# Posts by MathMate

Total # Posts: 12,086

**Trigonometry**

set sin²(x) = 1-cos²(x) 16(1-cos²(x))=16-8cos(x) and substitute c=cos(x) 16c²-8c=0 c(2c-1)=0 c=0 or c=1/2 Find all solutions for c=0 in [0,2π) and all solutions for c=1/2 in [0,2π). Substitute back the solution and check that they are valid.

**Math**

Tia, You may or may not realize that here there are tutors who answer 50 to 100 posts a day on a voluntary basis just in order to help students. Any repeated post may get read 8 times by 8 different tutors, and worse, could also end up with a duplicate answer which you may not...

**statistics**

To get the first number right is 1 out of 31 choices. For the second number, there are only 30 choices (five different numbers)... So the probability of getting all five numbers right would be: (1/31)(1/30)...(1/27).

**calculus**

Calculus question: Let x=length remaining below winch. and ρ=mass density Work done winding up a length of dx is equivalent to bringing the length dx up by a distance of x, i.e. dW=ρg xdx Integrate W=ρg∫xdx from 0 to L =ρg L²/2 Physics question: ...

**STATS**

Initially, 49 out of 55 returns do not contain errors. So probability of selecting the first (first trial) correct return is 49/55. After this, there are 48 correct returns out of 54, so....48/54 For all three trials to succeed, we multiply the probabilities of all three ...

**statistics**

The probability for at least one correct answer, P(X>=1) is the same as probability of not getting ALL wrong answers or 1-P(X=0). P(X=0) is getting every one wrong, with a probability of (1/2)^n, where n is the number of questions guessed.

**chem**

Note: 1L = 1000mL, so 100mL = 0.1L Use proportions: 3 mol are required to make 1 L of 3.0M solution. x mol are required to make 0.1 L of 3.0M solution. x=3 mol * 0.1L /(1L) =0.3 mol

**statistics**

Events: A=from store A B=from store B D=defective then probability of defective player given it is from store A: P(D|A)=P(D∩A)/P(A)=P(D∩A)/0.3=0.027 then probability of defective player given it is from store B: Solve for P(D∩A) P(D|B)=P(D∩B)/P(B)=P(D∩B)/0....

**Physics (Tension and Springs)**

. T . . . F----- . ...

**Kinematic**

Yes, Emily's approach will give the correct answer. You can also use another kinematics relation to solve for distance x: V1^2-V0^2=2ax where V1=final velocity = 0 V0=initial velocity = 12 m/s a=acceleration = -3 m/s² x=distance travelled in m.

**Statistics**

Exponential distribution has mean = λ where λ is the number of occurrences in a unit time, say one hour. So λ=60/15=4 The exponential probability distribution function is given by: P(T=t)=λe-λt and the cumulative distribution function: P(T<...

**Calculus check**

You're asking for minimum value of f'(x) for 0≤x≤6 where f(x)=6x²-x³. First we need to know if f'(x) is increasing, decreasing, or there's a minimum within [0,6]. We can find out by first finding f'(x)=12x-3x² Find critical points for f...

**Calculus check**

First step, substitute x=1 to get (x^3-1)/(x^2-1)=0/0 need to do something. Then since both numerator and denominator are factorizable readily, we have Limit (x->1) (x^3-1)/(x^2-1) =Limit(x->1) (x-1)(x^2+x+1)/[(x-1)(x+1)] =Limit(x->1) (x^2+x+1)/(x+1) since x≠1 =...

**calculus**

perhaps you have confused the answer with that of a different problem, the answer is not 3/2. Since putting in x=1 gives 0/0, you can either use d'Hôpital's rule, or simply multiply by the conjugate (sqrt(x)+1) of the numerator to create the common factor (x-1). ...

**Calculus**

f'(x)=sin(x) then by the derivative of trig functions, f(x)=-cos(x)+C Now solve for C in f(π)=-cos(π)+C=3

**Please check my Calculus**

It would help you if you say why you chose B. An inflection point is the point (x,f(x)) such that f"(x) [i.e. second derivative) equals zero. f(x)=x^n f'(x)=nx^(n-1) f"(x)=n(n-1)x^(n-2) So solve for f"(x)=0 when n is odd, say n=3, 5, 7... and solve for f&...

**Calculus check**

The slope is f'(x)=d/dx(tan2x)=2sec²(2x) so evaluate f'(pi/8) and make your choice again!

**MATH EQUATIONS**

1. S=(-7,-4) 4(-7)= 28≠-10 =2(-4)-2 so S is incorrect. 2. S=(-1,4) (-1)+2(4)=7 = 7 3(-1)-2(4)=-11 = -11 Yes, S is correct 3. S=(4,12) 4(4)-3(12)=-20 =-20 5(4)-7(12)=-64 =-64 Yes, S is correct. 4. S=(2,1) 2(2)-5(1)=-3 ≠-1 So S is not correct.

**Math - Equations**

See your other post.

**PHYSICS**

E=mass of earth M=mass of moon D=distance between centres of earth and moon. r=distance from centre of the earth m=mass of a certain object of the experiment Using Newton's law of gravitation, F=GMm/r^2 G=gravitational constant then force due to earth Fe=GEm/r^2 force due ...

**Calculus check**

Hmm... Mean value says that (f(x2)-f(x1))/(x2-x1) = f(x0) where x0∈[x1,x2] (f(x2)-f(x1))/(x2-x1) = (5-7)/2 = -1 f'(x)=-3/x^2 f'(sqrt(3))=-3/3=-1, Yes, C is correct.

**math**

Set up a contingency table and work from there: Contingency table of probability -------------------------------- case (treated) (not treated) outcome dies...(1/10)....(7/10) lives...(9/10)....(?/10)

**Calculus check revised.**

Yes, B is correct, again using chain rule.

**Calculus check**

Yes, B is correct. f'(x) d(sin^2(3-x))/dx Apply chain rule =2sin(3-x) dsin(3-x)/dx =2sin(3-x)cos(3-x)d(3-x)/dx =-2sin(3-x)cos(3-x) Then calculate f'(0) from above.

**Math**

log(y-1)=-log(y-9) using the property of logarithms, log(x) = -log(1/x), then log(y-1)=log(1/(y-9)) take anti-log on both sides, y-1 = 1/(y-9) then solve for quadratic in y after cross-multiplication.

**Statistics**

What do you do when you have the third object to be placed and supposed to place in a box already filled with two object? You would skip that case. How many of these cases do we have?

**Statistics**

Assuming the 10 boxes are distinguishable or ordered. There are 10 ways to put the first item, 10 for the second, and 10 for the third. So by the multiplication rule, there are 10^3 ways to place the three objects.

**math**

If the y-coordinate of P is missing, you need to supply it. If it is not given, then use w to complete the problem. P(5,w),Q(-1,2), Mid-point: M((5-1)/2, (w+2)/2)=(Mx,My) Slope of PQ: m=(2-w)/(-1-5) slope of perpendicular: m'=-(-1-5)/(2-w)=6/(2-w) Perpendicular bisector ...

**math**

Rule for translation: (x,y)-> (x+h, y+k) Solve for h,k from (-2,3)->(10,10) (a) hence find the image Q' of Q. (b) if mp-nq=(-12,9), this means m(-2,3)-n(1,3)=(-12,9) Split into individual equations for x and y to get -2m-n = -12 3m-3n = 9 Solve for m,n.

**physics**

Vf^2-Vi^2=2aS a=acceleration/deceleration Vf=final velocity = 0 Vi=initial velocity = 50 or 100 S=distance travelled. By proportion, double the initial velocity, will quadruple the stopping distance, with the same Vf and a.

**Physics**

Assume fine wire has zero mass Newton law of gravitation Weight=mg=GMm/r^2 where units are in m, kg, seconds R1=6400000 (at top of tower) R2=(6400000-20)=6399980 (at bottom) M=6*10^24 G=6.673*10^(-11) Difference in weight =GMm(1/R1^2-1/R2^2) Evaluate. Hint: the difference is ...

**mathematics**

Hints: 1. Use basic laws of logarithm: log(a)+log(b)=log(ab) log(a)-log(b)=log(a/b) log(a^b)=b(log(a)) and use the fact that all the numeric values are powers of 2: 2^6=64 2^2=4 2^3=8 2^10=1024 2. I'll get you started: r^2s^2+3t^2+r^2t^2+3s^2 =(r^2s^2+r^2t^2)+(3t^2+3s^2 ) ...

**Physics**

Assuming the raft is navigating in fresh water with ρ=1. Archimedes principle of floatation says that the mass of a floating body equals the mass liquid displaced. So until the mass exceeds the mass of liquid (fresh water) displaced by the volume of the raft, it will float...

**Probability**

Total of (13+17+15+11)=56 balls, out of which 17 are orange and 11 are white. Assume no replacement of balls. The first orange: 17 out of 56 (17/56) The second orange: 16 out of 55 (16/55) The white: 11 out of 54 (11/54) The probability of pulling in the given order is the ...

**Chemistry( I NEED HELP, PLEASE!!!!, IM DESPERATE)**

You're welcome! :)

**Chemistry( I NEED HELP, PLEASE!!!!, IM DESPERATE)**

From the ratio of molar masses according to the equation, find the required mass of H2 for 45.9 g of CuO. If the required mass of H2 is greater than 2.57g, then the limiting reagent is H2. If the required mass of H2 is less than 2.56g, then the limiting reagent is CuO. MM for ...

**statistics**

Order is not important, so 5 ways to find a male, and 7 ways to find a female. Using the rule of multiplication, the number of ways to find a male and a female actor is 7*5=35 ways.

**physics**

Since it is braking, the acceleration is negative. Use the standard equation Vf^2-Vi^2=2(a)S where Vf = final velocity (=0) Vi = initial velocity (90 km/h=90*1000/3600=25 m/s) a=acceleration required (m/s^2) S=distance = 1.3 km = 1300 m 0^2-25^2=2(a)1300 Solve for a (in m/s^2)

**chemistry**

Molecular mass of CH4=12+4=16 Molecular mass of H2O=16+2=18 Use the combustion equation: CH4+2O2=CO2+2H2O or 16 grams of CH4 should produce 2*18=36 grams of H2O. If there are only 9g of H2O produced, use proportions to calculate the mass of CH4 that produced the H2O, and hence...

**Algebra please explain!!!**

Use depreciation formula: Future value = Present value (1-rate)^(number of years) rate is in % per annum = 0.15 number of years = 10 Present value = 92000

**physics**

Use F=ma For top string, m=2*3.75=7.5 kg a=1.6 m/s62 T1=force in top string For staionary masses, T=mg If in addition, T1 casues upward acceleration, then (T1-mg)=ma or T1=m(a+g)=7.5(1.6+9.81)=85.75 N For the lower string (T2), use same argument, but with a different mass.

**nscc**

Probability =number of successful outcomes/number of possible outcomes. A standard deck has 4 kings and 52 cards. What constitutes a successful outcome is drawing a king. The number of possible outcomes is the number of cards in a deck. So use the definition given at the ...

**programming in c++**

Make a data structure (or simply a table) to store the pricing schemes. Use a pseudocode to plan the program flow. It should roughly look like the following: 1. Initialize pricing data 2. Prompt for input, e.g. number of persons, category/destination, etc. 3. Perform ...

**Statistics**

(a) p=0.87, q=0.13, n=212 need P(X>=50) mean = np = 212*0.87 = 184.44 variance = npq = 23.9772 σ = sqrt(variance) = 4.8967 To find P(X>=50)=P(Z>(50-184.44)/4.8967) =P(Z>-27.45)=1.000 from Normal probability table. Do a similar calculation for (b) using p=0.13

**math**

The easiest way is to make a Venn diagram (which you probably know how to do). Draw a box containing 50 students. Draw a circle containing 22 skateboards Draw another circle, overlapping the first, with 18 roller shoes. The overlap represents 6 students with both. So the ...

**statistics - can someone please Help me**

You're welcome!

**statistics - can someone please Help me**

Note on log: At college and university level, log to the base 10 is rarely used, so often log stands for natural log, sometimes also written as ln. Log10 is used for log to the base 10. If you are not sure, check ln(0.5)=log(0.5)=-0.6931472 log10(0.5)=-0.3010300 To start, we ...

**Chemistry**

To find the ions, we need to know the properties of some metals. Since we added chloride and carbonate ions and obtained precipitates, we need to know the solubilities and colours of the following salts: (S=soluble, I=insoluble) Salt Solubility Colour AgCl I White CuCl2 S blue...

**Check Answers (Math)**

In a typical function y=ax²+k k will shift the graph up and down, so does not affect the width. a is the vertical stretching factor. The greater its absolute value, the narrower the graph gets. A negative value of a will flip the graph about the x-axis, but will not ...

**finite math**

The two dice are assumed distinct. How many ways are there to get the desired outcomes (success): Sum 4 1-3,2-2,3-1 so 3 5 1-4,2-3,3,2,4,1 so 4 6 1-5,2-4,3-3,4-2,5-1 so 5 7 1-6,2-5,3-4,4-3,5-2,6-1 so 6 ... Continue until 11 (less than 12) and add the total number of ways to ...

**Foreign Language, French**

For #3, you can also say: Le serveur a couvert la table d'une nappe.

**statistics**

Let N=event of picking a nickel (5 cents) D=event of picking a dime (10 cents) X()=value of outcome P()=probability of outcome Possible outcomes: NN : X(NN) = 10 P(NN)=(3/5)(2/4)=3/10 ND : X(ND) = 15 P(ND)=(3/5)(2/4)=3/10 DN : X(DN) = 15 P(DN)=(2/5)(3/4)=3/10 DD : X(DD) = 20 P...

**Math help please!!!**

"Min is 4 " I do not find a 4 in the data. Is there a typo in the answer or the question? Q1 is the median of the left half of data, which is 13,13|20,21 For the given data, Q1 equals the mean of 13 and 20, which makes 16.5. Good work!

**Calculus**

dy/dx = 4y separate variables, dy/y = 4dx Integrate log(y)=4x+C or y=Ce^4x At x=7, y=6, so 6=Ce^(4*7) C=6/e^28 So y=6e^(4x-28) Check: y'(x)=dy/dx=24e^(4x-28) y'(2.5)=3.655*10^-7 y(2.5)=9.138*10^-8 y'(2.5)/y(2.5)=4.000 ok

**Raptor flowchart software**

zobon, Raptor is a visual software that does not quite express in words. It is quite visual and almost syntax-free, and you should have no problem working with it. You can also post your particular difficulty, if you have any. If you want your work checked, you can post an ...

**Useful information for Kaytlin**

Some selected ways to lower the priority of your question: 1. Multiple questions in the same post 2. Multiple questions in the same post of the same category 3. Multiple questions in the same post of the same category, and show no sign of any effort. 4. Multiple questions in ...

**geography help needed**

geography help needed

**french (for Mya)**

For French as in math, you cannot make a choice by guesses. You have to understand the rule/method to get the right answer, and then choose the correct one. These questions are based on the following: the noun which the pronouns replace must agree in gender and number. Gender ...

**Math Help!**

Range of a dataset is the highest data value minus the lowest data value. In light of this, would you change your answer, and why?

**Math**

Hint: Domain of a set of ordered pairs is the set of all the "x-values", or the first value of each ordered pair. Range is the set of y-values of the ordered pairs.

**Math**

In general, the line y=ax+b is in the slope intercept form, meaning that a=slope of the line, and b=y-intercept. For example, y=x+2 will have a line that has y-intercept =2 (i.e. the point (0,2)) and a slope of 1. So graph a point at (0,2), and draw the remaining line passing ...

**math**

We need to find a and b, so we will look for two equations. The first one is simply the point (1,1), which tells us that 1=y(1), or 1=a(1^3)+b(1)=a+b, or a+b=1............(1) The second one is the fact that the gradient (dy/dx) at (1,1)=-5. Since dy/dx = 3ax²+b, we have -...

**math**

The domain of a polynomial is R (real). The domain of a rational function (polynomial divided by another) is R less the points where the denominator becomes zero. The given function g(x) is a rational function where the denominator can be factorized into (x^2-36)=(x+6)(x-6) ...

**Math (Asap)**

You're welcome! :)

**Math (Asap)**

Example: A trinomial with ab as a common factor can be created by doing 2ab(3+5x+7x^2)=6ab+10abx+14abx^2 The common factor will be the GCF as long as the trinomial in brackets does not contain any common factor with 2ab.

**Math**

As long as you mean Tk=1/(5k) is the rule for term k of the given sequence Tk, you're correct. Perhaps 1/(5^k) refers to a different series.

**physics**

The question is heat can never flow from_________. We know that heat flows from hot to cold, so the answer is "cold to hot". Cold is not a physical quantity, heat is (measured in calories or joules).

**Math**

You're welcome! :)

**Math**

For an open-top rectangular prism with width w, length L and height h, the area of the base is wL. The area of the 4 sides is 2h(w+L) So the surface area of the open prism/bag is A=wL+2h(w+L). The correct answer is one of the given choices.

**science**

I do not see how you can get 13.0. Please show your work (must use consistent units, kg, N, s, m) F=1.2kN=1200N m=490 kg g=9.8 or 9.81 m/s^2 Perhaps it was a mistake on the calcultor, so please try again. μ should be between 0 and 1.

**science**

Draw the free body diagram which reveals the net forces on the body. The force F at 20 degrees with horizontal has an upward component of Fsin(20) which has the effect of reducing the normal reaction N from mg to mg-Fsin(20). The horizontal component of Fcos(20) is the only ...

**Math**

15 - 7 2/5 = 14 + 5/5 - 7 2/5 = 14-7 + (5/5-2/5) = 7 + (5-2)/5 = 7 + 3/5 = 7 3/5

**Math**

The answer is a fraction of the money he has. he spent: 1/2 (on candy) and 1/5 (on chocolate) for a total of 1/2+1/5. To add the fractions, we first find the common denominator, which is the LCM of 2 and 5 =10. 1/2+1/5=5/10+2/10=(5+2)/10 = ?

**maths**

It falls under the binomial theorem or binomial expansion when there are finite terms (this case). When the number of terms is infinite, such as (2-x/2)^(-3), then it falls under Taylor's series. Following are some typical references: http://mathworld.wolfram.com/...

**math**

Another possible reason is that your keyboard code has a different value for the "+" sign, which is rare.

**math**

An identical previous post been answered. The disappearance of the + sign is because you have probably have copied and pasted, and the original + sign was not in ASCII code if it was in another application. If you have to cut and paste, try to first paste it in an ascii editor...

**help! Physics**

Ask yourself the question: Will a greater coefficient of friction speed up the movement or slows it down? Then try to formulate your answer to the posted question.

**math**

We are given a lot, but the information has to be related some how. Can you check the question please?

**please assist me with science**

You're welcome! :)

**please assist me with science**

I have m(9.8)sin(28)+m(9.8)cos(28)*0.387=588 from which m=588/(9.8(sin(28)+0.387cos(28)) Do you have the same expression?

**please assist me with science**

What did you get for N?

**please assist me with science**

I get about half of that, which is pretty small for a car. A small MG-midget weighs more than that, unless it is an ATV. Can you check if you have a factor of 2 missing somewhere? If you don't spot it, tell me what you have for N (normal component), the value of g that you...

**please assist me with science**

First step: draw a free body diagram, showing 1. W=mg 2. down-plane component: mg sin(θ) 3. normal component, N: mg cos(θ) 4. friction (parallel to plane, downwards) = μN 5. applied force, F=588 N Since car is moving up the plane at constant velocity, forces ...

**Maths**

Put x=5-7y Substitute in the circle (5-7y)²+y²=15 Solve for the two values of y. Find corresponding values of x to give two ordered pairs which are solutions to (a) for P and Q. For (b), use the mid-point formula M=((x1+x2)/2, (y1+y2)/2) If you need further help, ...

**Calculus 2**

First step: decompose into partial fractions (probably the hardest part of the problem) Factorize the denominator (if possible) x^3+x^2+x+1=x^2(x+1)+1(x+1)=(x^2+1)(x+1) so we can decompose the given fraction into: 1/(x^3+x^2+x+1) =1/2(x+1) + (1-x)/2(x^2+1) which can be ...

**matLab**

If you know the syntax for plotting in Matlab, then it would be similar to your previous problem in the name of Jasmine.

**MatLab**

* n=11, or Sum(11)

**MatLab**

Do you mean y=Σ 2^n/n for n=1,3,...11 ? If you are already familiar with the syntax of Matlab, you can use the following pseudocode: function [S] = Sum(n) sum=0; for i=1:n:2 sum=sum+2^i/i; end S=sum; end The calling program has to supply i=11 to evaluate the required ...

**Math**

I interpret "adding the square root of 16 and -8" as "adding the square root of 16 and the square root of -8" which gives sqrt(16)+sqrt(-8) = 4+2√2 i which is a complex irrational number. If I interpret "adding the square root of 16 and -8" ...

**math**

Use the mortgage payment formula: and assume 2% is per annum and compounded monthly, A=PR^n(R-1)/(R^n-1) where A=monthly payment ($850) n=number of months (=30) P=principal (amount borrowed) R=monthly interest rate + 1 =(0.02/12+1) Solve for P P=A(R^n-1)/(R^n(R-1)) It should ...

**Math**

All correct, to the nearest tenth of a degree.

**Calculus II**

The hydrostatic pressure at a distance of x, measured along the plate from the top of the plate is P(x)=ρg(6m + x sin(30°)) For a horizontal strip of width dx, and length w (=3 m), the force is dF=pressure × area =P(x)*w*dx =P(x)*w*dx Total force = ∫dF =∫...

**Please help and explain engineering science n3**

Component of force acting down the incline F1 = mg sin(θ) Normal component of weight (affects friction) N = mg cos(θ) Frictional force Fr = μkN Force exerted by engine to overcome gravity and friction F= Fr + F1

**Math**

Sine rule states that: sin(A)/a = sin(B)/b = sin(C)/c Here you are given both a and A, so knowledge of c will let you solve for sin(C). Sin(C)=c*(sin(A)/a)=0.96225 and sin-10.96225=74.207° or 105.793° since sin(x) is symmetrical about 90°. If the sum of the larger ...

**physics**

If you used 47kg and 37 degrees, you need to redo your calculations. Check your calculator for the trig functions to see if it is set in degree mode. In degree mode: cos(60)=0.50000000 In radian mode: cos(60)=-0.95241298...

**physics**

(45.0)*(9.80)*(sin35 degrees)= a number 45kg or 47kg?

**Pre-Calculus (Trigonometry)**

You're welcome! :)

**Pre-Calculus (Trigonometry)**

The sine curve is symmetrical about 90 degrees. So sin(x) has the same value as sin(180-x). Review of the unit circle will certainly help as well.

**Algebra 2**

See other post please.

**No alias please**

Nancy, Ann, Brooke, etc. We prefer you to use a single name at this site for continuity. Thank you for your cooperation.