Monday
March 27, 2017

# Posts by MathMate

Total # Posts: 11,744

Math
The future value FV can be calculated by summing payments and simplification using factorization: FV = S(1+(1+r)+(1+r)^2+...+(1+r)r^(n-1)) =S((1+r)^n-1)/((1+r)-1) =S((1+r)^n-1)/r FV=future value S=Semi-annual payment r=interest per period (6-months) n=number of periods (6-...
March 18, 2015

Algebra
fourth term: ar^4 7th term: ar^7 Let common ratio = r then 7th term / 4th term = ar^7/ar^4 = r³ therefore r = cube root of r³ Fifth term = fourth term * r
March 18, 2015

math
The first step in evaluating a limit would be to substitute the limiting value into the expression. If it evaluates to a valid number, that is the limit. Example: limit x->1 x²/x =1²/1 = 1 Since sinx/tanx + tanx.sinx ≡ 1/cos(x) so the limit is 1/cos(0)=1.
March 18, 2015

Math
Solve for x in 1500+0.04x=5000
March 18, 2015

The number of CD's between Q1 and Q3 should be half of the total number of CD's. From the plot, you will not know how many cost less than \$14.6, but since Q1 is 14.6, there are at most one quarter of the number of CD's cost less than \$14.60. (One quarter of 12 CD&#...
March 18, 2015

Sum and Difference
Sum and difference problems are solved as follows: Larger number = (sum+difference)/2 Smaller number = (sum-difference)/2 So 1/p = (4+3/2)/2 = 11/4 p = 1/(11/4) = 4/11 I will leave it to you to do the smaller number (1/q).
March 18, 2015

maths
We are given x²+y²=137 (x-y)=7 this means 49=(x-y)² =x²-2xy+y² =x²+y²-2xy =137-2xy From 49=137-2xy can you solve for xy? The longer way: equation 1: x-y=7 equation 2: x²+y²=137 Now solve the non-linear system in x and y.
March 18, 2015

Math
Use law of exponents (ax)^b = a^b × x^b y=kx^3 y1=k(1.5x)³=k(1.5^3)x³=3.375kx³=...
March 18, 2015

math
There is an ambiguity in the question to be clarified about the interest rate. Generally annual interest is quoted. The wording of the question casts a doubt as to 7.2% is monthly or annual interest. Considering that 86.4% annual interest is illegal in some countries, 7.2% ...
March 18, 2015

See later post
March 17, 2015

Math
You're welcome. Also note a correction is required: 0.02/5 = 0.004/1 < 0.01=1%
March 17, 2015

Math
Convert the given fraction to an equivalent fraction with either 1 or 100 as the denominator. We know that 1% = 1/100 = 0.01/1 So say, 0.2/5 = 0.004/1 < 0.01=1% 2/500 = 0.4/100 < 1/100 = 1% etc.
March 17, 2015

Repost, see previous discussions
http://www.jiskha.com/display.cgi?id=1426619198
March 17, 2015

French, foreign language
Yes, you need to correct the sentences where the verb and complements do not agree. "Ce sont" is followed by a noun in plural, and "C'est" is followed by a singular noun. Examples: Ce sont des carottes. (Ce sont....plural) C'est un hamburger. (C'...
March 17, 2015

Ouch! question says "Determine which ordered pair is not a solution of "
March 17, 2015

substitute x (first number in parentheses) into the right-hand side of the equation and check if the value equals y (second number in parentheses). For example, let's check (9,-48) which is not taken from the choices: -5(9)-4=-45-4=-49 but -49 does not equal -48, so (9,-48...
March 17, 2015

Math
Question says: If not, then you lose your discount and you pay a 20% premium on the usage outside of that time. Check that you have calculated without the 15% discount.
March 17, 2015

Math
Since usage is greater outside the prescribed period, there will be a 20% premium for those kW-h. Can you please show us how you got \$51.08?
March 17, 2015

Vectors
Yes, b is correct. Your method works well without having to memorize formulas. If the equations had been in the slope intercept form: y=-x+8 and y=-x then you could also calculate using distance = y-intercept difference / &radic(1²+(-1)²) =8/√2 =4√2
March 17, 2015

Vectors
Actually, the expression is the expanded form of (x+2)(y-3)=0 which by the zero-product property means x+2=0 => x=-2, or y-3=0 => y=3, or both of the above. So yes, (a) is correct.
March 17, 2015

Algebra 2
If you are working on polynomials, then binomial is a polynomial with 2 terms, for example, (x+4) is a binomial, or (x³ - 2x²) is a binomial. The first example is a binomial with a degree of 1 (highest power of the variable), and the second is a binomial of degree 3...
March 17, 2015

physics
The parallelogram of forces yields a triangle with vectors 10,15 and 20. where 20 is the resultant. The angle between the two vector is the supplement of the angle (between vectors 10 and 15) solved by the cosine rule. Draw the parallelogram of forces to understand why it is ...
March 17, 2015

physics
If the quarter circle has the radii horizontal and vertical, the difference in height equals the radius=1.6m. Neglecting friction and other dissipative forces, then conservation of energy holds, and so KE+PE=0,or (1/2)mv^2 + mg(h-h0)=0 Solve for v where h=0, h0=1.6m and g=9.81...
March 17, 2015

math
Very often the phrase "of the" means multiply. So he packed 1/3. 1/2 "of the" 1/3 were shipped, this means (1/2)*(1/3) = 1/6 were shipped.
March 17, 2015

Do you have a diagram?
It is not clear to me how M1 and M2 are related, are they linked vertically by a string, are they released at the same time?
March 17, 2015

Vectors
To Sara: I got 5/√2 as well. Perhaps it is time to check if there are typos in the question or the answer. Also, to print s∈R, you can write s & i s i n ; R, but skip the spaces.
March 17, 2015

Physics
Anne throws a ball horizontally... so the problem reduces to a free-fall over 50m. The equation Dy=-50m = V0t+(1/2)gt^2 will let you solve for the time to hit ground, and where v0=initial vertical velocity = 0, and g=acceleration due to gravity = -9.8 m/s² During this ...
March 16, 2015

calculus trigonometric substitution
You're ok so far. You only need to convert sin(u)cos(u)/54 back in terms of x, which should be x/(18x²+162). You can start by sin(u)cos(u)/54=cos^2(u)tan(u)/54 =3tan(u)/[162(sec²(u)) =...
March 16, 2015

EES
Hint: think of what you find in the kitchen.
March 16, 2015

computer applications
It would be much easier for you to open a spread sheet and try it out. I suggest you do some practical work because it will help you understand how it works, and it will help you recall the procedure in the future.
March 16, 2015

Vectors
Let's check: r1=(3,2,-1)+s<1,1,1> When s=0, r passes through the point (3,2,-1). Now check the product of the two direction vectors: <1,1,1> dot <1,1,-2> =1+1-2 =0 So the two lines are perpendicular and r1 satisfies the required conditions. Note: multiple...
March 16, 2015

engineering
Stress=σ=Force/Area Strain=ε=σ/E Change in length = ε*Length. Useful conversion factors 1 GPa = 10^9 Pa 1 kN = 10^3 N 1 m = 1000 mm Try to do calculations in standard units, namely kg, m, s.
March 16, 2015

programming
You can work on the flow-chart based on a pseudocode such as: enter ID, ID enter number of policies sold, N if N > 25 print ID, N endif
March 16, 2015

maths
1 pascal = 1 N/m² 1 MPa = 10^6 Pa Stress = Force /area, all in appropriate units. = 91*10^3 N / (π0.030²/4) m² Evaluate and convert to MPa.
March 16, 2015

engineering
1. find average acceleration, a Vi=0 S=(1/2)at^2 139 m =(1/2)a(8.7²) a=3.6729 m/s² 2. Find work done, W a. using F=ma, W = F*S = ma*S where m=1100 kg, S=139 m, a=3.6729 m/s² or b. using energy (neglect loss) final velocity, Vf = at where t=8.7 s final energy =(1...
March 16, 2015

Math
If we select 6 out of 300 subjects, we can assume that the probability remains approximately constant, thus use of the binomial distribution is applicable, where n=6 p=0.58 bin(6,0.58, 3) =C(6,3)*0.58^3*0.42^3 =0.2891 approximately To be more precise, we calculate the ...
March 16, 2015

stats
The question satisfies requirements for a binomial distribution, where n=10 p=1/2 Probability of r girls out of n =P(G=r) =(n, r)p^r (1-p)^(n-r) where (n,r)=combination n choose r = n!/(r!(n-r)!) For at least 2 girls out of 10, P(G>=2)=1-(P(G=0)+P(G=1)) 1-(1)(1)(1/1024)-(10...
March 16, 2015

Math
Expected value is the sum of the product of all possible outcomes and the respective probability. Example of rolling one six-sided die: Payout equals the number appearing on top face. expected value = 1*1/6+2*1/6+3*1/6+4*1/6+581/6+6*1/6 =3.5
March 16, 2015

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.
March 16, 2015

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...
March 16, 2015

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).
March 16, 2015

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: ...
March 16, 2015

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 ...
March 16, 2015

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.
March 16, 2015

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
March 16, 2015

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....
March 16, 2015

Physics (Tension and Springs)
. T          .         .       . F-----       .     ...
March 16, 2015

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.
March 16, 2015

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<...
March 15, 2015

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...
March 15, 2015

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 =...
March 15, 2015

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). ...
March 15, 2015

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
March 15, 2015

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&...
March 15, 2015

Calculus check
The slope is f'(x)=d/dx(tan2x)=2sec²(2x) so evaluate f'(pi/8) and make your choice again!
March 15, 2015

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.
March 15, 2015

Math - Equations
March 15, 2015

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 ...
March 15, 2015

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.
March 14, 2015

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)
March 14, 2015

Calculus check revised.
Yes, B is correct, again using chain rule.
March 14, 2015

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.
March 14, 2015

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.
March 14, 2015

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?
March 14, 2015

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.
March 14, 2015

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 ...
March 14, 2015

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.
March 14, 2015

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.
March 14, 2015

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 ...
March 13, 2015

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 ) ...
March 12, 2015

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...
March 11, 2015

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 ...
March 11, 2015

Chemistry( I NEED HELP, PLEASE!!!!, IM DESPERATE)
You're welcome! :)
March 11, 2015

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 ...
March 11, 2015

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.
March 11, 2015

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)
March 11, 2015

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...
March 11, 2015

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
March 11, 2015

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.
March 11, 2015

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 ...
March 11, 2015

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 ...
March 11, 2015

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
March 10, 2015

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 ...
March 10, 2015

You're welcome!
March 10, 2015

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 ...
March 10, 2015

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...
March 10, 2015

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 ...
March 10, 2015

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 ...
March 10, 2015

Foreign Language, French
For #3, you can also say: Le serveur a couvert la table d'une nappe.
March 10, 2015

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...
March 10, 2015

"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!
March 10, 2015

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
March 9, 2015

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 ...
March 9, 2015

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 ...
March 9, 2015

geography help needed
geography help needed
March 9, 2015

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 ...
March 9, 2015

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?
March 6, 2015

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.
March 6, 2015

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 ...
March 2, 2015

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 -...
March 2, 2015

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