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The LCM of 6 and 8 is 24, so express both fractions in terms of 24ths:

2/6 = 8/24

3/8 = 9/ 24

So:  8/24 + 9/24 = 17/24

I assume you are talking about a 30-60-90 degree right angled triangle.  There are an infinite number of possible side lengths!  However they will all be in the ratios 1:2:sqrt(3). (where the 2 represents the hypotenuse).

The energy required to stretch the spring away from equilibrium by distance x is given by (1/2)kx^2, so, in this case:

(1/2)k(1.25^2 - 0.75^2) = 100

k(25/16 - 9/16) = 200

k = 200 N/m.     (Since 25/16 - 9/16 = 1)

(Note that the energy is the integral of force with respect to distance here, as it becomes increasingly difficult to stretch the spring the further it is away from equilibrium).

Let their rate  in still water = x

So....the downstream boat travels at [ x + 8 ] km/h

And the upstream boat travels at [ x - 8 ] km/h

And Distance /  Rate   = Time  .......so....since they travel the same time, we have

56/ [ x + 8]   =  24/ [x - 8]       cross-multiply

56 [ x - 8]   = 24 [ x + 8]      simplify

56x  - 448  =  24x + 192       subtract 24x from both sides, add 448 to both sides

32x  =  640       divide both sides by 32

x  = 20 km/h    =  their rate in still water

Let x be the number of liters of 77% solution

Then  72 - x    is the number of liters of 89% solution .......and we have

.77x  +  .89 (72 - x)   =  .83 (72)   simplify

.77x  + 64.08  -  .89x    =  59.76

-.12x + 64.08   = 59.76    subtract 64.08  from each side

-.12x   = -4.32     divide both sides by -.12

x = 36 liters  of the  77% solution

72 - 36   = 36 liters of the 89% solution

This was much appreciated

We can only add/subtract like terms [terms having variables to the same power]

Since  8x²   has a different exponent on x than 6x, we cannot add/subtract them

4x + 6y = 6    (1)
3x - 3y =12   (2)       multiply this equation by 2  →   6x - 6y   = 24    (3)

Add equation 3 to equation 1

10x   =  30        divide both sides by 10

x  = 3    substitute this into any equation to find y  [ I'll use 2 ]

3(3) - 3y   = 12

9 - 3y   = 12       add 3y to both sides, subtract 12 from both sides

-3 =  3y               divide both sides by  3

-1  = y

So   {x , y }   =   { 3, -1 }

3(x – 1) ≤ 4x – 2       simplify the left side

3x - 3 ≤  4x - 2         add 2 to both sides, subtract 3x from both sides

-1 ≤  x

Spring constant    F =  kx      and we know (or should know)  F = ma (Newtons)   and   ONE joule = ONE Newton-Meter

Stretch distance = 1.25 - .75 = .5 m

100 j = 100 N-m

F= 100 N-m / .5 m = 200 N

F=  kx

200 = k(.5)

200N / .5m = k = 400 N/m  ??????      Hmm...... second time today that I got an answer that does not match your variable choice answers..........I do not know what to think..... At what answer did YOU arrive???

ANYONE???

Thanks, EP, for correcting my obvious mistake !!!

d/dx of  2 x^2  = (2) 2x^(2-1) = 4x

d/dx of a constant is '0'                     so f'(x) = 4x

Just substitute in for 'x
 

-3 (-1)^3 + 2 (-1)^2 = -3(-1) + 2(1) = 3 + 2 = 5

-3(1/2)^3 + 2(1/2)^2 = -3(1/8) + 2 (1/4) = -3/8 + 2/4 = 1/8

Boat "a" distance travelled without the water current=56 - 8=48.

Boat "b" ditance travelled without the water current =24 + 8=32

48 - 32 =16 Km that the two boats are apart due to water current

16/8 =2 hours since the two boats left.

56/2 =28 Km/h - 8 Km/h =20 Km/h speed of boat "a"

24/2=12Km/h + 8 Km/h =20 Km/h speed of boat "b"

log 10 with base 5

Log(10) / Log(5) =1.4306765580..........so that:

5^1.4306765580 =~10

Sqrt(48) =6.9282032302.......It is irrational.

Find the derivative of the following via implicit differentiation:
d/dx(f(x)) = d/dx(5+2 x^2)
The derivative of f(x) is f'(x):
f'(x) = d/dx(5+2 x^2)
Differentiate the sum term by term and factor out constants:
f'(x) = d/dx(5)+2 d/dx(x^2)
The derivative of 5 is zero:
f'(x) = 2 (d/dx(x^2))+0
Simplify the expression:
f'(x) = 2 (d/dx(x^2))
Use the power rule, d/dx(x^n) = n x^(n-1), where n = 2: d/dx(x^2) = 2 x:
f'(x) = 2 2 x
Simplify the expression:
f'(x) = 4 x
Expand the left hand side:
Answer: |  f'(x) = 4x

A² + B² = C²

it helps us find if a triangle is a right angle by knowing what the hypotenuse is so we can find that A² + B² has to be equal to C².

That's wrong

For your example, you can only do 2x(4x-3)

6

Multiply 12 by 8, then multiply by 37.5/100. That gives 36. The square root of 36 is 6.

where did you get the 80 from?

On the web2.0 calculator for this website, if you want to find the inverse sine of a value, you would type in "Arcsin". It would be the same for other trignometric functions (ex. Arccos, Arctan etc.).

Also hate to call you out KitKat.. but you kinda just copied and pasted from Wikipedia. Good stuff though, very helpful information

Hmmmmm.... I don't get ANY of those answers......Are the charges separated by AIR or something else?????

Use Coulomb's Law   F = k Q1Q2 / d^2      Where k=Coulomb's constant 9.0 x 10^9 N M^2/C^2  (for AIR)

=  9 x 10^9  (2 x 10^-6)(44 x 10^-6) / (5 x 10^-3)^2       (the distance between the charges is 5mm per pythagorean theorem)

= 792 x10^-3 / (25 x 10^-6)  = 31.68 x 10^3 N

Hmmmm....    I think the charges must be in something besides AIR which changes the value of 'k'