do a simple subtraction of course 50-32 = 18 as MathMate had
*May 9, 2014*

**Algebra**

let amount of stronger solution to be used be x L amount of weaker solution is 50-x L .8x + .3(50-x) = .62(50) .8x + 15 - .3x =31 .5x = 16 x = 16/.5 = 32 needs 32 L of the stronger and 36 of the weaker solution.
*May 9, 2014*

**math**

.48x = .35 x = .35/.48 = appr .73
*May 9, 2014*

**Algebra**

original width --- x original length --- y xy= 280 y = 280/x new width --- x+1 new length --- y-5 new area = (x+1)(y-5) = (x+1)(280/x - 5) = 280 - 5x + 280/x - 5 = 275 - 5x + 280/x = (275x - 5x^2 + 280)/x = -5( x^2 - 55x - 56)/x perfect squares in the neighbourhood of 280 are ...
*May 9, 2014*

**Algebra**

1/12 = 1/30 + 1/r The LCD is 60r , so multiply each term by 60 r 60r(1/12) = 60r(1/30) + 60r(1/r) 5r = 2r + 60 3r = 60 r = 20 or 1/12 - 1/30 = 1/r 5/60 - 2/60 = 1/r 3/60 = 1/r 1/20 = 1/r cross-multiply r = 20
*May 9, 2014*

**Algebra**

rate of passenger boat --- x mph rate of freighter --------- x-6 mph 2592/(x-6) - 2592/x = 72 , assuming they travel 24 hours per day multiply each term by x(x-6) 2592x - 2592(x-6) = 72x(x-6) 2592x - 2592x + 15552 = 72x^2 - 432x 72x^2 - 432x - 15552 = 0 9x^2 - 54x - 1944= 0 (x...
*May 9, 2014*

**Calculus**

#1 ??? #2. dy/dx = x cos x^2 y = (1/2) sin x^2 + C when x=0, y = -3 -3 = (1/2) sin 0 + c -3 = 0 + c c = -3 so y = (1/2)sin x^2 - 3 when x = π y = (1/2) sin (π^2) - 3 = -3.215... #3. let N = a e^(kt) when t = 2 ---> 100 = a e^(2k) when t = 4 ---> 300 = a e^(4k) ...
*May 9, 2014*

**Algebra**

From the choices of answers, I think you typed the equation incorrectly Looks like it should be y = 3√(6x+42) since we cannot take the square root of negatives, 6x + 42 ≥ 0 6x ≥ -42 x ≥ -7 , which is your last choice.
*May 9, 2014*

**Calculus**

at its vertex. the x of the vertex is -b/(2a) = -40/-10 = 4 it will change direction at t = 4 seconds
*May 9, 2014*

**Math**

There can't be a^2 in your answer just looking at the a's you had a^2/a^3 which is 1/a once more: 54 a^2 b^3 ___________ 81 a^3 b^2 = (3/2) (1/a) (b) = (3/2)b/a or 3b/(2a)
*May 9, 2014*

**Math**

You are right, I should have had (3/2)b/a or 3b/(2a)
*May 9, 2014*

**Math**

54 a^2 b^3 ___________ 81 a^3 b^2 = (54/81)(a^2/a^3)(b^3/b^2) = (2/3) b/a or 2b/(3a) I don't see that choice, but that is your answer.
*May 9, 2014*

**calculus-answer check**

1st two are corrrect #3. my derivative was f ' (x) = 15(x+1)(x-1)^9 (x+2)^4 = 0 for x = -1, 1, -2 verify at Wolfram http://www.wolframalpha.com/input/?i=plot+y+%3D+%28x-1%29%5E10%28x%2B2%29%5E5
*May 9, 2014*

**Algebra**

t=√(d/16) so you want √(d/16) > 1 square both sides d/16 > 1 d > 16
*May 9, 2014*

**Mathematics**

sketch triangles in quad 2 and quad 1 for the given info if sin a = 3/5 in II cos a = -4/5 if sin b = 5/13 in I cos b = 12/13 sin(a+b) = sina cosb + cosa sinb = (3/5)(12/13) + (-4/5)(5/13) = (36 - 20)/65 = 16/65
*May 9, 2014*

**math**

(3/5)(84+72+96)/3 + (2/5)x ≥ 80 times 5 84+72+96 + 2x ≥ 400 2x ≥ 148 x ≥ 74 check: average of first 3 tests = 84 going towards final mark = (3/5)(84) = 50.4 final mark = 74 (2/5) of that is 29.6 final mark = 50.4 + 29.6 = 80
*May 9, 2014*

**MATH**

two identities you should have in your bag of ID's is csc^2 Ø -1 = cot^2 Ø , and sec^2 Ø - 1 = tan^2 Ø LS = left side = csc^2 Ø - 1 + sec^2 Ø - 1 = csc^2Ø + sec^2 Ø - 2 = 1/sin^2 Ø + 1/cos^2 Ø - 2 = (cos...
*May 9, 2014*

**Maths**

For this one the 30-60-90° and the 45-45-90° right-angled triangles are your friend. from those you should know cos30°= √3/2 sin30° = 1/2 cos60° = 1/2 sin60° = √3/2 sin45° = √2/2 cos45°=√2/2 cos15 = cos(45-30)° = ...
*May 9, 2014*

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