# Posts by Reiny

Total # Posts: 38,760

Maths
I read the question as consisting of 3 legs of the journey. Funny thing is that I answered the same question back in February, as seen from the Related Question below. http://www.jiskha.com/display.cgi?id=1486127947 Damon's answer yields the same result

Maths
missing the distance along the 45° path

Maths
Make a sketch and you should have two similar triangles each of sides 5 and 8. Assumption: we will assume the ball travels in a straight line, and we will ignore the small actual curvature. The sum of the two acute angles in each triangle = 90° So the angle between the two...

6th grade AC math. Rates? I think
distance = 3(1/5) = 3/5 miles time = 3/2 minutes speed = distance/time = (3/5) / (3/2) mpm = (3/5)(2/3) mpm = 2/5 miles/minute or .4 miles/minute

Math - Calculus
let the height be y and each side of the base be x cm Surface area = SA = x^2 + 4xy = 1200 y = (1200 - x^2)/(4x) = 300/x - (1/4)x V= x^2 y = x^2(300/x - (1/4)x ) = 300x - (1/4)x^3 dV/dx = 300 - (3/4)x^2 = 0 for a max of V (3/4)x^2 = 300 x^2 = 1200/3 = 400 x = ?400 = 20 largest...

geometry
Look at one of the 8 congruent triangles. The height of one of those is 5 m and let the base be b each triangle has an area of 80/8 = 10 m^2 (1/2)(b)(5) = 10 5b = 20 b = 4 so we 8 sides of 4 m, for a perimeter of 32 m

Statistics
So he wants MMMH, where M is miss and H is hit prob(of your event) = (.35)^3 (.65) = ....

math
I made your sketch and filled in all the angles . From triangle MPQ QM/sin15 = 18/sin60 QM = 18sin15/(?3/2) = 16sin15/?3 in triangle RMQ cos15 = QR/QM QR = QM cos15 = (36sin15)/?3 * cos15 = 18(2sin15cos15)/?3 = 18(sin30)/?3 = 18(1/2) / ?3 = 9/?3 = 9/?3 * ?3/?3 = 9?3 /3 = 3?3

#2 buses arrive at : 7:00, 7:11, 7:22, 7:33, 7:44, 7:55, 8:06, 8:17, 8:28 Ahhh you just missed the 8:17, so ...... d) 8:28 - 8:18 = 0:10

Math
sin20(tan10+cot10) = sin20(sin10/cos10 + cos10/sin10) = 2sin10cos10(sin^2 10 + cos^2 10)/(sin10cos10) = 2(sin10cos10)/(sin10cos10 ( 1) = 2

Math
first stage: i = .03/12 = .0025 n = 9(12) = 108 second stage: i = .06/52 = .001153846 n = 8(52) = 416 after first stage: amount = 3290(1.0025)^108 = \$4308.33 after 2nd stage: amount = 3290(1.0025)^108(1.001153846)^416 = \$6960.66

Algebra
.01x + .06(12000-x) = .03(12000) take over

Trig
I am sure you meant: f(x)=4cos^2 x -3 for the x-intercepts: 4cos^2 x -3 = 0 cos^2 x = 3/4 cos x = ±?3/2 ---> so x is in all 4 quadrants. I know that cos ?/6 = ?3/2 so x = ?/6, ? - ?/6, ? + ?/6, and 2?-?/6 or x = ?/6, 5?/6, 7?/6, and 11?/6 for the y-intercept, let x...

statistics
prob(your event) = C(22,2)*C(15,1)/C(37,3) = 33/74

math- factoring
Your teacher wanted you to match up the corresponding terms. compare ax^2 + bx + c with 2x^2 - 13x + 21 , and it says they are equal so 2 matches with a, -13 matches with b, and 21 matches with c

Math
from sinØ = 2/5, sketch a right-angled triangle Use Pythagoras to find cos Ø cos^2 Ø + sin^2 Ø = 1 cos^2 Ø = 21/25 cos 2Ø = cos^2 Ø - sin^2 Ø, you should know that identity cos 2Ø = 21/25 - 4/25 = 17/25

Math
we know cos (2x) = 2cos^2 x - 1 so cos a = 2cos^2 (a/2) - 1 -31/49 + 1 = 2cos^2 (a/2) 18/49 = 2cos^2 (a/2) 9/49 = cos^2 (a/2) cos (a/2) = ± 3/7 but we were to assume that cos (a/2) is negative, so cos (a/2) = -3/7 Check with your calculator

math help
Sarah, I did this for you here http://www.jiskha.com/display.cgi?id=1489951802 I also do not see any posts by Cory, so it looks like Ms Sue has taken care of it, and banned him.

math
f(x)=7-2x In f(x+5) you have replaced the x with x+5, so do the same thing on the right side f(x+5) = 7 - 2(x+5) = 7 - 2x - 10 = -3 - 2x <-----> same as 7-(2x+10) , you had it

Trigonometry
LS = (sinx - sinx/cosx)^2 = ( (sinxcosx - sinx)/cosx )^2 = ( sinx(cosx - 1) )^2 / cos^2 x = (sin^2 x/cos^2 x)(cosx - 1)^2 = tan^2 x (cosx - 1)^2 = RS

MATH
let the sides be 4x , 3x, and x 2(4x)(x) + 2(4x)(3x) + 2(x)(3x) = 950 8x^2 + 24x^2 + 6x^2 = 950 38x^2 = 950 x^2 = 25 x = 5 the sides are 20 cm, 15 cm and 5 cm

Math
5 litres will take you 45 km 1 litre will take you 9 km so, 12 litres will take you 108 km or , just use a simple proportion: 5/45 = 12/x 5x = 540 x = 540/5 = 108

math
so the odds against multiple of three = (2/3) : (1/3) = 2 : 1 the odds in favour of multiples of three = 1 : 2

Math
smaller --- x larger ---- x+4 5x + x+4 = 58 take over

Algebra
parametric equations of the line L x = 1 - 2t y = -1 - 4t z = -5+ 3t plug those values into -x + y - 3z = -1 and solve for t once you have t, sub it back into the parametric equations to get the (x,y,z)

College Algerbra
By the "just look at it" theorem, I would say 5.2% as an instantaneous rate. If you want the rate per annum, compounded annually ..... e^(.052(1)) = 1.0533775... so appr 5.34%

algebra
5c^2-24cd-5d^2 What methods have you learned? What have you got so far?

Math 120
C(8,3) x C(7,3) = 56(35) = 1960

College Algebra
4/(x+7) +3 = -2/13 4/(x+7) = -2/13 - 3 4/(x+7) = -41/13 52 = -41x - 287 41x = -339 x = -339/41 <----- noting extraneous about that

Pre calc
I am positive that you meant: P(t) = 640 e^(kt) given: when t = 9, P(t) = 160 640 e^(9k) = 160 e^(9k) = .25 9k = ln .25 k = ln.25/9 = -.154033 640 e^( -.154033 t) = 40 e^(-.154033 t) = .0625 -.154033 t = ln .0625 t = ln .0625/-.154033 = 18 days

Math
Yes

Math
How many days in a year ???

Algebra
1/(Y+5) - 1/Y =1/10 <----- you had 10 LCD is y(y+5) y - (y+5) = y(y+5)/10 -50 = y^2 + 5y y^2 + 5y + 50 = 0 no real solution.

Calculus/Optimisation
Where is "s" in your question ?

Math
cost = 5000(1.0309)^15 = ....

Math
x(1.0583)^45 = 32000 x = appr \$2500 ------- ( 2498.93) reasonable , I paid \$24,000 for my new 1965 MGB sportscar back then

Calculus/Optimisation
number of \$6 increases ---- n right now: number rented = 80 rent = 180 after increase: rent = 180+6n number rented = 80-n revenue = (180+6n)(80-n) - 18(80-n) =14400 + 300n - 6n^2 - 1440 + 18n = -6n^2 + 318n + 12960 = -6(n^2 - 53n - 2160) d(revenue)/dn = -6(2n - 53) = 0 for a ...

Calculus/Optimisation
let the base be x m by x m , and let the height be y m V= x^2y 8 = x^2y ---> y = 8/x^2 Surface area = SA = x^2 + 4xy = x^2 + 4x(8/x^2) = x^2 + 32/x d(SA)/dx = 2x - 32/x^2 = 0 for a min of SA 2x = 32/x^2 x^3 = 16 x = 16^(1/3) = appr 2.52 m y = .....

math
speed of boat in still water ---- x km/h speed of current ------ y km/h distance with the current = 4(x+y) distance against the current = 5(x-y) we know that 3.5(x+y) = 70 x+y = 20 but 4(x+y) = 4(20) = 80 then 5(x-y) = 80 x-y = 16 x+y=20 x-y=16 add them 2x = 36 x = 18 , then y...

math
number of books on first shelf ---- x number of books on 2nd shelf ---- 55-x after re-location first shelf --- (55-x)/2 + x 2nd shelf ---- (55-x)/2 (55-x)/2 + x = 4(55-x)/2 times 2 55-x + 2x = 220 - 4x 5x = 165 x = 33 before the shift: 1st shelf ---- 33 books 2nd shelf ---- 22...

Math - Trigonometry
Did you make your sketch. After I filled in the angles I found angle A to be 90° so you have a right-angled triangle. Yeahhh, Pythagoras! I can find the other angles! tanB = 800/280 = ... angle B = appr 70.7° then angle C = 90-70.7 = 19.3° state the result as a &...

Math - Trigonometry
Like I pointed, as did writeacher, the ' here means minutes of angle, the seconds of angle would be '' so 30° 45' 4'' would be 30° + 45/60° + 4/3600° = 30 + .75 + .001111.. = 30.75111..°

Math - Trigonometry
Suggestion: Sketch a rectangle ABCD, with A at the topleft corner. AB as the width of 3.8 and AD as the length. Draw the diagonal BD. Now look at the right-angled triangle BCD angle DBC = 32° 15' The unit measure of and angle in common notation is the degree. There are...

Algebra
I think the key wording is "exactly one pair of parallel sides" That rules out square, rectangle, rhombus, parallogram, since those have opposite sides parallel, thus 2 paris of parallel sides. That leaves you with "trapezoid", sometimes called trapezium. ...

Math
smaller ---- x larger ----- x+21 2x + (1/2)(x+21) = 38 each term times 2 4x + (x+21) = 76 should be easy to solve for x

Mink high school MatheMatics
Ahh, now you are going to use a different formula amount = Principal (1 + i)^n , where i is the interest rate per interest period, and n is the number of periods for yours , i = .0625, and n = 6 plug in and work that calculator.

Maths
same stuff as before, show your steps so I can see if you are doing it correctly.

Maths
Use the same formula I showed you before

Maths
.9375x = 7.5

Maths
Done, when you were Regina

Maths
Interest = principal x rate x time rate = 6 1/4% = .0625 plug in the values

algebra
speed of passenger train ---- x km/h speed of express ------ x+20 km/h Time = distance/rate 360/x - 360/(x+20) = 3 , saying the difference in their times is 3 hours multiply each term by x(x+20), the LCD 360(x+20) - 360x = 3x(x+20) 3x^2 + 60x - 7200 = 0 x^2 + 20x - 2400 = 0 (x...

math
If 1 cm -----> 15 cm 5 cm -----> 5(15) or 75 cm 3 cm -----> .........

pre-Calculus
Use the Remainder theorem let f(x) = x^40 - 3 if f(x) is divided by x+1 , the f(-1) is the remainder, so f(-1) = ......

Math
I will assume you want to prove the identity to be true. The way you typed , the statement is NOT an identity You must have meant: (secx+tanx)/(secx- tanx) = (1+2sinx+sin^2x)/ cos^2x LS = (1/cosx + sinx/cosx) / (1/cosx - sinx/cosx) = ( (1+sinx)/cosx)/( (1-sinx)/cosx) = (1+sinx...

Algebra HELP ASAP!!!
You MUST know how to find the equation in the form y = mx + b, if given a point and the slope let's start with y = (3/5)x + b but (-3,-1) lies on it, so replace the x and y of the equation and solve for b PLug it back in and you are done!

Math
More information is needed. e.g. is the rectangle 55 by 100 or how about 50 by 110 , or how about 44 by 125 ? Each case would have a different semicircle at the ends.

Math
number of dogs --- 2x number of cats ---- 3x (notice 2x : 3x = 2 : 3 ) given: 2x + 3x = 15 5x = 15 x = 3 number of cats = 2x = 2(3) = 6 number of dogs = 3x = 3(3) = 9

Algebra
How many different riders could come in first ? 6 That leaves how many to come in second? 5 what is 6x5 ??

math
Number of \$3 tickets ---- x number of \$8 tickets ---- 4-x 3x + 8(4-x) = 22 solve for x and interpret or Number of \$3 tickets ---- x number of \$8 tickets ---- y then x+y = 4 3x + 8y = 22 solve for x and y and interpret

" I *think* it might be C but I'm not sure." Unacceptable in mathematics. If you know your material there is no such thing as "I'm not sure" Your lessons, text or notes will show the following steps to find the inverse: let y = 2x+4 step1: ...

number of ounces = 60(2.5) ounces = 150 ounces As I recall, there are 16 ounces in a pound, so .....

Calculus
I will assume that you are finding the derivative with respect to x. let u = x^2/35 or u = (1/35)x^2 let y = sin u dy/du = cos u , and du/dx = (2/35)x dy/dx = (dy/du)(du/dx) = (cos u)(2/35)x = (2x/35)cos (x^2/35) your aim will be to reach that final line directly.

Math Algebra
Steve's "big hint" applies to all 3 of your questions. I will use it on #3 comparing: y = ax^2 + bx + c , and y = -3x^2 - 12x + 3, ---> a=-3, b=-12, c=3 the x of the vertex is -b/(2a) = -(-12)/-6 = -2 which also means that the axis of symmetry is x = -2 to get...

maths
I assume you made a sketch. I sketched a right-angled triangle by letting the radius of the circular base of the cylinder to be r and the distance to the centre of the sphere to be be h then h^2 + r^2 = 18^2 ----> r^2 = 324 - h^2 volume of cylinder = ? r^2 (2h) = ?(324 - h^...

Math
I will use the sum and product of roots properties. for the given : sum of roots = p + q = 1/2 product of roots = pq = -4/2 = -2 new roots are p- q/p and q - p/q sum of new roots = p - q/p + q - p/q = p^2q + q^2p - q^2 - p^2 = pq(pq + qp) - ( (p+q)^2 - 2pq) = -2(-4) - (1/4 + 4...

math
sketch your triangle, I called BC = 21 , AB = 17 By the cosine law we can find angle B then sinB = altitude/17 altitude = 17sin B

math
number of dimes ---- x number of quarters ---- x+10 x + x+10 = 52 continue please

math
prob(2boys of 3 children) = C(3,2)(1/2)^2 (1/2) = 3/8 or, you could list them: BBB BBG BGB BGG GBB GBG GGB GGG There are 3 with 2 boys, 1 girl prob(your event) = 3/8

scrap my solution , go with Steve - calculus
messed up in 4th step.

calculus
I will assume that y3 is y^3 1/(y+x+3) * (dy/dx + 1) = x dy/dx + y + 3y^2 dy/dx plug in the point (-4,2) : 1/(2-4+3) * (dy/dx + 1) = -4dy/dx + 2 + 12 dy/dx 1/ln1 * (dy/dx + 1) = 2 + 8dy/dx arggghhh , 1/ln1 = 1/0, which is undefined so we have a vertical tangent at (-4,2) ...

Algebra 1
I assume you want to simplify the first two 1. (3?6 + 5?10)^2 - 286 + 60?15 You must know how to square a binomial ... = 54 + 30?60 + 250 - 286 + 60?15 = 18 + 60?15 + 60?15 = 18 + 120?15 2. the first part is the expansion of a difference of squares pattern, you must know that ...

Geometry
let the length, the width and the height be a , b, and c respectively make a sketch to see that 4a + 4b + 4c = 76 ---> a+b+c = 19 or c = 19 - a - b 2ab + 2ac + 2bc = 206 ---> ab + ac + bc = 103 abc = 165 or c = 165/(ab) 19-a-b = 165/ab 19ab - a^2 b - ab^2 = 165 ab(19 - a...

College statistics- SCWK450
You will find this most useful for these type of questions http://davidmlane.com/normal.html enter 78 and 4 for the mean and sd click on below and enter 80 you should get .6915 so appr the 69 percentile

sorry about the confusion , I just look back at my solution, that should have been 20 seconds (at 3 rotations per minute --> 1 rotation in 20 seconds) the math stays the same, t is in seconds

(?6)?(a+2b?3c?4d)?(?2)?(?4a?3b+2c+d) = -6a - 12b + 18c + 24d - (8a + 6b - 4c - 2d) = -6a - 12b + 18c + 24d - 8a - 6b + 4c + 2d = .....

math
A simple ratio will do it: h/16 = 2.5/4 solve for h

Maths
5 days : 20 hours = 120 days : 20 days = 120 : 20 = 6 : 1

Math (Sinking fund)
i = .078/12 = .0065 n = 25 payment --- P P( 1.0065^25) - 1)/.0065 = 16000 on my calculator ... P = 591.48

Math
i = .08/12 = .00666... don't round off, carry answer in your calculator's memory n = 72 amount accumulated = 255( 1.00666...^72 - 1)/.0066.... = 23,466.46

Algebra
x square-2(7x+16)=0 x^2 - 14x - 32 = 0 if = 16 is a root, then (x-16) is a factor so (x-16)(x + ?) = 0 to get a final product of -32 at the end of the quadratic, we need +2 in the second bracket (x-16)(x+2) = 0 so the other root is x = -2

Calculus
You need the intersection of y = e^x and y = e^2 e^x = e^2 so x = 2 then area = ? e^2 - e^x from 0 to 2 = [e^2 x - e^x] from 0 to 2 = 2e^2 - e^2 - (0 - e^0) = e^2 + 1

@Henry - pre calc
It said exponentially. You made it a linear decay.

pre calc
Both Scott and I did this for you here , and we both got the same answer http://www.jiskha.com/display.cgi?id=1489120237

math
We know that (a+b)^2 = a^2 + 2ab + b^2 = ...

I did this a few days ago http://www.jiskha.com/display.cgi?id=1488730046

Calculus
you have to integrate the velocity to get to distance let the distance be s(t) s(t) = (3/8)(t^2 - 1)^(4/3) + c s(0) = (3/8)(1) + c = c + 3/8 s(3) = (3/8)(8)^(4/3) +c = c + 81/8 distance = c+81/8 - (c + 3/8) = 39/4 ft

geometry
A(n)=-2+(n-1)(-2.2) = -2 - 2.2n + 2.2 = .2 - 2.2n since term numbers are labeled with whole numbers, n ? 1 and the first term is -2 and the common difference is -2.2 the fourth term = a + 3d = -2 + 3(-2.2) = -8.6 then tenth term = .....

further maths
Just use your formulas that you learned for this topic. sum of 8 terms = (8/2)(first + last) = 4(6 + 46) = 208 #2 sum(10) = (10/2)(2a + 9d) = 60 2a + 9d = 12 ** sum(15) = (15/2)(2a + 14d) = 165 2a + 14d = 22 *** subtract ** from *** 5d = 10 d = 2 sub into ** 2a + 18 = 12 a = -...

Work Ethics
Look at this post from last year. It contains all of your individual question all in one post http://www.jiskha.com/display.cgi?id=1472922204

I suppose you are solving ? x^2 - 5x - 5 = 0 It does not factor, so your other option are to complete the square or to use the quadratic equation. Your choice.

math
Use a Venn diagram with 3 overlapping circles named after the reason for failing, use C, H, T as suggested as their labels Place 8 in the intersection of all three. Now work on the intersection of two at a time. e.g. 14 would go in the intersection of C and T, but we already ...

Math
so the field is 300 by 200 m and the road would be 10 m by 300m Surely you can find the area of the road.

Math
width --- x length --- x+16 2x + 2(x+16) = 200 solve

mathematics steve
So you got your orange, leaving 14 fruits remaining. prob(mango) = 5/14

math
Ok, let's go with that So the number of boys is x , and so is the number of girls Total at the party = 2x boys with part-time jobs = x/4 girls with part time jobs = 2(x/4) = x/2 total part-timers = x/4 + x/2 = 3x/4 no part-time jobbers = 2x - 3x/4 = 5x/4 5x/4 = 30 x = 24 ...

Math
learly you are studying the quadratic function , which when graphed is a parabola. One of the first things you learn is how to find the vertex. Go to your text or you class notes to look at the example and do the same thing.

algebra
child's ticket --- x adult ticket ---- 3x 5x + 2(3x) = 98 take over

MATH
That would be an answer, since all we need is two numbers or expressions which when multiplied give us 6x^2-3x-3m^2. I have a suspicion that the middle term should be -3xm, then we could go further: 3(2x^2-x-m^2) = 3(2x + m)(x - m) but since we want only two factors, namely ...

Math
As you should know, Interest = Principal x Rate x Time in #1 and #2 question plug in the given values, and solve for the missing variable compound interest: Amount = Principal (1 + i)^n , where i is the interest per period, and n is the number of interest periods. Again, plug ...

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