# Posts by Jai

Total # Posts: 1,998

Science
Speed is distance traveled over time, or v = d/t Let x = time needed for the next 60 km 120 km/hr (average) = [(speed1) + (speed2)] / 2 120 = (60 + (60/t)) / 2 240 = 60 + 60/t 60/t = 240 - 60 60/t = 180 km/hr (speed2) time needed to achieve this speed is t = 60/180 = 1/3 hr

Algebra 2
I interpreted it as: 2/x + 1/(2x) = 4/(2x) + 1/(2x) = 5/(2x) But we can also interpret it as: 2/x + (1/2)x = 2/x + x/2 = 4/(2x) + x^2/(2x) = (4 + x^2) / 2x It depends on the expression is shown or typed. Placing parenthesis can help clarify the expression. hope this helps~ `u`

ap calculus
I interpreted it as: [ (-1/2 - h) - 1 ] / h Therefore, = ( -h - 3/2 ) / h = (-2h - 3) / 2h = -(2h + 3) / 2h

math
Yes, the 9 in 259 is in the ones place, while the 9 in the .689 is in the thousandths place.

CALCULUS
Even: Replace t to -t, and if the resulting function is still the same, that is, f(-t) = f(t), then it is even. And the graph is symmetric about the y-axis. Odd: Replace t to -t, and if the resulting function is the negative of the original function, that is, f(-t) = -f(t), ...

algebra
It decreases from x = negative infinity to 2, then becomes constant at x = 2 onwards.

Maths-Proportions
#1 Recall that rate is distance traveled over time. r = d/t or solving for distance, d = rt We can therefore write the proportion as (rate1)*(time1) = (rate2)*(time2) (500)*(8.4) = (420)*(time2) Now solve for time2. Units in hours. #2 Same what you'll do here in #2. (rate1...

Math- Need Help
No, both the x and y values are incorrect. Notice in your elimination method, you forgot to multiply one of the equations by -1 so that when added will cancel the variable y. This one: 15x + 12y = 18 16x + 12y = 20 should be: 15x + 12y = 18 -16x - 12y = -20 so that when added...

Chemistry
The given percentage for C and H do not add up to 100%. There might be a typo or incomplete info given...

math.fraction
1/2 = red 1/4 = blue ? = green Since one whole is 1, then the sum of the fractions must be equal to 1. 1/2 + 1/4 + (green) = 1 green = 1 - (1/2 + 1/4) green = 1 - (3/4) green = 1/4

psychics
(B) How high does the ball go? Since the ball is in uniformly accelerated motion, we can use the formula, vf^2 - vo^2 = 2gh where vf = final velocity vo = initial velocity g = acceleration due to gravity h = height Since at maximum height, the ball stops moving (vf = 0). Thus...

Chemistry Ap
A sprinter completes the 100 yard dash in 9.30 seconds. How long would it take her to complete 100. meters if she continued at the same speed? 1. 10.2 sec 2. 10.9 sec 3. 10.7 sec 4. 9.30 sec

Math
d / 4

math
We're going to perform operations on a + 1/a = 6 until we arrive at a^2 + 1/a^2. Square both sides. (a + 1/a)^2 = 6^2 a^2 + a*1/1 + a*1/a + 1/a^2 = 36 a^2 + 2 + 1/a^2 = 36 a^2 + 1/a^2 = 36 - 2 a^2 + 1/a^2 = 34 Hope this helps~ `u`

Geometry
V,cube = sidelength^3 V,cube = (1 cm)^3 V,cube = 1 cm^3 Since there are 20 ice cubes, V = 20 cm^3 V,cylinder = pi * r^2 * h V,cylinder = 3.14 * 3.5^2 * 9 V,cylinder = 346.185 cm^3 This is the volume of mug when full. Since 20 cm^3 is allotted for the ice cube, thus, 346.185 - ...

physics
Acceleration is change in velocity over time, or a = (v2 - v1) / t Substituting, a = (0 - 9) / 1.5 a = ? Now solve for a, note that it's negative since the final velocity is smaller than the initial velocity. Units in m/s^2 Hope this helps~ `u`

chemistry
From the periodic table, the molar weight of Na and Cl: Na - 23 Cl - 35.45 Thus molar mass of NaCl is 58.45 g/mol Molarity is moles solute over liters of solution. To get the moles, we divide the given mass by the molar mass: 5.85 g NaCl / 58.45 g/mol = 0.10 mol NaCl Thus, M...

math
Recall geometric mean. Let g be the geometric mean, so the geometric mean of a1, a2, a3 ... an is equal to g = nth root of (a1 * a2 * ... * an) Applying this to the problem, we have only two terms involved, which is 2x and 19x-2, thus n = 2. And g is given, which is 7x-2. ...

Physics
You should draw a free-body diagram. Represent the unknown forces with variables. Let F1 = force on the left side Let F2 = force on the right side Since the ropes are tied 60 degrees from the vertical, it's 90 - 60 = 30 degrees from the horizontal. Summation of all forces ...

Math
Operations should be performed in order PEMDAS: Parenthesis - Exponent - Multiplication - Division - Addition - Subtraction. But Multiplication and Division operations can be performed from left to right, no need to perform multiplication first then division. That is also ...

physics
We can use the formula: vf^2 - vo^2 = 2ad where vf = final velocity vo = initial velocity a = acceleration d = distance Substituting, 300^2 - 0^2 = 2(a)(0.9) a = ? Now solve for a. Units in m/s^2 Hope this helps~ `u`

physics
a. The stone is experiencing free fall, and therefore the motion involved is uniformly accelerated motion (UAM). We can use the formula, h = vo*t - (1/2)gt^2 where vo = initial velocity t = time g = acceleration due to gravity = 32.2 ft/s^2 Since it's free fall, vo = 0. ...

physics
a. The stone is experiencing free fall, and therefore the motion involved is uniformly accelerated motion (UAM). We can use the formula, h = vo*t - (1/2)gt^2 where vo = initial velocity t = time g = acceleration due to gravity = 32.2 ft/s^2 Since it's free fall, vo = 0. ...

math
Let n = number of eggs she bought. It was said she used 1/2 of them, then 1/4 of remainder, then she had 9 eggs left. Thus, (total eggs) minus (used eggs) equals the 9 eggs remaining, or n - [(1/2)n + (1/4)(1/2)n] = 9 Solving for n, n - (0.5n + 0.125n) = 9 0.375n = 9 n = 9 / 0...

Science
It's the third one, the 10.0m/s[E] since it has direction, which makes it a 'vector' quantity. The other three choices only measure the speed, while 10.0m/s[E] is velocity.

Chemistry
Their outer shell is already full, so they won't react easily. For Helium, that's 2 electrons, while for the rest of noble gases, it's 8 electrons.

MATH
The answer is yes for both questions.

algebra
Well this is just direct substitution of the given values. I'll do #1 and #2, and you do the rest: #1. apx + 1 = ? Since it was given that a = -10, p = -1 and x = 6, substituting, (-10)(-1)(6) + 1 = ? 60 + 1 = 61 #2. ry - c = ? Since it was given that c = -2, r = 3, and y...

Chemistry
Moles is given mass divided by the molar weight, or n = m / MW Substituting, n = 0.50 / 4 n = 0.125 mol He

calculus
A = Ao*e(^0.000124t) If the final amount, A, is equal to 10% of initial amount, Ao, thus 0.1*Ao = Ao*e(^0.000124t) 0.1 = e(^0.000124t) Get the ln of both sides: ln (0.1) = ln(e(^0.000124t)) ln (0.1) = 0.000124t Now solve for t. Just one clarification, I think the exponent of e...

college geometry
Let x = angle It was said the other angle is 30 deg more than four more the smaller, so Let 4x + 30 = other angle Since complementary angles sum up to 90 deg, x + 4x + 30 = 90 5x + 30 = 90 x = ? Now solve for x. Hope this helps~ `u`

chemistry
Assuming the gas is ideal, we can use Boyle's Law: P1 * V1 = P2 * V2 where P is pressure and V is volume. Substituting, 1.4 * 20.9 = P2 * 12.9 P2 = ? Units in atm. Hope this helps~ :3

chemistry
First write the balanced reaction: 2 NaOH + MgCl2 ---> Mg(OH)2 + 2 NaCl Then we determine the moles of each reactant using the given volume and concentration (molarity). Recall that molarity is moles of solute per liter solution, or M = n / V Solving for moles, n = M * V ...

math
Calculate the determinant (3 x 3 matrix). Then divide it by two and get the absolute value. That's the area. Let the z-coordinate be equal to 1: -10 | 5 | 1 15 | 5 | 1 10 | 12 | 1 The determinant of this set up is 175. Area is therefore, | 175/2 | = 87.5 units Hope this ...

Maths
If that means log 'base 10' then, log (y) + 2*log (x) = 2 Recall that we can rewrite the number that is multiplied by the the log expression as exponent of the term inside the log. For instance, a * log (x) = log (x^a) Thus, log (y) + log (x^2) = 2 Recall that when log...

Math
1/13 = 0.076923 076923 ... You can see here that the repeating numbers are 076923. There are six numbers in all so, 100/6 = 16 remainder 4 Counting four places, the 100th place is 9.

Math
Yes it is. :)

MATH
The given expression could mean a lot of things. It's because of the arrangement and lack of brackets/parenthesis. I suggest you type it again. It could mean for example, 0.4771 = x / (2.303*8.14[(50/323)*373]) Thus in this case, x = 516.42 It could also mean, 0.4771 = (x...

Math
Breadth is also the width. recall that area of rectangle is length multiplied by width: A = l * w Substituting, 900 = l * 45 l = 900 / 45 l = 20 m

maths
The given expression could mean a lot of things. It's because of the arrangement and lack of brackets/parenthesis. I suggest you type it again. It could mean for example, 0.4771 = x / (2.303*8.14[(50/323)*373]) Thus in this case, x = 516.42 It could also mean, 0.4771 = (x...

Algebra
No, it's not C. f(-3) means substitute x = -3 to the function: f(x) = x^2 - 4x + 3 f(-3) = (-3)^2 - 4(-3) + 3 f(-3) = 9 + 12 + 3 f(-3) = ?

chemistry
From the periodic table, the atomic masses of each are: K = 39 Mn = 55 O = 16 Divide the percentage to the respective atomic mass: K: 24.8 / 39 = 0.636 Mn: 34.77 / 55 = 0.632 O: 40.5 / 16 = 2.531 Divide each by the smallest number. The smallest number here is 0.632: K: 0.636...

Chemistry
First we determine the limiting reactant. The molar mass of NH3 is 17 g/mol. Getting the moles of NH3, we just divide the given mass by the molar mass: 25 g / 17 g/mol = 1.47 mol NH3 We determine the moles of NO produced by making mole ratios from the balanced reaction, such ...

college geometry
Use the distance formula: d^2 = (y2 - y1)^2 + (x2 - x1)^2 where d = distance (x1, y1) and (x2, y2) = points Thus, 3.5^2 = (3 - 3)^2 + (7 - b)^2 12.25 = 0 + 49 - 14b + b^2 Now solve for b.

Math
Your answer is actually correct. It should be raised to -6, not -5. For the solution: 1 Light Year = 9.46 x 10^12 km Thus, 58,000,000 km * (1 light year / 9.46 x 10^12 km) = 6.131 x 10^-6 light year

Math
You need to type it again and use parenthesis or brackets. It's necessary, because it's difficult to interpret the expression above.

Calculus
lim f(x) as x-->5 = 7

math
Let x = width Let 2x = length Perimeter of rectangle: P = 2*(length + width) Substitute: 60 = 2*(2x + x) 60 = 2*3x 60 = 6x x = 10 ft (width) 2x = 20 ft (length)

Algebra
This is a Fibonacci sequence, where the next term is the sum of two preceding terms. For instance the 3rd term (which is 1), is the sum of -2 and 3, and the 4th term (which is 4), is the sum of 3 and 1, and so on. Therefore, -2, 3, 1, 4, 5, 9, 14, 23, 37, 60, ...

Math
123 / 350

Math
Light Year is the distance traveled by light in one year. The speed of light in vacuum is approximately 3 x 10^5 km/s. And 1 year = 31,536,000 seconds. Thus, 1 Light-Year = 3 x 10^5 km/s * 31,536,000 s = 9.4608 x 10^12 km

Math
The geometric sequence is 1/4 , 1/16 , 1/64 , 1/256 , ... And the ratio is r = 1/16 / (1/4) = 1/4 This infinite geometric sequence converges because the ratio is in the range of -1 < r < 1. Getting the sum, we use the formula, S = a1 / 1 - r S = 1/4 / (1 - (1/4)) S = 1/4...

maths
String P is 3 times as long as string Q: P = 3Q String R is 3m longer than half the total length of strings P and Q: R = (1/2)(P + 3Q) + 3 The total length of all three strings is 5400 cm: P + Q + R = 5400 Substituting (such that everything is in terms of Q): 3Q + Q + (1/2)(3Q...

Geometry
Let n = pints of blue paint needed Use ratio and proportion. 3 blue : 4 red = n : 14 red Rewriting, 3/4 = n/14 n = (3/4) * 14 n = 42/4 n = 21/2 pints of blue paint

science
Percent Yield = (Actual Yield / Theoretical Yield) x 100 I think your data is insufficient, since we don't know how much is the theoretical yield.

maths
Let x = theta 2 cos(2x - π) = -2 Divide everything by 2 cos(2x - π) = -1 Expand the left side by applying the difference of cosines: cos(A ± B) = cos(A)cos(B) ∓ sin(A)sin(B) Thus, cos(2x)cos(π) + sin(2x)sin(π) = -1 cos(2x)*(-1) + sin(2x)*(0...

math
When an object is immersed completely in water, the displaced volume of water is equal to the volume of the object. The volume of cube is given by V = s^3 where s = side length Thus, V = 5.5^3 V = 166.375 cm^3 The volume of cylinder is given by V = π(r^2)(h) where π...

math
Well you already have the steps. :) (1) First, use the slope formula to find slope: m = (y2-y1) / (x2-x1) From the table of values, let's take the first two points (2,1) and (4,2), and substitute them into the formula for slope: m = (y2-y1) / (x2-x1) m = (2 - 1) / (4 - 2) ...

trigonometry
Recall that sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B) Thus, sin(6x)cos(11x) - cos(6x)sin(11x) = -0.1 sin(6x - 11x) = -0.1 sin(-5x) = -0.1 -sin(5x) = -0.1 sin(5x) = 0.1 5x = sin^-1 (0.1) x = [ sin^-1 (0.1) ] / 5

Math
(sin^2 (x) - 1)^2 = cos(2x) + sin^4 (x) We'll only modify the left side. Expand the left side: (sin^2 (x) - 1)^2 sin^4 (x) - 2 sin^2 (x) + 1 Recall that 1 = cos^2 (x) + sin^2 (x) : Pythagorean identity. sin^4 (x) - 2 sin^2 (x) + cos^2 (x) + sin^2 (x) sin^4 (x) + cos^2 (x...

Caclulus
Yes it is. :)

Math.
4^4 / 4^6 One way to solve this is to expand the numerator and denominator and simplify the fraction to its lowest term. Another way to solve this is to apply some laws of exponent. We can see here that the numerator and denominator has a term with the same base (which is 4). ...

math
Tens = 7 Ones = five less than the tens = 2 Hundreds = four times the ones = 8 Thousands = same as hundreds = 8 Let n = ten thousands digit If their sum is 33, n + 7 + 2 + 8 + 8 = 33 n = 8 Thus the number is 88,872 Hope this helps~ `u`

Calc 1
Derivative of displacement (with respect to time) is velocity. Derivative of velocity (with respect to time) is acceleration. Thus, v(t) = ∫ (a(t)) dt v(t) = ∫ (t + 6) dt v(t) = (1/2)t^2 + 6t + C To find C, you know that at t = 0, v(0) = 4. You can substitute it ...

Calc 1-oops
I mean for the second question, integrate v(t) further and evaluate from t=0 to t=4: D(t) = ∫ v(t) D(t) = ∫ (t^2 + 2t - 3) D(t) = (1/3)t^3 + t^2 - 3t + C at t = 0: D(0) = (1/3)(0)^3 + (0)^2 - 3(0) + C D(0) = C at t = 4: D(4) = (1/3)(4)^3 + (4)^2 - 3(4) + C D(4) = ...

Calc 1
Derivative of displacement (with respect to time) is velocity. Derivative of velocity (with respect to time) is acceleration. Thus, v(t) = ∫ (a(t)) dt v(t) = ∫ (2t + 2) dt v(t) = t^2 + 2t + C It was said that at t = 0, v(0) = -3. v(0) = (0)^2 + 2(0) + C = -3 v(0...

Math
If you draw the figure, you'll have a right triangle with the ladder as the hypotenuse. Let x = how far up the wall the ladder goes We can use sines: sin (angle) = opposite / hypotenuse sin (15°) = x / 12 x = 12 sin (15°) x = ? Units in meters. Hope this helps~ `u`

Calc 1
Check you other posts, the questions are related. Derivative of displacement (wrt time) is velocity. Thus, integral of velocity is displacement. D(t) = ∫(t^2 − 2t − 15) dt D(t) = ? After you solved for the integration, evaluate this from time t=1 to t=7.

math
The amount of flour needed is 1/2 cup more than twice the amount of sugar: 2 * (2 1/2) + 1/2 = 5 + 1/2 = 5 1/2 cups

Math 100
Surface area of a prism: SA = (area of the base) + (lateral area) Imagine the shape. Triangular prism is the shape of a toblerone box. So, SA = 2*(area of triangle) + 3*(area of rectangle) Recall that area of triangle is just A = bh/2 And area of rectangle is A = lw Therefore...

Chemistry
The first one is used, just one arrowhead (not the equilibrium arrow sign).

Calc 1
Use integration to get the exact area: ∫ y dx ∫ x^(1/5) dx Recall that ∫ (x^n) dx = 1/(n+1) x^(n+1) Thus, for example, ∫ (x^2) dx = (1/3)x^3 Try this method on ∫ x^(1/5) dx , and evaluate it from 0 to 32.

Calc 1
We use integration. ∫ y dx = ∫ 6 sin(x) dx = -6 cos(x) | from 0 to π = -6 cos(π) - (-6 cos(0)) = -6(-1) - (-6)(1) = 6 + 6 = 12

Calc1
To get the area, we use integration. From the graph, we can draw vertical strips that run from 0 to π/4. ∫ y dx = ∫ sec^2 (x) dx = tan x | from 0 to π/4 = tan (π/4) - tan (0) = 1 - 0 = 1

math
If you draw this you'll have a figure of a rectangle with a triangle on its top. The base of the triangle is 12 meters (equal to side length of rectangle). Half of the base is 6 m, and drawing a line as the height of the triangle, you can form two right triangles. Thus, ...

math
(2a + 3b)(2a − 3b) Distribute each factor or use the FOIL method. = (2a)(2a) + (2a)(-3b) + (3b)(2a) + (3b)(-3b) = 4a^2 - 6ab + 6ab - 9b^2 = 4a^2 - 9b^2

maths
I don't know the SMALLEST number that should be multiplied to 103875 to make it a perfect square. But the most obvious answer here is to multiply it by 103875 (the number itself), since 103875 * 103875 = 103875 ^ 2

1. Yes 2. Yes 3. Yes 4. Yes 5. Yes

Algebra 104
Let x = side length of square discarded The volume of rectangular solid is given by V = lwh where l, w and h are the length, width and height respectively. When the flaps are folded up, it acquires a height, and this height measures x inches, since you cut a square with a side...

geometry
This actually depends on you definition of faces and edges. If face is not necessarily flat, and edge is where two faces meet, then A cylinder has 3 faces, 2 edges and 0 vertices. Area of the base of cylinder: A cylinder has base in shape of circle, and there are two circles...

Math
To solve algebraically, a 4 two-credit courses has total of 4 x 2 = 8 credits. Substituting to the equation, T = (1/4)c + 6 T = (1/4)(8) + 6 T = 2 + 6 T = 8 Since the units of T is in hundreds of dollars, the tuition is \$800. I'll leave the graphing to you since graph ...

maths
When an object is immersed completely in water, the displaced volume of water is equal to the volume of the object. The volume of cube is given by V = s^3 where s = side length Thus, V = 5.5^3 V = 166.375 cm^3 The volume of cylinder is given by V = π(r^2)(h) where π...

Physics
The object is experiencing uniformly accelerated motion (UAM). We can apply the formula: h = (vo)(t) - (1/2)(g)(t^2) where vo = initial velocity t = time g = acceleration due to gravity = 9.8 m/s^2 Solving for the height after 2 seconds, h = 37(2) - (1/2)(9.8)(2^2) h = 54.4 m ...

Math-oops
Sorry. I see that r = 0.81 according to the problem, not 0.8. Well substituting again, d = 16 + (0.81)(32 / (1 - 0.81)) d = 152.4 ft.

Math
This is an example of infinite geometric sequence. Formula for sum of infinite geom sequence: S = a1 / (1 - r) Total distance traveled: d = (distance ball dropped) + (1st bounce up) + (1st bounce down) + (2nd bounce up) + (2nd bounce down) + ... d = 16 + 16(0.8) + 16(0.8) + 16...

Math
In an arithmetic sequence, an = a1 + (n-1)d where an = nth term a1 = first term n = number of terms d = common difference The sixth term is 20.6 so, 20.6 = a1 + (6-1)d 20.6 = a1 + 5d The ninth term is 30.2 so, 30.2 = a1 + (9-1)d 30.2 = a1 + 8d Now you have two equations, to ...

Functions
Even: Algebraically, we substitute x as -x and if it goes back to original function, then it's even. Thus, f(-x) = f(x). Visually, if this function is graphed and you see that it is symmetric to y-axis, then it's even. Odd: If f(-x) = -f(x). I will assume the function ...

Math: Line Symmetry and Reflection
1. Yes 2. It's D, since y-coordinate is increased by 3. 3. Yes 4. If a point is reflected over the x-axis, the y-coordinate of the point changes its sign to opposite. So the points become A'(2,5), B'(-3,-5) and C'(3,3).

college math
In the word "Tallahassee", there is only one letter T out of 11 letters, so the probability of getting a T is 1/11. There are 2 letter E in the word, so probability of getting an E is 2/11. The probability of getting a letter T OR letter E is therefore 1/11 + 2/11 = ...

College math
In the word "Tallahassee", there is only one letter T out of 11 letters, so the probability of getting a T is 1/11. There is no letter F in the word, so probability of getting an F is 0/11 or 0. The probability of getting a letter T OR letter F is therefore 1/11 + 0...

math
159 gallons are being burned per second, so if two seconds have passed, 159 x 2 = 318 gallons Thus, to get the total volume in gallons burned after some time, we just multiply the rate (159 gal/s) by the time passed (in seconds). So if three seconds have passed, 159 x 3 = 477 ...

math
Let x = food or meal Thus the share of each men is x/120. And the share of each children in x/200. It was said in the problem that 150 children took the meal, so the total meal taken by these children is number of children multiplied by the share of each: 150 * x/200 = 3x / 4...

math
Formula for slope: m = (y2 - y1)/(x2 - x1) Take the first two points: m = (-1 - 1)/(6 - 3) m = -2/3

maths
Yes that's right. You have to equate the expressions for widths and for the lengths, since left and right widths (and lengths) have the same dimensions. You may rewrite the equation for y=3x+3÷6 as y = (3x + 3)/6 And now you have an expression for y, we can ...

Algebra 2
Tangent is opposite / adjacent, so we can say that in tan (theta) = 1/2, the 1 and 2 are the sides of the right triangle and c^2 = a^2 + b^2 c^2 = 1^2 + 2^2 c = sqrt(5) is the hypotenuse. Cosine is adjecent / hypotenuse, so cos(theta) = 2 / sqrt(5) Method is the same for other...

Math
1/10

Pre-Algebra (Probability)
Let n = number of sections If 2/3 of n is the number of even numbered sections, which is 8, then, (2/3)n = 8 n = 12

PreCal
2|5x - 5| + 4 = 20 There are two cases here, where the absolute value term is + or - Case 1: 10x - 10 + 4 = 20 10x - 6 = 20 10x = 26 x = 2.6 Case 2: -10x + 10 + 4 = 20 -10x + 14 = 20 -10x = 6 x = -0.6

physics
Use the formula: h = vo*t - (1/2)gt^2 Since the rock experiences freefall, initial velocity (vo) is zero: h = -(1/2)gt^2 Substitute: h = -(1/2)(-9.8)(3.8^2) h = ?

physics
Use the formula: h = vo*t - (1/2)gt^2 We know that vo = 41 g = 9.8 h = 0 (since it strikes the ground) 0 = 41t - (1/2)(9.8)t^2 Solve for t. One of the answers is t = 0, but this is the time before the release of the ball. Get the other value of t.

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