plumpycat

Take upwards and direction of travel as positive. Horizontally: Fa + Ff = 0 10cos(60) N + Ff = 0 Ff = -5 N Vertically: Fa + Fg + Fn = 0 10sin(60) N + (-100) N + Fn = 0 Fn = 100 - 5sqrt(3) N

8 years ago

Let x be Harry's original amount of money. Let y be Tom's original amount of money. Let z be Dick's original amount of money. x + y + z = 107.60 x + 2.10 + x + 2.10 + z = 107.60 x + 3.10 + x + 2.10 + x + 3.10 = 107.60 Solve the system of equations.

8 years ago

e^1 --> substitute 1 wherever you see x: e^1=1 + 1/1! + 1^2/2! + 1^3/3!+⋯,-∞<x<∞ Add as many terms as you need to, until the sum stays at the same 4 significant figures. Similar idea for x=2

8 years ago

Try some samples to see: i = 1, j = 1: k from 1 to 1 --> 1 Hello i = 1, j = 2: k from 1 to 2 --> 2 Hellos i = 1, j = 3: k from 1 to 3 --> 3 Hellos . . . i = 1, j = 10: k from 1 to 10 --> 10 Hellos So for i = 1, sum the numbers from 1 to 10 (triangular for...

8 years ago

Yes, that's correct.

8 years ago

Let the short side be x inches long. Then the long side is 2x + 2 inches long. Now make an equation using the area formula for a rectangle: L * W = A (2x + 2)*x = 1200 And solve for x. (Remember x is the short side length; you can now use this to find the...

8 years ago

4c2*6c2

8 years ago

Proportion submersed = density of wood/density of Dead Sea = 800/(1.24 *10^3) ~ 0.65 or 65 % So the proportion above the surface would be 1 minus that.

8 years ago

I encourage you to sketch parallelogram ABCD and mark it up accordingly as you read through this. Let point E be the midpoint of BC, and hence also the point where angle A's bisector meets BC. Let point F be the point where angle B's bisector meets AD. Dr...

8 years ago

Radius = 4.6/2 = 2.3 Area = pi*(2.3)^2*(210/360)

8 years ago

The time was measured at post 5 and post 14. The number of post gaps between post 5 and post 9 is 14 - 5 = 9 We know each post gap is 2.5 m long. So the horse ran 2.5 m x 9 = 22.5 m West This displacement of the horse occurred in 11.5 s - 9 s = 2.5 s. Vel...

8 years ago

If it starts with a 1, 2, 3, or 4: 4 choices for the first number 6 choices for the second number 5 choices for the third number If it starts with a 5: 1 choice for the first number 1 choice for the second number 1 choice for the third number Therefore, 4...

8 years ago

Correction: it can't start with a 5 as there are no zeroes to choose. So just 4*6*5 = 120

8 years ago

g = (1/3)s + 2....eq1 m = g + 5....eq2 Sub eq1 into eq2 to get m in terms of s.

8 years ago

He has 3 choices of pants and 5 choices of shirts. Therefore, the number of possible outfits he can wear = 3 x 5 = 15 Only 1 of these possible outfits is black pants/ red shirt. Therefore, probability is 1/15.

8 years ago

Look at total volume of solution: Mixing 15 L of first solution and 30 L of second solution gives 45 L of final solution. (i.e., 15 + 30 = 45) Now look at total volume of alcohol portion only: 36% of 15 + 45% of 30 = x% of 45 In other words, 0.36(15) + 0....

8 years ago

A table can be helpful: Real time Clock time (p.m.) (p.m) 1:00 1:00 2:00 2:20 3:00 3:40 4:00 5:00 5:00 6:20 Clock time: We can see that the desired clock time of 6:00 occurs in the interval between 5:00 and 6:20. From 5:00 to 6:20 is an 80 minute gap, but...

8 years ago

There must be some typos in the above. The correct answer is f(x) = -10cos((2π/3)x) + 10

8 years ago

Where is the table of Joel's results?

8 years ago

ρ(x) = ax + b ρ(0) = a(0) + b = 2 Thus b = 2 and we have: ρ(x) = ax + 2 Now, ρ(10) = a(10) + 2 = 17 Thus a = 1.5 and we have: ρ(x) = 1.5x + 2 Mass: M = ∫ (1.5x + 2)dx from 0 to 10 = [0.75x^2 + 2x] from 0 to 10 = [0.75(10)^2 + 2(10) - 0] = ____ kg Centre o...

8 years ago

You are correct.

8 years ago

20% of 102,000 = 20,400 Loan amount = 102,000 - 20,400 = 81,600 3% of 81,600 = 2,448 Total downpayment = 20,400 + 2,448 = _____

8 years ago

P = L[c(1 + c)n]/[(1 + c)n - 1] Where: P is monthly payment L is 30,000 - 5% of 30,000 = ______ n = 20 yrs x 12 months/yr = ______ c = 10%/12 = 0.10/12 = _____ Once you've found the monthly payments, the interest you paid is: P*n - L Use a similar process...

8 years ago

1 half life is 8 days. 48 days / 8 days per half life = 6 half lives that occur, so we halve our original amount 6 times. Amount remaining = 257 g * (1/2)^6

8 years ago

5 x 10^2 = 5 x100 = 500 3 x 10^3 = 3 x ____ = ____ Compare 500 and the next line's result to determine your answer.

8 years ago

Multiplication is the short method for repeated addition of the same quantity.

8 years ago

On a die, 3 numbers are prime (2, 3, 5) and 3 numbers are not prime (1, 4, 6). Since the chances of rolling a prime each time are the same as those of not rolling a prime each time, we can treat it much like a coin toss. 2 outcomes each roll (Prime or Not...

8 years ago

Let x be Deborah's age, in years. Therefore her father's age is 2x. Their ages add up to 45: x + 2x = 45 Solve for x. If you haven't learned to use variables and equations yet, you can set up a table with these headers: Deb's age.....dad's age....adds to...

8 years ago

It doesn't take long to list these cases, using uppercase letters to show correct placement and lowercase letters to show incorrect placement: ABdc AdCb AcbD dBCa cBaD baCD We see there are 6 ways for this event to happen, or 4c2, out of 4! total possible...

8 years ago

a) An efficient method is to consider the number of ways to include 0 or 1 teachers, then subtract that from the total number of ways to make a committee. 0 teachers: 10c5 Exactly one teacher: 6c1*10c4 Total ways to choose a committee with no restrictions...

8 years ago

Acceleration = change in speed/ change in time = (8 - 0) m/s / 6 s = ______ m/s^2

8 years ago

P(A hits,B misses) = (1/4)(2/3) = _____

8 years ago

Let Q1 be the larger charge. Let Q3 be the smaller charge. Let Q2 be the charge at the point where the total electric field is zero. Let x be the distance from the larger charge to this point. (kQ1Q2)/x^2 = (kQ3Q2)/(0.025 - x)^2 Divide out common factors...

8 years ago

We can't see a diagram on this forum. However, one way a staircase of 12 blocks could be built is: First step is 2 blocks wide and 1 block tall (2 blocks) Second step is 2 blocks wide and 2 blocks tall (4 blocks) Third steps is 2 blocks wide and 3 blocks...

8 years ago

Original cylinder volume: πr^2h Doubled height, halved radius cylinder volume: π(r/2)^2(2h) = π(r^2/4)(2h) = πr^2h/2 Therefore, this one is half the volume of the original cylinder. Halved height, doubled radius cylinder volume: ...you try this one...

8 years ago

Time required to get up to speed: theta = (1/2)(w0 + w)*t 5 rev = (1/2)(0 rev/s + 420/60 rev/s)*t t = 1/7 s Angular speed that the CD gets up to: 420/60 rev/sec *2 π rad/rev = 14 π rad/s Angular acceleration of CD: alpha = (14 π rad/s - 0 rad/s)/(1/7)s al...

8 years ago

There is not enough information given. Do you mean that PKLMN = 132 is the perimeter? If so, there are several answers; e.g.: LM = 8 KN = 9 KL = 57.5 MN = 57.5 or LM = 16 KN = 18 KL = 49 MN = 49 Etc.

8 years ago

Well you could solve it like this: Since LM/KN = 8/9, let LM = 8x and KM = 9x. Leg length = (132 - 8x - 9x)/2 Leg length = (132-17x)/2 As we can see, x can take on any value such that x < 132/17, giving a myriad of possible answers for leg length, 2 of wh...

8 years ago

Cost of one kg of sugar: = (₹ 825/4) / (11/2 kg) = (825/4) * (2/11) ₹/kg Divide out common factors 2 and 11: = (75/2) * (1/1) = 75/2 ₹/kg So the cost of 33/4 kg of sugar is: (75/2 ₹/kg) * (33/4 kg) = ______ ₹

8 years ago

1. First draw a picture of the situation, so that you can see where these charges are located on the Cartesian Plane, and the angles involved. 2. Use Coulomb's Law: Force of q1 on q3 (it pushes q3 away) F1= (kq1q3)/(r)^2 Force of q2 on q3 (it pulls on q3)...

8 years ago

Assuming 0.65 is the coefficient of static friction, u. If you resolve forces acting perpendicular to the ramp, with the direction of the normal force as positive: Fn - mg*cos30 = 0 Fn - (12)(9.81)*cos30 = 0 Fn = 101.95 N Then: Fs = u * Fn Fs = 0.65 (101....

8 years ago

1. Your url is incomplete - but why not just say in your question how many numbers are on the spinner ( e.g. 1-7? 1-8?) 2. What do you think are the answers?

8 years ago

Assuming simple interest, since compounding isn't mentioned in the question: 18 months = 1.5 years I = Prt 190 = 1500 * r * 1.5 r ~ 0.084 or 8.4 %/a

8 years ago

Draw ||gm ABCD, with AB and CD as the short sides and angle ABC obtuse. Draw diagonal BD = 14 cm and diagonal AC = 16 cm. Let E be the point of intersection of the two diagonals. Diagonals of a ||gm bisect each other, so BE = ED = 7 and AE = EC = 8 It is...

8 years ago

I'm assuming your first ship is 3 km from the harbour, since you said "also 3 km" for the second ship. Drawing a simple picture with a pencil and ruler, reasonably to scale, is very helpful for bearing questions like this one. Draw a compass (N, S, E, W l...

8 years ago

a) v-s relationship is v = ds/dt. Did you mean to say v-t relationship? If so that is: v = ∫ a dt v = ∫ (6t) dt v = 3t^2 + c 4 = 3(1)^2 + c c = 1 v = 3t^2 + 1 b) s = ∫ v dt s = ∫ (3t^2 + 1) dt Continue similarly to a) above.

8 years ago

F = (kq1q2)/r^2 0.078 N = (9 * 10^9 N*m^2/C^2)(3.7 * 10^-6 C)(q2)/(1.3 m)^2 q2 = 0.078 N * (1.3 m)^2/((9 * 10^9 N*m^2/C^2)(3.7 * 10^-6 C)) q2 = _______ C

8 years ago

Also note that q2 will be negative because the force is attraction.

8 years ago

Assuming "bottom of the incline" means the mass is on the incline already, with a velocity of 5.0 m/s parallel to the incline surface. Fa - Ff - Fg = 0 (3 kg) * a - 20N + (3 kg)(-9.81 m/s^2)sin37 N = 0 a = -12.57 m/s^2 vf^2 = vi^2 + 2ad 0 = (5 m/s)^2 + 2...

8 years ago

M.A. = V.R. * Efficiency M.A. = 5 * 40 / 100 M.A. = 2 Effort = Load / M.A. Effort = 100 N / 2 Effort = 50 N

8 years ago

M.A. = Load/Effort M.A. = 40 N / 60 N M.A. = 2/3 V.R.= M.A./ Efficiency V.R.= (2/3) / (40/100) V.R.= _______

8 years ago

T = 654 min * 60 s /min = 39240 s G = 6.673 * 10^-11 N*m ²/kg ² M = 5.98 * 10^24 kg T ² = 4 π ² a ³ / (GM) Rearrange: a ³ = T ² GM / (4 π ²) Substitute the above values of T, G, amd M, and solve for a. e = 0.40 Number of m above earth's surface at closest...

8 years ago

Intensity 1 = k / r ² Intensity 2 = k / (5r) ² = k / 25r ² = (1/25) k / r ² = (1/25) Intensity 1

8 years ago

The horizontal component is: 35cos15 m/s = _______ m/s (round to 2 decimal places) Which trig ratio would you use, then, for the vertical component? Constructing a simple diagram of the situation is very helpful.

8 years ago

Vf ² = Vi ² + 2ad Vf ² = 0 + 2(9.8)(20) Vf ² = 392 Vf ~ 19.80 m/s when it lands. Initial speed coming back up: (3/4)(19.80) = 14.85 m/s Equation of motion for second bounce: d = Vit + (1/2)at ² d = 14.85t + (1/2)(-9.8)t ² Substitute d = 0 (to represent th...

8 years ago

If you take the time to construct this quadrilateral and its diagonal, it can be seen that there are two triangles that each consist of a Pythagorean triad: 9, 12, 15 and 5,12, 13, meaning that both triangles are right angled. Area of a right angled trian...

8 years ago

One way to solve is to look at a Combinations version of Pascal's triangle. Find the diagonal along which all the "choose 3" combinations live. Then compare this to the Number version of Pascal's triangle to see where 120 occurs, and you'll quickly see wh...

8 years ago

A rhombus has four sides equal in length and opposite sides parallel. Opposite interior angles are equal. Also, the diagonals bisect the interior angles. Try constructing a rough sketch of a rhombus with a pencil and ruler. Label all 4 sides with"10" and...

8 years ago

√3: 3 is not a perfect square, but the nearest perfect squares are 1 and 4. Thus √3 lies somewhere between √1 and √4. Picture the numbers 1, 3 and 4 on a number line. It takes 2 jumps to get from 1 to 3. It takes 3 jumps to get from 1 to 4. That means 3 i...

8 years ago

It's kind of an oddly worded question - it states a speed of 6cm/sec, but goes on immediately in part 1. to change this to 8cm/s... 1. A point on the wheel travels a distance of the circumference of the wheel in one rotation, or 2π * 5 = 10π cm 10π cm div...

8 years ago

x - a - 1 = x - (a+1) The remainder will be P(a+1): P(a+1) = (a+1) ³ -2a(a+1) ² +1 Expand and simplify.

8 years ago

(15/13)(3/4) = _____ L used to water the plants. If 3/4 of the water was used, 1/4 of the water is left: (15/13)(1/4) = _____ L

8 years ago

Wavelength is the distance from crest to next crest or from trough to next trough. 15 cm from crest to next trough represents half a wavelength, so take 15 cm * 2.

8 years ago

Search the phrase: calculation of pressure forces on submerged plates First result takes you to an example of a rectangular plate submerged in the way your question describes.

8 years ago

Torque = force applied * lever arm = 50.0 N * 0.400m = _____ N*m Torque = angular acceleration * moment of inertia You know the torque and are given the moment of inertia; substitute these into the above equation and solve for the angular acceleration.

8 years ago

The entire structure has a height of 5, or just the hemisphere? Either way, there's not enough information to answer the question.

8 years ago

Change minus to plus and then it's all good.

8 years ago

First, calculate the mean, x̄, by adding the data items together and dividing by the the total number of data items, 10. Using your data in the order you provided it, the standard deviation is now: s = √ [ ( 1.3 - x̄ ) ² + ( 2.4 - x̄ ) ² + ..... + (1.8 -...

8 years ago

Average velocity = displacement/ total time Train travels 1/2 h * 54 km/ h E = 27 km E Train travels 2/3 h * 54 km/ h N = 36 km N A rough sketch of the above displacement vectors is helpful: use the Pythagorean Theorem to find the magnitude of the resulta...

8 years ago

A = Ao (1/2)^(t/h) 274 = 280 (1/2)^(6/h) (274/280) = (1/2)^(6/h) This can now be solved with logarithms, but if you haven't learned those yet, trial and error is the way to go.

8 years ago

Time it takes her to drive = distance/speed = 24 miles / 30 miles/h = 4/5 hours Convert to minutes to compare to the desired time of 45 min.

8 years ago

LS = (1+tan21) (1+tan28) (1+tan24) (1+tan17) = [(1+tan21) (1+tan24)] [1+tan28) (1+tan17)] = [1+ tan24 + tan21 + tan21tan24] [...] = [1+tan(24+41)(1-tan21tan24) + tan21tan24] [...] = [1+ tan45(1-tan21tan24) + tan21tan24] [...] = [1+ 1(1-tan21tan24)) + tan2...

8 years ago

E(X) = (5¤ - 5¤) * 10% + (100¤ - 5¤) * 1% + (0¤ - 5¤) * 89% E(X) = 0 * 10% + (95) * 1% + (-5) * 89% = -3.5¤ SD(X) = √ [ (0 - (-3.5)) ² * 10% + (95 - (-3.5)) ² * 1% + (-5 - (-3.5)) ² * 89%] SD(X) = _______

8 years ago

To get started, search for: Newton's Laws of Motion - NASA

8 years ago

First question: try again Second question: try

8 years ago

Search for THE HALF-LIFE OF DICE - Vicphysics It explains very well how to do this.

8 years ago

A baseball diamond is a square. The runner runs along the edges of the square.

8 years ago

Find Z: Z = (x - μ) / σ Z = (6000 - 5274) / 600 Z = 1.21 Now look at a Z table for normal distributions. Z = 1.21 corresponds to a probability of 0.8869. This means that P(X ≤ 6000) = 0.8869. So P(X > 6000) = 1 - 0.8869 = ______ The middle 50% is bordered...

8 years ago

(1/2)x + (1/3)x + 50000 = x Solve for x.

8 years ago

Everything you've mentioned is correct. You might check that the boundaries are shown correctly: The absolute value graph should have a solid circle at (-3, 3) and an open circle at (2, 2). The linear function should have an arrow on the downward-left end...

8 years ago

There must be some error here. Suppose x = 5, a = -1, b = -10. Then: x ² + 2ax + b = 5 ² + 2(-1)(5) + (-10) = 25 - 10 - 10 = 5 And: b ² -a ² = (-10) ² - (-1) ² = 100 - 1 = 99 5 < 99 Thus x ² + 2ax + b can be less than b ² -a ².

8 years ago

Power = work/time Look at the equation - If time increases, would power increase or decrease? If you're not sure, plug some numbers into the equation.

8 years ago

You're mentioning the y coordinate for the first end and the x coordinate for the other end, so it's a little confusing. There should be an open circle at (0,1.25), and a horizontal line from there to (1, 1.25), where we should see a closed circle. Then a...

8 years ago

Please clarify your question. Currently, it is asking what the diagonal is, but also stating that the diagonal is 14 m.

8 years ago

A single positive charge = 1.6 * 10^-19 C qvB = mv ² / r Rearrange to find m: m = qrB / v m = (1.6 * 10^-19 C)(1.8 m)(0.315 T) / (2.4 * 10^5 m/s) m = _______ kg

8 years ago

I'm going to assume you meant 45.0 m tall for the building (rather than cm). Vertically (take upward as positive): d = vit + (1/2)at ² -45 = 0*t + (1/2)(-9.81)t ² t ~ 3.0 s Horizontally (take direction of throw as positive) d = vit 24 = vi (3.0) vi ~ 8 m/...

8 years ago

1st Question: try again 2nd question: correct

8 years ago

B is correct. Probability of rolling a 3 or a 5 is 2/6 = 1/3 (1/3)(180) = 60

8 years ago

No worries.

8 years ago

This is a great investigation into numbers...I encourage you to start a systematic table, working out the LCM for: 1 1, 2 1, 2, 3 1, 2, 3, 4 Etc. You may then see a pattern developing that will help you answer your question.

8 years ago

A recent study looks to have been done by the University of Turku, Finland, and published in the journal Molecular Ecology...your school library may allow you free access to this journal. Otherwise, several sites come up with summary articles when you sea...

8 years ago

Assume the web strands have negligible weight. (Hint: It is helpful to draw a FBD of each of these situations to better understand the forces and angles involved.) a) vertical forces sum to 0: Ft - Fg =0 Ft - ( 8.00 * 10^-5 kg )( 9.81 m/s ² ) = 0 Ft = ___...

8 years ago

K.E. = (1/2) mv ² K.E. = (1/2) ( 0.5 kg )( 10 m/s ) ² K.E. = ______ J M.E. = K.E. + P.E. M.E. = ______ J + 0 J M.E. = ______ J

8 years ago

Reiny's answer requires another factor, 5. 23*5*x

8 years ago

1:3000 means that 1 cm on the map represents 3000 cm in real life. Thus, 9.5 cm on the map represents 9.5*3000 cm in real life. Once you calculate this, you may wish to convert it to metres to make it more readable/understandable.

8 years ago

Greatest resultant occurs when the forces act in the same direction: Resultant = 12 N + 8 N = 20 N, in the direction of the forces. Least resultant occurs when the forces act in opposite directions: Resultant = 12 N - 8 N = 4 N, in the direction of the 12...

8 years ago

It will slightly reduce the mass of water in the calorimeter, but may also slightly increase the water's change in temperature (smaller amount of water to heat up).

8 years ago

Yes, looks good.

8 years ago

Volume = length * breadth * height ft³

8 years ago

Q = mc ΔT -9750 J = (335 g)(4.18 J/(g.°C))(Tf °C - 65.5 ° C) Tf = ______ °C Exothermic processes release heat, while endothermic processes absorb heat.

8 years ago