# Posts by MathMate

Total # Posts: 11,744

**Linear Algebra**

Your answer is correct. The fact that t2=0 means that t1 and t3 are linearly dependent, resulting in two independent variables in R3. This is still a linear dependent set.

**Math**

To check whether a triangle is a right-triangle, add the square of the two shorter sides. If the sum equals the square of the longest side, then it is a right-triangle. Example: Triangle ABC has sides 5,12,13. 5²+12²=169 = 13² therefore the ABC is a right ...

**math**

A+P=25 P+B=19 B+A=16 Buy one from each deal and you will get 2 apples, 2 pears, and 2 bananas for (25+19+16)=60 pesos. How much would you spend if you buy only one of each?

**Chemistry**

Answer is correct! Q=mcΔT However, use of the equality sign is valid only when both sides of the sign are equivalent. You could write: Energy required =13g * 1.00 cal/g°C * 2 °C =26 cal

**math - ratios**

Given: Girls : Boys = 7 : 3 Girls+Boys:Girls-Boys = 10:4 = X:200 where X is the total number of children (Girls+Boys) or 10/4=X/200 Cross multiply to find X=200*10/4 = 500

**math - correction**

Since going around once reduces the width and length by 4', 9.26'/4'=2.315 Nala would need to mow around the lawn between 2 to 3 times to finish half the work.

**math**

Total area = 25*45 = 1125 sq.ft. Half of the area = 562.5 sq.ft What is needed is the size of the inside rectangle left, or (25-x)(45-x)=562.5 Solve for x to get x=9.26' and reject the other root which exceeds 25. Since 9.26'/2'=4.63 strips, so Nala has to go ...

**chem**

Half life = 15h Activity A(t)=A(0)*2^(-t/15) Solve for t in A(t)=5000=80000(2^(-t/15)) to get t=60 (hours)

**Calculus**

The position function for a free fall from rest is: x(t)=(1/2)gt² In metric units (x in metres, t in seconds), x(t)=(1/2)*(-9.8)t² =(1/2)(-9.8)6.7² =-220 m approx.

**PHYYYYYSICS 10**

Horizontal component of velocity = 18 m/s Vertical component of velocity, Vf, is given by Vf²=Vi²+2*a*Δx Vi=initial vertical velocity=0 m/s a=acceleration due to gravity=-9.8 m/s² Δx=-41 m Vf=sqrt(0+2(-9.8)(-41))=28.4 m/s (downwards) angle with ...

**physics**

Assuming the crate moves upwards. The applied force P is upwards whether the crate moves upwards or downwards at a constant velocity. coeff. of kinetic friction, μ = 0.75 angle of incline, θ = 46° (with horizontal) If crate moves upwards with a constant velocity, ...

**Mechanism and Machines**

It's surprising that your teacher did not mention any application when the subject was being taught. The linkage essentially converts rotational motion into a straight line movement. The rotational motion usually comes from a motor, and the straight line movement can be ...

**math - fractions**

Father does the work in x hours, or father does 1/x of the work in one hour. Son does 1/(2x) of the work in one hour. Together, they do 1/x+1/(2x)=1/6 of the work in one hour. 2/(2x)+1/(2x)=1/6 3/(2x)=1/6 Cross multiply 2x=18, x=9 So father does the wok in 9 hours.

**Math**

Profit = 0 is break even. So solve for x in P(x)=-37x²+1073x-7548 = 0 to give x=12 or x=17 The profit is given by the maximum of the P(x) function, which is located at x=(12+17)/2=15.5, or the maximum profit is P(15.5). (substitute 15.5 for x and evaluate the profit).

**Math - ratio**

Use ratio / cross multiplication 18:162 ≡ 36:x x=162*36/18 = 324

**math-fractions**

Total (in fraction) = 1 Woodwinds = 1-2/5-1/3=(15-6-5)/15=4/15 half of woodwinds (4/15) are clarinets, so clarinets = (4/15)÷2= 2/15 One eighth of brass are tubas, so tubas = (2/5)÷8 = (2/40)=1/20 whole : 240 1/20 : x (number of tubas) x=240*(1/20)÷1 =240/...

**math-addition**

Both Minnie and Amanda have 11 cds, so they have the same number of cds.

**Physics - kinematics**

Given Vi=36 m/s θ=30 Vix=36cos(30)=31.18 m/s Viy=36sin(30)=18 m/s Vy(t)=Viy*t+(1/2)gt² =18*1+(1/2)(-9.8)*1² =13.1 m/s velocity=sqrt(Vix²+Vi(1)²) =sqrt(31.18^2+13.1^2) =33.82 m/s

**Math - compound interest**

i=4% p.a. compounded quarterly = 1% per period Let R=(1+i), n= number of quarters/periods Future value FV=100(1+R+R²+R³....+R^(n-1) ) =100(R^n-1)/(R-1) =100(R^n-1)/i For FV=10000 we have 10000=100(R^n-1)/i R^n=(10000/100)*i-1 =2 n=log(2)/log(1.01)=69.66 It will take ...

**French**

You can also say (formally) "De quel pays êtes-vous venu/venus/venue/venues?" depending on the gender and number of persons to whom you're addressing.

**trigonometry**

Sorry, don't know if you have used Word or other word processors to write the equation, but they do not translate corectly. Here most HTML symbols are recognized, or you could use ^2 to mean square, and sqrt( ) to mean square-root, etc. Also please write the appropriate ...

**chemistry**

Solubility is defined as the number of grams of solute that will saturate 100 grams of solvent at a given temperature. So at 20 degrees, we know that the solubility of CuSO4 is 25. Mass of water (solvent)=80 g Use ratios: 25:100 = x:80 Solve for x to get x=25*80/100=20g

**Algebra**

slope intercept form is in the form y=ax+b If you start from the equation above, you would isolate (solve for) y in terms of x and the constants, then simplify the right-hand side to remove parentheses. Isolate y means use algebraic operations to leave only y on the left-hand ...

**math**

Probability of rolling two even numbers = (1/2)(1/2)=1/4 Expected value of the game, E(x) is the sum of the following: outcome X, probability P(X), X*P(X) 2 evens=+$8, 1/4, +$2 at least one odd=-$2, 3/4, -$3/2 The sum of X*P(X) = $0.50 The expected value is thus $0.50 for each...

**computer science**

Command interpreter is a system where it would execute a command at a time, according to the command the user types in. The turtle graphics window is much the same as a command interpreter, except that the command are simpler (turn, move, etc.) and it displays a graphics ...

**real analysis**

Correction: Somewhere the -8 was inadvertently written as -7, so after corrections, |Xn|≤|-8|+|-1/(n+1)| ∀n∈N or |Xn|≤9 (or M=9)

**real analysis**

Try and improve on the following. R=set of all real numbers. N=set of all natural numbers Let Xn=-8+n/(n+1), where X∈R then Xn=-8 + (n+1)/(n+1) - 1/(n+1) =-7 - 1/(n+1) => |Xn|≤|-7|+|1/(n+1)| (triangle inequality) But |1/(n+1)|≤1 ∀n∈N, therefore |Xn|&...

**COMPUTER SCIENCE**

See response: http://www.jiskha.com/display.cgi?id=1410758490

**Statistics**

A normal distribution is symmetric and unimodol. Therefore an asymmetric bimodal distribution cannot be normal. But beware: A symmetric and unimodal distribution is not necessarily normal. These are necessary but not sufficient conditions.

**Physics**

Acceleration = (final velocity - initial velocity)/ time =(0 - 22 m/s ) / 2 s = -11 m/s² The negative sign indicates that it is a deceleration (slowing down).

**physics**

The police car catches up 2.68 m/s for every elapsed second. So to catch up 25.8 m/s, it will take t=25.8 m/s^2 / 2.68 m/s = 9.63 s Since the speeder travels at a uniform speed of 25.8 m/s, the distance travelled can be calculated by Distance = speed * time.

**French**

The second question is: "Où sont-ils placés par rapport aux noms?" It means where are they ("les mots soulignés", or what you identified in question 1) placed/located relative to the nouns (noms).

**French**

It is a good idea to have the complete context of the question which in this case concerns grammar. I suppose you have learned about the different groups, of which groupe nominal (GN) is one. The (GN) consists mainly of the noun (nom) and determinants. Determinants can belong ...

**engineering mechanics**

Try to doodle a triangle of forces and find that the greatest and least resultants occur when the two forces (x,y) are colinear. When they are additive, we have x+y=17 kN, and when they oppose each other, we have x-y=5 (if x>y). Thus solution of the system of equations ...

**Physics**

Your work is correct, here's the explanation. In a projectile problem, the horizontal (x) motions are independent of the vertical (y) motions. In the case of a horizontally fired projectile from a given height, the problem is equivalent to a free fall from the given height...

**engineering science**

It is not clear if 30 degrees is above or below the incline. The following solution assumes the supporting force is above the incline. You can do a similar calculation if it is below. First, draw a free-body diagram. Resolve all forces along (+ downwards) the incline, and ...

**math**

The usual notation for [x] is the greatest integer that is equal to or less than x. For example, [2.5]=2, [-3.4]=-4, but -[3.4]=-3 because the [ ] function applies to a positive number. The greatest integer not exceeding 3.4 is 3. On the other hand, for [-3.4], the greatest ...

**statistics**

Sorry, I had a miscount. The number of terms of the expansion of (a+b+c+d)^6 is 84 (not 86).

**statistics**

This problem is the same as putting 6 items in 4 bins. Different ways of solving this problem would be: 1. enumerate in a systematic way: 0006 0015 0024 0033 ... 6000 and count how many you've come up with. Note that since the children are of different ages, and the gifts ...

**Computer Science**

Explanation of the pattern follows: ^a specifies the string begins with "a" b\$ specifies that the string ends with "b" d* allows 0 or more embedded d's. (cd+)* requires a "c" to be followed by at least one "d". This can happen 0 or ...

**Computer Science**

Try my $pat="^ad*(cd+)*b\$" Use this pattern to match strings according to the rules specified. Note that $pat will match a qualifying string, but does not define a string. Hope someone else can answer the second part.

**math**

Outer perimeter: 4s=4*10'=40' Spacing = 6" = 0.5'/plant Number required = 40'/0.5'/plant = 80 plants Since the perimeter is a closed figure, there is no need to add one "at the end" as in the case of a linear row with two ends.

**math urgent please**

Don't know if you paraphrased the question, but the question is indeed confusing. First it gave the length of 320 cm and width of 320/2=160 cm. So there is no variable to optimized. Then it talks about maximizing 4 faces, and then jumped to optimizing 3 faces. Finally, it ...

**calculus - insufficient information**

Unfortunately we cannot see fig 2c unless you describe it or send a link.

**math**

Since it is not stated in the question, we assume that the unit of f(x) is in feet. There is inconsistency with the two expressions for f(x), namely f(x)=(1/2)x²+(4/5)x, and later f(x)=(1/12)x²+(4/5)x Solving the first. If the second expression is intended, you can ...

**physics**

Average acceleration =(0-30) m/s ÷ 5 s = -6 m/s² Force = ma = 80 kg * (-6 m/s²) = -480 N (resistive force)

**math**

correct!

**Physics**

Stress = force/area 1. stres= 6.5*10^5 dynes / (π(0.3)²/4 cm²) = 9195619 dynes/cm² = 919.6 kPa Young's modulus nor strain cannot be derived from the given information. 2. Stress = force /area 10 kg * 9.8 m/s² ÷ (π0.004²/4 m²) = 7....

**Chemistry**

Use C1*V1 = C2*V2 For example, to dilute 100 mL of 36M solution to 6M, we put 36M *100 mL = 6M * V2 Solve for V2 = 36M*100mL/6M = 600 mL This means that the 100 mL of 36M solution must be diluted to give a final volume of 600 mL.

**math**

1. -f is the reflection of f about the x-axis. 2. f(-x)=f(x) => f(x) is even 3. f(-x)=-f(x) => f(x) is odd Good job! :)

**math**

Sum of squares = p²+(p+5)² =625 Expand p²+p²+10p+25=625 2p²+10p=600 p²+5p-300=0 (p-15)(p+20)=0 p=15 or p=-20, reject negative root The sides of the squares are therefore: p=15 p+5=15+5=20

**statistics**

A five-number summary represents the following qualifiers: minimum Q1 median Q3 maximum the interval minimum/median represents 50% of the data in the lower half. the interval median/maximum represents 50% of the data in the upper half. the interval Q1/Q3 represents 50% of the ...

**Precedence rules for the algebra community**

Precedence of operators In simple algebra, there is a set of precedence (priority) of operations that should be respected in order that everyone evaluates mathematical expressions in the same way. Although these rules have been taught in elementary school or junior high school...

**physics**

Assuming the mass of the object is negligible compared to the mass of the person and the boat, then the speed of the object is 30km/h in addition to the speed of the boat. Using a terrestrial frame of reference, the apparent speed of the object by a stationary observer on the ...

**proportions**

35' : 0.28 kg x' : 7.2 kg Cross multiply and solve for x x=35' * 7.2 kg / 0.28 kg = 900'

**college algebra**

typo: N = (x+5)*x²/(x+3) =(x³+5x²)/(x+3)

**college algebra**

First, observe the rule of operator precedence, i.e. BEDMAS (brackets,exponents, division/multiplication, addition/subtration) in that order. Q1. I suspect the expression should have been written as (x+5)/(x+3) to be interpreted correctly. Based on that, we know that the new ...

**mathzzz want answer in simple way**

Let x=number of rows, and since number of rows = number of persons per row, we have x*x=3249, or x=sqrt(3249) take out your calculator and find x.

**math**

Sum of angles of a quadrilateral = 360° sum of the other two (C & D) = 360-150=210 If C : D = 2:3, then C+D=210, C: C+D = 2 : 5 = 84 : 210 C=84, D=210-84=126 The first two angles (A & B) add up to 150, which could be A=100, B=50, or A=75, B=75, etc. Without additional ...

**Math**

Correct! Well done! :)

**isu**

mass (m) = density (ρ) * volume (v) = 1.46 g/mL * 59.9 mL = 87.5 g

**Business Math**

Assuming the investment is placed for exactly one year, then the future value is FV=Principal*(1+i) =2989(1+0.03) = $3078.67

**math**

markdown: 12% : $1.20 sale price : 100% : X Cross multiply and get sale price, X = 1.2*100%/12%=$100

**Math**

Probability of getting the first white sock out of 30 socks is 24/30 Probability of getting the second white sock out of the remaining 29 socks is 23/29 Since he needs a pair of white socks, both of the above events (steps) must succeed, for which the probability is the ...

**physics**

Convert values to consistent units: 66 mi/h = 66 mi/h *5280 ft/mi ÷ 3600 s = 96.8 ft/s similarly 55 mi/h = 80.67 ft/s acceleration = -14 ft/s² Time required=(80.67-96.8)/(-14) = 1.15 s Do not forget to add the reaction time, which could exceed the mechanical ...

**Statics**

The angles are not precisely specified. It is not clear whether the a-axis makes an angle of -20 (340) with the x-axis, or -160 (200) with the x-axis. Same problem for the force F. Could you specify forces and axes using the following conventions: 1. All angles are measured ...

**Statics**

So you have three forces, the magnitude and angles of which two are known. You will need to first compile a table of known and unknown values. To avoid confusion, you need to follow these rules for describing forces: 1. All angles are to be measured counter-clockwise from the ...

**Statics**

A description of the accompanying figure is required. Minimally, the directions of F1 and the magnitude of F2 are required.

**Statics**

If Pa and Fb are both 305N, then angles aOF and FOb are equal to 38 ° See http://www.twiddla.com/1746657 Since F*cos(38)=305N, F=305N/cos(38). You can work out the orientation of b from the figure.

**math**

Please proof-read your question. ># is meant for which symbol? To take the limit, x-> ?

**math**

If you divide the second equation by 2 and transpose terms to the same form as the first equation, you will find that the two equations are identical. This is a situation where the two equations represent coincident lines, hence there is an infinitely many solutions.

**Logic / Discrete Mathematics**

You're welcome! :)

**Logic / Discrete Mathematics**

With simple expressions like these, the easiest proof is to make a truth table...unless it is specifically prohibited in the question. Also, there are precedence in the logical operators, just like + - * ÷. see http://en.wikipedia.org/wiki/Logical_connective The ¬ ...

**science, physics**

The heat of fusion of ice is 79.8 cal/deg C. Let T = final temperature, and sum heat change = 0 8 kg (T-20) + 2 kg ((T-0)+(79.8))=0 cal-kg Solve for T to get T=+0.04 deg. C.

**3D Modling**

One of the ways is to download the (free) software, and get familiar with it through tutorials. This way, the question (and many others) will be answered.

**Business/Finance**

June: 30-6=24 July: 31 August:31 September:30 October: 8 Total=24+31+31+30+8=124 days Discount period: The period of time between the date a bill of exchange is drawn and the date on which payment is due. So discount period = 200-124=76 days

**physics**

Kinetic energy, KE = (1/2)mv² resistive force = constant Retaining half the velocity means (1/2)^2=1/4 of the kinetic energy. Since 50% of the KE penetrates 25 cm, so 25% of the (remaining) KE penetrates 12.5 cm.

**physics**

p(t)=3t²-2t+1 W Δp =p(4)-p(2) =41-9 =32 W

**physics**

Power =mgh/Δt / efficiency =100kg*10m/s²*10m/5s / 60% = 2000/0.6 = 3333 W = 3.33 KW Thank you for posting the answers, but there are too many decimal points that I cannot make anything out of them. In addition, (C) and (D) seem identical to me.

**Physics**

585 zag/zoyear =585 *(1/0.18) zig/ (0.4 years) =(585/0.18) zig / (0.4*365*24 hours) = 0.928 zig/hour

**Engineering**

Try http://faculty.uoh.edu.sa/m.touahmia/CE353-CH3.pdf

**math**

The distance between two points with coordinates P1(x1,y1) and P2(x2,y2) is given by the distance formula: D(1,2)=sqrt((x2-x1)²+(y2-y1)²)

**Math**

36 students B:G = 3:1 = 27 : 9 Add x girls, 27/(9+x)=9/5 Solve for x by cross multiplication.

**algebra 2**

|x|-2≤-3 |x|≤-3+2 |x|≤-1 => x≤-1 or -x≤-1 => x≤-1 or x≥1 => on the number line: <------ -1.......0...... 1 ------>

**Chemistry**

The question is not complete. I assume you are asked to find the quantity of CO2 produced by heating 25g of CaCO3. Molecular mass of CaCO3=40+12+48=100 From the equation, 1 mole of CaCO3 produces 1 mole of CO2. Since 25g is 0.25 mole of CaCO3, we conclude that 0.25 mole of CO2...

**Chemistry**

The question is not complete. I assume you are asked to find the quantity of CO2 produced by heating 25g of CaCO3. Molecular mass of CaCO3=40+12+48=100 From the equation, 1 mole of CaCO3 produces 1 mole of CO2. Since 25g is 0.25 mole of CaCO3, we conclude that 0.25 mole of CO2...

**algebra**

* outcome 3 is "hit neither"

**algebra**

Calculate expected gain, E(X), of the venture. If E(X) is positive, it would probably be advantageous to sink a well. Expected value is the following sum: E(x)=Σ G(X)*P(X) where X is a possible outcome, G(X) is the net gain of the outcome, and P(X) is the probability of ...

**computer science**

Looks good to me!

**algebra**

To find the x-intercept, set y=0 and solve for x.

**maths**

You're welcome!

**maths**

Area of each triangular face = (1/2)base*height Surface area of tetrahedron = 4*area of each face.

**Math**

3768 grains mean 3768*1 second=3768 seconds. Convert to hours, minutes and seconds: 3768 seconds / 60 s/min. =62 minutes 48 seconds = 1 hour 2 minutes 48 seconds. The other rewards may be worked out in a similar way.

**math**

4C3(1/2)^3(1/2)^1 =4(1/16) =1/4

**math**

2=2^1 3=3^1 4=2^2 5=5^1 6=2*3 7=7^1 The least common multiple must have factors that satisfy all of the above: 2^2*3*5*7=420

**math**

Mid-point of (3,8) and (9,16) =((3+9)/2, (8+16)/2) =(6,12) Mid-point of (8,11) and (x,13) =((8+x)/2, (11+13)/2) =((8+x)/2, 12) To have the same mid-point, the x- and y-coordinates of the mid points must match. so (8+x)/2 = 6 Solve for x.

**statistic**

Total number of balls = 5+6+6=17 P(RR)=Probability of two reds =(5/17)*(4/16) P(WW)=(6/17)*(5/16) P(BB)=(6/17)*(5/16) Probability of two same coloured balls =P(RR)+P(WW)+P(BB)

**math**

You have assumed compound interest compounded monthly. Assuming these assumptions are correct, then we have total amount F, R=monthly installment deposited at the end of the month, i=monthly interest, n=48, I=1+i, F=R(I^(n-1)+I^(n-2)+...+I^(0)) =R(I^n-1)/(I-1) =500((301/300)^...

**Basic Algebra**

Also, note that factors must exceed 8, from the context of the question.

**Basic Algebra**

See http://www.jiskha.com/display.cgi?id=1408443950