agrin04

Since you cut a 2 in. x 2 in. square from each corner, you'll get a 2 in. height The volume of the box will then be: Vol = length x width x height = 22 x 16 x 2 = 704 in^3 Note: the volume is the same for all cases, regardless of the condition of the lid...

14 years ago

Since you cut a 2 in. x 2 in. square from each corner, you'll get a 2 in. height Length now becomes = 22 - 4 = 18 in. Width now becomes = 16 - 4 = 12 in. The volume of the box will then be: Vol = length x width x height = 18 x 12 x 2 = 432 in^3 Note: the...

14 years ago

6 sec^2 (5?/4) - 7 sin (5?/4) = = 6 (1/(-1/sqrt(2)))^2 - 7 (-1/sqrt(2)) = 6 (2) + 7/sqrt(2) = 12 + 7/sqrt(2)

14 years ago

Say that the other length is expressed in y. So, the answer will be: y = (59 - x) cm

14 years ago

From the basic formula: f(x) = sin (u), where u = g(x) f'(x) = u'. cos(u) We now set that: u = e^4x u' = 4e^4x So, we have: f(x) = sin(e^4x) f'(x) = 4e^4x. cos(e^4x)

14 years ago

|cos^nx dx = |cos^(n-1)x. cosx dx Take: u = cos^(n-1)x du = (n-1) cos^(n-2)x. (-sinx) dx dv = cosx dx v = sinx By integration by part formula we have: |cos^nx dx = = cos^(n-1)x. sinx + (n-1)|sin^2x. cos^(n-2)x dx = cos^(n-1)x. sinx + (n-1)|(1-cos^2x). cos...

14 years ago

The change in altitude: da/dt = 3 cm/min The change in area: dA/dt = 7 cm^2/min The change in base: db/dt From the formula of area of triangle: A = (a x b)/2 66 = (22 x b)/2 b = 6 cm Differentiate the formula above with respect to time: dA/dt = (b. da/dt...

14 years ago

State as followings: P(P) = #students take physics = 32 P(C) = #students take chemistry = 51 P(P and C) = 15 P(neither) = 10 Total students = P(P) + P(C) - P(P and C) + P(neither) = 78

14 years ago

u = 20 ÷ 6 2/3 = 20 ÷ 20/3 = 20 x 3/20 = ?

14 years ago

(1) ar^(n-1) + ar^(n-2) + ar^(n-3) = 1024 (a + ar + ar^2) ar^(n-3) (1 + r + r^2) = 1024a (1 + r + r^2) r^(n-3) = 1024 It is known that the third term is 5, so: ar^2 = 5 The last term will be: ar^(n-1) = ar^2. r^(n-3) = 5 x 1024 = ? (You can finish the res...

14 years ago

(1) Convert into cm first, so: 420 m = ___ cm Then, divide that number with 8000 (2) Multiply 31.4 with 15000 (in cm), then convert the result into km

14 years ago

Supplementary angles: x + y = 180 From the problem, we can state that: y = (1/4)x Substituting back to the first equation, we have: x + (1/4)x = 180 (5/4)x = 180 x = ? (You can calculate this yourself) As to find the supplementary angle, you can use the r...

14 years ago

Find the first derivative of the function: dy/dx = (2-x)^(1/2) - (1/2)x.(2-x)^(-1/2) = (4-3x)/2sqrt(2-x) You have to be careful in this matter, especially since you've encountered a square root form in the denominator. * take the denominator, ignore the c...

14 years ago

State that the difference to be 'b' y = x + b b = y - x. ..(1) z = y + b = x + 2b b = (z - x)/2. ..(2) Combining equations (1) and (2): b = y - x = (z - x)/2 y = (z + x)/2

14 years ago

1 rotation = 2pi 1/8 rotation = 1/8 x 2pi = pi/4 State y as the height difference created from the rotation of the wheel and the bottom of the ferris wheel (not the ground) height = y + 1 = r - r cos {(2pi/20)t - (pi/4)} +1 = r(1 - cos pi{(t/10) - (1/4)})...

14 years ago

Just change the variable x with the value x = 2. So, we get: f(x) = 2x^3 + mx^2 + nx - 3 f(2) = 0 = 2(8) + 4m + 2n - 3 0 = 13 + 4m + 2n. ..(1) g(x) = 3mx^2 + 2nx + 4 g(2) = 0 = 12m + 4n + 4 0 = 6m + 2n + 2. ..(2) Using elimination and substitution for bot...

14 years ago

What do you have if you squared a value or a number? You'll get a positive number the whole time. Except for 0, of course. In this case, the range will be at least 0, or >=0, regardless of the value of x

14 years ago

All real numbers

14 years ago

|x^2*cos^2(x) dx = =|x^2*(1/2)(1+cos(2x)) dx =(1/2)|x^2 dx + (1/2)|x^2*cos(2x) dx =(1/6)x^3 + (1/2)|x^2*cos(2x) dx Using integration by part: u = x^2 du = 2x dx dv = cos(2x) dx v = (1/2) sin(2x) |x^2*cos(2x) dx = = (1/2)x^2*sin(2x) - |xsin(2x) dx Again, u...

14 years ago

|cot^4(1-2x) dx = = |cot^2(1-2x)*cot^2(1-2x) dx = |{cosec^2(1-2x) - 1}*cot^2(1-2x) dx = |cosec^2(1-2x)*cot^2(1-2x) dx - |cot^2(1-2x) dx = |cosec^2(1-2x)*cot^2(1-2x) d(cot(1-2x))/(-cosec^2(1-2x)*(-2)) - |{cosec^2(1-2x) - 1} dx = (1/2)|cot^2(1-2x) d(cot(1-2...

14 years ago

df(x,y)/dx = 2x df(1,2)/dx = 2 df(x,y)/dy = -2y df(1,2)/dy = -4 Directional derivative = = <2,-4> • <(3/5),-(4/5)> = (6/5) + (16/5) = 22/5

14 years ago

From point (2,1) to (1,3): u = <1-2,3-1> = <-1,2> Note that vector u above is not a unit vector, so we need to make this a unit vector by dividing it with its magnitude. u = <-1,2>/sqrt(5) <dz/dx,dz/dy>•<-1/sqrt(5),2/sqrt(5)> = -2/sqrt(5) -dz/dx + 2dz/dy...

14 years ago

2048 = 2^n n = 11

14 years ago

Oops... Sorry. Something missing. Originally, there are 2 mice So, jojo will have 2048 mice after: 11 - 1 = 10 months

14 years ago

Circle equation generally: (x-a)^2 + (y-b)^2 = r^2 The center is in x-axis (b = 0), giving: (x-a)^2 + y^2 = 1 ((sqrt(2)/2)-a)^2 + (sqrt(2)/2)^2 = 1 ((sqrt(2)/2)-a)^2 + (1/2) = 1 (sqrt(2)/2)-a = ±sqrt(1/2) (sqrt(2)/2)-a = sqrt(1/2) a = 0 So: x^2 + y^2 = 1...

14 years ago

In general: (x-a)^2 + (y-b)^2 = r^2 Center point in 8x + 5y = 8, meaning: 8a + 5b = 8. ..(1) Circle passing (2,1): (2-a)^2 + (1-b)^2 = r^2. ..(2) Circle passing (3,5): (3-a)^2 + (5-b)^2 = r^2. ..(3) Use equations (2) and (3) to eliminate r, we now have a...

14 years ago

|2^(-1/t)*(1/t^2) d(-1/t)/(1/t^2)= |2^(-1/t) d(-1/t) = 2^(-1/t)/ln2 + const

14 years ago

Height after 4th bounce = 8x(7/8)^4 Total = 8 + 8*(7/8)*2 + 8*(7/8)^2*2 + 8*(7/8)^3*2 + 8*(7/8)^4

14 years ago

Take: u = ln(2x+1) du = 2/(2x+1) dx dv = dx v = x |ln(2x+1) dx = = xln(2x+1) - |2x/(2x+1) dx = xln(2x+1) - |{1 - 1/(2x+1)} dx = xln(2x+1) - |dx + |1/(2x+1) dx = xln(2x+1) - x + (1/2)ln(2x+1) + const

14 years ago

You can use long division method or you can use Horner method. Horner is easier and faster. 3 | 3 -11. 10 -12 | 9 -6 12 --------------- 3 -2 4 0 So, the quotient is 3x^2 - 2x + 4

14 years ago

cos(40)/sin(40) - sin(50)/sin(40) = sin(90-40)/sin(40) - sin(50)/sin(40) = 0

14 years ago

2r - 3r sin¤ = 6 2sqrt(x^2 + y^2) - 3y = 6 2sqrt(x^2 + y^2) = 3y + 6 =3(y+2) 4(x^2 + y^2) = 9(y + 2)^2

14 years ago

Only consider the denominator. this expression is undefined when p^2 - 49 = 0 Factorise this and you'll get the results

14 years ago

f(x) = 1/(6x^2) = (1/6)x^(-2) f'(x) = (-1/3)x^(-3) f''(x) = x^(-4) = 1/x^4 As to answer question b, just change x with 3 and calculate the result

14 years ago

sec^4(x) - tan^4(x) = = (1 + tan^2(x))^2 - tan^4(x) = 1 + 2tan^2(x) + tan^4(x) - tan^4(x) = 1 + 2tan^2(x) QED

14 years ago

Assume that for all cases that both m and n are integers. For m = n: |(from -pi to +pi) cos^2(mx) dx = = |(from -pi to +pi) (1/2)(1 + cos(2mx)) dx = (1/2)(pi + pi) + (1/4){sin(2mpi) - sin(-2mpi)} = pi For m not equal n: |(from -pi to +pi) cos(mx) cos(nx)...

14 years ago

(a) 1500*2^(t/0.5) = 1500*2^(2t) (b) 1500*2^(2*20/60) = ? (c) 1500*2^(2*9) = ?

14 years ago

cos ¤ = (4^2 + 5^2 - 6^2)/(2*4*5)

14 years ago

Length of string = 100/cos(57)

14 years ago

(w^9 - 2y^5)(w^9 - 7y^5)

14 years ago

(a) 3log (3^3) = 3 (b) 5log (5^(-1)) = -1 (c) f(e^x) = ln(e^x) = x

14 years ago

Right triangle

14 years ago

(a) {people who are more than 20 years old and enrolled in college} (b) {4} (c) {}

14 years ago

1. tan(36 - 2) = tan 34 2. sin ? = 4/5 --> cos ? = 3/5 cos ? = -9/41 --> sin ? = -40/41 sin(?-?) = sin?*cos? - cos?*sin? = ? 3. tan x = sqrt(143) tan 2x = 2tanx/(1 - tan^2(x)) = ?

14 years ago

(2x-3)(x+1)

14 years ago

Vertical asymptote: denominator = 0, so: x^2 - 9 = 0 Horizontal: lim x->(infinity) f(x) Since the degree of nominator is higher than the denominator, then the horizontal asymptote does not exist. Slant: use long division method to find the quotient. That...

14 years ago

Use the cosine rule: x^2 = 52^2 + 23^2 - 2(52)(23)cos96 After calculating, you'll get x = 59

14 years ago

For logarithmic expression, the value of u in ln u should be more than 0. So: (13x + 6)/(5 - 17x) > 0 Use the number line to solve this, you'll get the result. If my calculations are correct, then: (-6/13,5/17)

14 years ago

10 = 2 x 5 60 = 2^2 x 3 x 5 32 = 2^5 GCF = 2 LCM = 2^5 x 3 x 5 = ?

14 years ago

|(x+6)/5 dx = = (1/5)|(x+6) dx = (1/5)*{(1/2)x^2 + 6x} + const = (1/10)x^2 + (6/5)x + const

14 years ago

Just add the two costs: 5x^2 + 4x - 7 + 8x + 8 =?

14 years ago

You can use either long division method or Horner. -2/3 | 12 -22 -44 -16 | -8 -20 128/3 --------------------- 12 -30 -64 80/3 Quotient = 12x^2 - 30x - 64 Remainder = 80/3 Or, you can write as: 12x^3 - 22x^2 - 44x - 16 / 6x+4 = 12x^2 - 30x - 64 + (80/3)/(6...

14 years ago

Oops... Sorry. I've made a few errors in my calculation. Should be: -2/3 | 12 -22 -44 -16 | -8 20 16 ---------------- 12 -30 -24 0 Since the denominator has 1 degree of polynomial and its coefficient is 6, we divide the quotient with 6. So, we have: Quoti...

14 years ago

S = 4pi*r^2 dS/dr = 4pi*2r = 8pi*r V = (4/3)pi*r^3 dV/dr = 4pi*r^2 dV/dt = dV/dr * dr/dt 2 = 4pi*r^2 * dr/dt dr/dt = 1/(2pi*r^2) dS/dt = dS/dr * dr/dt = 8pi*r * 1/(2pi*r^2) = 4/r If r = 12, just plug the value to the last equation

14 years ago

w^(4+1+5) = w^10

14 years ago

Yes

14 years ago

If you are not given the value, that means you have to write the steps I told you until the very last equation. If you are given the value (of r), you don't have to put the value in every equation. Just follow my steps until the last equation, then plug t...

14 years ago

Each monkey has to eat one banana? So the total will be 8 bananas? The answer will be just 1 minute (assuming that all monkeys eat at the same time)

14 years ago

And the question is?

14 years ago

Diagonal = 16 = sqrt(2x^2) x = 8*sqrt(2) mm Perimeter = 4*x = ?

14 years ago

A = l* w dA/dt = l*dw/dt + w*dl/dt Plug in the values and calculate

14 years ago

For |x|, we have 2 situations. |x| = x, for x >= 0 |x| = -x, for x < 0 So: ¤ for x>=0: d/dx (2(x^2 + 3x)) = ? ¤ for x<0: d/dx (2(x^2 - 3x)) = ?

14 years ago

y=x/8

14 years ago

Cross multiple means: nominator of left side x denominator of right side = nominator of right side x denominator of left side So for this case: 9 * (x-3) = 4 * (x-7) 9x - 27 = 4x - 28 Now, let's collect the variable x on the left side, and the rest on the...

14 years ago

The first problem is correct. As for the second problem, take: u = ln x du = (1/x) dx So: S (ln u) du = ? Try it yourself

14 years ago

Oh sorry. It should be: S sin(u) du

14 years ago

Assume that the distance travelled before turning 60 degrees is x The total distance travelled = x+10 Distance A-B in straight line = x + 6 Use the cosine rule: (x+6)^2 = x^2 + 100 - (2*x*10*cos(120)) Finish the calculation, you'll find x. Total distance...

14 years ago

Assume that the perimeter is x x = 28 + (4/9)x + (2/5)x x(1 - 4/9 - 2/5) = 28 Solve the calculation above, and you'll get the answer

14 years ago

Find the area first, then multiply the result with the price

14 years ago

dy/dx = y cos(x) dy/y = cos(x) dx ln y + const = sin(x) + const ln y = sin(x) + const ln 3 = sin(0) + const const = ln 3 ln y = sin(x) + ln 3 ln y - ln 3 = sin(x) ln (y/3) = sin(x) y/3 = e^sin(x) y = 3e^sin(x)

14 years ago