# Posts by MathMate

Total # Posts: 11,744

**Math**

(10,6) means x=10, y=6. To check if (10,6) is a solution to y=x-4, substitute into the equation values of x and y, i.e. y=6 (left hand side) x-4=10-4=6 Since left equals right hand side, (10,6) is a solution of y=x-4. Go through each of the answer choices to choose the correct...

**Math**

Mark-up percentage equals (selling price-cost price)/(cost price). For example, if I buy a case of oranges for $25 and sell it for $30, the mark-up is ($35-30)=$5 and the percentage mark-up is $5/$25=20%.

**Vector Calculus**

In your previous post, you have been asked what R3 stands for, and you have not clarified. We do not know yet if 3 is a superscript, a subscript, or just a number written in the wrong place. Yes, ? equals a vector < -sinφ, cosφ, 0 >. Also, are R,φ and z ...

**what happen i need an answer**

Another way to find out where you got stuck is to formulate your question in multiple posts. This way you can zoom in to where the problem lies. Or replace vectors <i,j,k> with (i,j,k), etc. but state that (i,j,k) is a vector.

**Dynamics**

Only the vertical component counts for the time for descent. Assuming no air resistance, we have from kinematics, S=ut+(1/2)at^2 where S=distance = 6400 ft u=initial velocity (=0 ft/s vertical in this case) a=acceleration due to gravity, g=32.2 ft/s² Substitute values, ...

**physics**

Use kinematics equation: v1²-v0²=2aS v1=final velocity (0 m/s) v0=initial velocity (20 m/s) S=distance travelled (100 m) solve for a=acceleration (negative because it's a deceleration) Use Newton's second law F=ma m=mass F=average (uniform) force over the ...

**Chemistry**

First the chemical equation, combustion of a hydrocarbon yields CO2 and H2O most of the time. 2C2H2(g)+5O2(g) ? 4CO2(g) + 2H2O(g) We see that 2L of C2H2 produces 4L of CO2 and 2L of H2O. However, when cooled to STP, H2O condenses to water (l.)

**frenche**

Please send an example of what you would like to do, then in addition to helping you with the example, we will have an idea where your difficulty is. Dictionaries is one way to help, and verb conjugators (such as the Bescherelle) would help with verb forms.

**math**

Let r=radius of pizza. Each sector has a radius of 2 times radius plus 1/8 of the circumference, or 10"=2r+(2πr)/8 Solve for r. Then calculate πr²=area of whole pizza.

**Chemistry**

If the temperature remains constant, then Boyles law applies: PV=constant Here P1=745 mmHg V1=65 L P2=745(1-0.3)=521.5 V2=? P1V1=P2V2 745*65=521.5*V2 Solve for V2.

**bearings**

As in all geometry problems, a detailed sketch will help you understand, and often solve, the problem. Define P as the origin of the Cartesian plane. Knowing that mPQ=40 km, then coordinates of Q are given by Q=P+40<cos(41),sin(41)> =Q(30.188,26.242) Similarly, R is ...

**Math**

Kite ABCD with AD=AB means AC is the line of symmetry, => ∠B=∠D. => 2x=(5x-147) Solve for x, and hence determine angles B & D. Using ∠A+∠B+∠C+∠D=360° Find ∠C and hence the smallest angle of the four.

**math**

See reply to your other question: http://www.jiskha.com/display.cgi?id=1484320142

**math**

A proportional relationship is represented by y=mx where m is a constant. If there is a y-intercept, it would be y=mx+b in which case the relationship is no longer proportional. For example, y=x+4 x y 1 5 2 6 3 7 is not proportional, because 1/5≠2/6≠3/7... Example of a ...

**algebra**

I believe the first equation has a typo due to missing parentheses because as is, it is already a quadratic equation. I think you mean 0.2=x^2/(55-x) Remember to insert parentheses in all numerators and denominators. To convert the equation to a quadratic, multiply both sides ...

**math check please**

Please show your work to find where your calculations went wrong (if applicable).

**Calculus**

Explicit form involves y on the left side, and no variable y on the right side, e.g. y=x^2, or y=sqrt(x)+2x Implicit form would have mixed x and y on either side, or both. Example: xy+ysup3;=3x²y

**science**

vegetative propagation is the propagation of a species by making simple copies of itself, sometimes through a stem, sometimes through the roots, or leaves, or bulbs. Advantage is that the plant does not need another plant nearby to reproduce (like in pears). However, since ...

**Computing**

Area of triangle can be calculated as follows: Area=(1/2) base * height or using Hero's formula, Area=sqrt(s(s-a)(s-b)(s-c)) where a,b,c are lengths of the three sides s=(a+b+c)/2

**math;););)**

Yesit'scertainlyweird,butthequestionisquiteinteresting! Let C=(2,1) [centre of rotation] P=(4,6) [point to be rotated] t=π/12 [15°, angle of rotation] The first part of the problem is solved as follows: Rotated point, P', is obtained by 1. translating the point ...

**math**

Math is intriguing because there are many ways to solve the same problem. Here's another way by minimizing the distance between the line and the point. 1. find the parametric form of the line AB, which is relatively easy because the line passes through the origin, so the ...

**Chemistry**

I don't know if you researched for answers, or if you researched for data. Whenever there are two cations and a single (or multiple) anions are in the same aqueous solution, we should first check if any of the combinations of cations and anions might be insoluble and hence...

**Calculus**

Use the product rule, d(sin(x)cos(x))/dx =cos(x)dsin(x)/dx+sin(x)dcos(x)/dx =cos²(x)-sin²(x) Next use sin²(x)+cos²(x)=1 to transform the above result to one of the provided answers. Note: an easier way to derive the given expression is to make use of the ...

**algebra**

What was posted does not represent an equation. Please check before posting. If I assume the second / is an equal sign, then the equation reads: (v^2 + 6v+8)/(v^2 + v - 12) = (v+2)/(2v-6) To solve this equation, we start by factoring the quadratic expression into: (v²+6v+...

**Algebra 2 (to Jazzy)**

Good, then you know what to change.

**Math**

Let the longest piece be 9x. Then we equate total length 294=2x+3x+9x=14x solve for x and hence calculate the longest piece equal to 9x.

**Physical Science**

It's normal that your book does not have the answers. However, it's time to review the topics "refraction" and "diffraction" with the help of your book.

**Mathematics**

Agree with your answer. Correlation coefficient of 0.793 is positive, but not strong. Follow following link to get a visual interpretation. https://www.mathsisfun.com/data/correlation.html

**physics**

The following link explains the solution to a similar problem and helps you get familiar with the standard formulas used in kinematics. http://www.jiskha.com/display.cgi?id=1426656652

**Science**

Here's an article that explains how MRSA's resistance to antibiotics has evolved, touching on horizontal and vertical evolution. http://evolution.berkeley.edu/evolibrary/news/080401_mrsa

**physics**

See answer to a similar problem: http://www.jiskha.com/display.cgi?id=1383603887

**physics**

See solution to a similar problem: http://www.jiskha.com/display.cgi?id=1321918140

**Calculus**

Use the power rule: https://www.mathsisfun.com/calculus/derivatives-rules.html

**Math**

f(x)=x^sup2;-5 Use the power rule to find f'(x) => f'(x)=2x at point P(2,-1), x=2 therefore f'(x)=f'(2)=2*2=4 Slope of the tangent equals the derivative of the function at the point in question.

**Physics**

If it means to boil dry the water in the tank, then it takes 540x calories to boil it dry, compared with 80x to raise the water to 100°C. However, question says: "will make the water boil and keep it at that state" and does not say the tank must be boiled dry!

**Physics**

The first option: 1 calorie raises the temperature of one gram of water by 1°C. So 80 cal raises the temperature of 1 g of water by 80 degrees. (80°=100°-20°) So it takes 80x cal.to raise the temperature of water to the boiling, where x is the mass of water in ...

**physics**

Use ΣmCΔT=0 Let m1=mass of ice required. m2=mass of water to be cooled = 200 g T11=-14 T12=10 T21=25 T22=10 Specific heat of water = 1 cal/g/°C Lf=latent heat of fusion of ice = 80 cal/g Heat lost by water: mCΔT =200*1*(25-10) =3000 cal. Heat gained by ...

**Physics**

Absolute pressure is the pressure on a surface including atmospheric pressure. Gauge pressure is the additional pressure acting on a surface over and above atmospheric pressure. At the ocean depth of 1000 m, gauge pressure is the pressure exerted by the weight of water above ...

**physics**

Let s=specific gravity of mercury=13.6 K=point at lower end of water column h=height of mercury above K in the other column then equate pressure at K on both arms: 13.6*1.00 = h*13.6 solving, h=1.00 cm This means that the mercury level was at 1.00/2=0.50 above K before adding ...

**physics (to Cameron/Tyler)**

Among the 9 physics questions you have posted within the last 24 hours, you have not shown any effort on your part. Is it because you have absolutely no idea about the subject, or is it because you'd like someone else to do the work for you? If it is the former, I suggest ...

**physics**

Assuming no loss in the impact(s), then, let M=mass of Juggles and equate gravitational potential energy (g=acceleration due to gravity) 75kg*g*2.5=M*3.7*g Solve for M.

**PLEASE HELP BEEN STUCK ALL DAY CALCULUS**

If we apply linear approximation using calculus, then: V=πr^2h dV/dr=2πrh ΔV≈2πrhΔr =2π(4)(12)(+0.2-(-0.2)) =2π(4)(12)(0.4) =38.4π

**Physics**

Newton is kg-m/s² Since both sides of the equal sign must have the same units, we conclude: a * m = kg-m/s² and B *kg/m = kg-m/s² Find the units of a and B by solving the two given equations.

**Physics**

Ignoring dissipative losses (air resistance, friction, etc.), difference of kinetic energy equals work done, => (1/2)m(28.3^2-23.3^2)=226000 j Solve for m.

**Maths**

There is at least one great circle that passes through any two non-coincident points lying on a sphere. If the two points are diametrically located, there is an infinite number of great circles that pass through the two points. The proof is relatively simple. The two points ...

**Maths**

Assuming the earth is a perfect sphere, and with a radius of 6400 km, there are exactly two parallels with a radius of 2500 km, located at approximately cos-1(2500/6400) =67° N or S.

**Maths**

See response to related/similar problem. http://www.jiskha.com/display.cgi?id=1454498132

**math**

The reflex angle of a given angle is the larger between the angle itself, and the angle formed by 360 minus the angle. For example, the reflex angle of 150° is 360-150=210°. Since angle pqr=1 1/2 right angles = 135°. Calculate the reflex angle of 135° by ...

**math**

We started with k tags. after students, we have k-k/2=k/2 left. after parents, we have k/2-100 left after teachers, we have (k/2-100)(1-3/5) left You can simplify the last expression to present the final answer.

**Statistics**

Use Z=(X-μ)/σ where Z=z-score X=variable value μ=mean σ=standard deviation Assuming normal distribution, the left-tail normal distribution table gives the probability of the z-score (or less). Example, part (a): If N=300 and random sampling, we can assume ...

**Math**

Draw a Venn diagram with three overlapping circles A, B and C. Hint: start with the area A∩B∩C (in the middle) and work outwards. When completed, it will be a snap to answer the given questions.

**math**

(a) N = 11 choose 2 (=11C2) (c) 11 choose 2 less 7 choose 2, i.e. N minus number of ways of choosing two men.

**Math**

If there are 14 people, there are 14C2 ways to choose the 2 alternatives. If there are 15 people, there are 15C14 ways to choose the 14 people. So the number of ways of choosing 12 jurors and 2 alternatives is 15C14*14C2

**Math**

We know that time=distance / speed In this case, time = total distance / total speed =1029 miles / (45+53) mph = ? hours

**Chemistry**

Use the ratio of atomic mass to the molecular mass. For example, to find the number of grams of Na in 20 g of NaOH atomic mass of Na = 23 molecular mass of NaOH=23+16+1=40 mass of Na in 20 g of NaOH =20g*(23/40)=11.5g

**EmberShy**

Yes, because (-6.8)² =(-1)²(6.8)² =(1)(46.24) =46.24 Be aware of usage of parentheses, for example: (-2)² =(-1²)(2²) =(1)(4) =4 BUT -2² =-(2²) =-(4) =-4

**Math 12**

The standard equation for depreciation is FV=PV(1-i)n where FV=future value PV=present value i=depreciation rate per annum, in decimals n=number of years Example: Find the value of a car after 10 years if it was purchased for 50000 and depreciated at 20% per year. PV=50000 i=0...

**Geology and soils**

Void ratio, e, is the volume of voids, Vv, divided by the soil volume Vs. Total mass, M=37.82-16.15=21.67 Mass of solids, Ms=34.68-16.15=18.53 Gs=S.G. of soil particles = 2.7 => Vol of soil, Vs=Ms/Gs=18.53/2.7=6.863 mL air-void content, ac=0 => all voids are filled with ...

**Chemistry**

The first three questions may be solved using the relation: molarity (mols) = number of moles / volume (L) where number of moles = mass (g) / molar mass (g). Example: 10.0 g of NaCl is dissolved to make 0.523 L of solution. Find molarity of the NaCl solution. number of moles...

**math**

Regular price = 4 shirts at sale price 2*regular price = how many shirts at sale price ?

**Science, Chemistry**

First write the neutralization equation: NaOH+HNO3 -> NaNO3+H2O so C1V1=C2V2 2.0M*0.25L=XM*1.050L Solve for X and compare with 0.48. Pay careful attention to significant figures.

**Physics**

Convert initial velocities to m/s 60 km/h=60*1000/3600 m/s=16.67 m/s 180 km/h = 50 m/s Use kinematic equation: v^2-u^2=2aS where u=initial velocity v=final velocity a=acceleration (deceleration is negative) S=distance travelled before stopping

**algebra**

The minimum of a parabola is the y-value of the vertex. See previous response.

**algebra**

By completing the square, y=x^2-4x-32 =(x-2)²-4-32 =(x-2)²-36 The line x-2=0 passes through the vertex, hence the vertex is (2,y(2))=(2, -36) The line of symmetry of a parabola that opens up or down is the vertical line through the vertex.

**algebra**

When the leading coefficient is positive, a parabola opens up. Leading coefficient is the coefficient of the term with the highest degree.

**math**

Answer is good up to (0.4k+0.6w) L. Since we do not know the values of k nor w, their coefficients cannot be added together. The correct answer would be (0.4k+0.6w) L.

**math**

Example to help you: 30% of 4L of orange juice is added to 70% of 5L of grapefruit juice, find the total volume. Volume of orange juice = 30% of 4L =0.30*4 =1.2L Volume of grapefruit juice=70% of 5L =0.7*5 =3.5L Total volume = 1.2L+3.5L=4.7L

**Physics**

(a) Law of conservation of momentum: m1v1+m2v2=(m1+m2)v since m2=0.1m1 m1v1+0.1m1v2=(1.1m1)v solve for v v=(m1)(v1+0.1v2)/(1.1m1) =(v1+0.1v2)/1.1 (b) Assuming no loss in total energy, and assuming v1>v2, then the shark itself (without food) has lost energy, since its ...

**kelvin**

In geometry, drawing a sketch from given information is half-way to the solution. Note bearing is measured clockwise from North. If you draw the sketch in Cartesian coordinates, using P at the origin, you will have P(0,0) Bearing 150°? ?=90-150=-60° in Cartesian ...

**Geometry**

You're welcome! :)

**Geometry**

By the law of segments, mCB+mBD=mCD so 4w-4 + 2w-8 = 24 Solve for w.

**Math**

Yes, your approach is correct, except watch for the following. (1) In principle, part (A) should be done using calculus. If you have not done calculus before, what you did is appropriate, EXCEPT that the interval for p between 4 and 2 is way too large because q(p) varies ...

**chemisry**

Solubility is the amount of solid that dissolves in 100g of water at the given temperature. 10.1 g dissolves in 50 g H2O at 25°C X g dissolves in 100 g H2O at 25°C Solve for X.

**chemistry**

Cu(II) oxide is CuO so 3CuO+2NH3 → 3Cu+N2+3H2O From 2NH3 and 3CuO, we conclude that 2 moles of NH3 reacts with 3 moles of CuO to form 1 mol of N2. Find the molar masses of NH3 and CuO and determine which is the limiting reagent. Use stoichiometric ratios to ...

**physics**

Kinematics equation with zero initial velocity: h=(1/2)gt^2 => time, t = √(2h/g) seconds h=49', g=32.2 ft/s² speed = distance/time = (80-3)/t ft/s =44.14 fps

**Algebra (math)**

horizontal lines have zero slope, so rate of change (=slope)=0. Any straight-line function has the form y=mx+b where m is the slope, and b is a constant. Compare this with the equation of function 2 to determine the slope. Since rate of change of function 1 is zero, so ...

**maths**

smallest number with 3 different digits: 100000...000002 assuming leading zeroes do not count. Add enough zeroes in the middle to satisfy the minimum number of digits. Example: 1,002 in the thousands 1,000,002 in the millions, etc.

**Math**

It depends on how many tests you have had, and what you will get for the final.

**Math**

Distribute and simplify: (1/3)x(15x-12y)-(1/2)(6x-4y) =x(5x-4y\)-(3x-2y) =5x²-4xy -3x +2y

**Maths**

A rhombus has four equal sides. One way is to prove that the two triangles on each side of a diagonal are congruent. Since the altitudes of these isosceles triangles are congruent and are the altitudes of the rhombus, the altitudes of a rhombus are congruent.

**chemistry**

See answer to your previous question: http://www.jiskha.com/display.cgi?id=1483510596

**chemistry**

Answer is in the products of the reaction. The reactants are already known. H2S (g) +Zn(NO3)2 (aq) &rarrow; ZnS (s) + 2HNO3 (aq)

**maths**

Each free cube has a surface area of 6(10²)=600 cm² exposed. Each cube with one face connected has 5(10²)=500 cm² exposed. Each cube with two faces connected has 4(10²)=400 cm² exposed. If n cubes are joined together, there are 2 (end) cubes with ...

**math**

Sorry, I don't understand what your "working" is trying to do, but in any case, 8+5≠13/2≠11.5 and so on, so some corrections on your part need to be done. Given that a:b = 8:5 and b:c= 3:4 What we need to do is to multiply each ratio appropriately so that ...

**geometry**

complement of angle X=90-X supplement of angle X=180-X => complement (C) =supplement (S) -90 C+S=126 C+(C+90)=126 2C=126-90 Solve for C and hence X.

**math**

Given R=6400 km arc=Rθ The first leg is equi-latitude at 40N with a meridian difference of θx=(38-22)=16° Distance travelled =Rθx cos(40) =6400*(16*π/180)cos(40) =1369.09 km The second leg is along a meridian with a latitude difference of θy(40-...

**Math**

height : shadow = 25 :15 = 40 : X? Cross multiply to get X=40*15/25=24 m

**Physics 1**

See related questions, for example: http://www.jiskha.com/display.cgi?id=1350232603

**Chemistry HELP! CONFUSED!**

First write the equation of the reaction: reactants: NaHCO3+CH3COOH products: CH3COONa+CO2+H2O From the molar masses of NaHCO3 = 23+1+12+3*16 = 84 CO2 = 12+2*16 = 44 We find the stoichiometric ratio of the two compounds to be 84:44 (approximately) Hence by proportions/ratios, ...

**Statistics**

Assuming probabilities work evenly for 30 times, then you would have won the $5 prize 30*0.15=4.5 times, with a total value of 4.5*5=$22.5 while paying $30 to play. So your expected winning (for one play) is 22.5/30-$1=0.75-1=-$0.25 i.e. you expect to lose 25 cents each time ...

**Engineering**

If you substitute any of the four answer choices into the equation: (y-2)^3=(y+2)^3 you will find that none of them is a good answer. So I suspect there is a typo for the question. The equation as shown above can be solved by assuming y=a+bi Expand both sides to give 12b^2-...

**maths**

Area of the (orange) right triangle =(3*4)/2 =6 units Area of the rectangular board =20*15 =300 units Assume that 1. a dart always falls within the rectangular board 2. the probability of hitting anywhere in the rectangle is equal then the probability of the dart striking the ...

**chemistry**

In chemistry, since there are more than 26 elements, some elements are represented by two letters of the alphabet. The first (or the only) letter of an element is ALWAYS written in capital letters to avoid confusion, since formulas of compounds are written without delimiters. ...

**Math**

Work from inside the parentheses, (g(f(3x))' for x=1 =(g(f(3(1)))' =(g(f(3))' =(g(2))' [from table] =g'(2) =5 [from table]

**math**

Assume "store one year" means 365 box-days and not "a year or part thereof". k=320000 boxes/year = 320000/365 boxes/day = 876.7 boxes/day If supplies are produced every n days, then it must produce nk boxes at each production, and storage requirements are P...

**Geometry**

What does [ABCD] represent? If it is the area of the kite, then we know that the area of a kite is the product of the diagonals ÷ 2. Note: You are fully expected to draw a duly labelled sketch in order to follow the following explanations. So AC*BD/2=60 AC*BD=60*2=120 ...

**computer,science, java**

See http://www.jiskha.com/display.cgi?id=1483264139

**mathematics**

For a (complete) sphere, volume=(4/3)πr³ The volume of material is the volume of whole sphere (radius r2) minus the volume of empty spherical space (radius r1). The thickness t is the difference between r1 and r2, i.e. r1+t=r2. Vm=(4/3)π(r2³-r1³) The ...

**Math**

Area of a rectangle = Length * width (or breadth) = L*W Take out your calculator to calculate the product. For someone who has done factoring, 11.5*12.5 =(12-.5)(12+.5) =12²-0.5² =144-0.25 =143.75 without using a calculator.

**math**

We know that diagonals of parallelograms bisect each other. Using this fact, we would draw two intersection lines with an included angle of 60° (and 120°). From the intersection, measure out four vertices 5/2=2.5 cm on each side of one line, and 7/2=3.5 cm on each side...