I've always had an opinion that conceptual Physics (and even advanced Mathematics) should be introduced at the primary school level.
It's just amazing that when I'm beginning to draw an airplane for an example problem explaining vectors, my 12 year old student goes off on a tangent when she explains in laymen's terms - Bernoulli's Principle.
I probably should've...
read more

given (a,b) = (2/5,5/8)
c = SQRT[(2/5)2+ (5/8)2]
Sin = (5/8)/SQRT[4/25+25/64]
Cos = (2/5)/SQRT[4/25+25/64]
Tan = (5/8)/(2/5)= 25/16
Csc = 1/Sin = SQRT[4/25+25/64]/(5/8)
Sec = 1/Cos = SQRT[4/25+25/64]/(2/5)
Cot...

The exercise is to match up the words with mathematical functions, and solve algebraically:
Let X = total money
"Jo spent 40": X -40
"and spent half of her remaining": -(1/2)(X-40)
"then spent 29.45": -29.45
(X...

For a standard bell-shape curve, the distribution:
a) From the Mean to 1 sdev = 36.1%
b) between 1sdev and 2sdev = 13.6%
c) between 2sdev and 3sdev = 2.1%
D) between 3sdev and 4sdev = 0.1%
1) Given the Mean is 84 and the sdev=7
98 is 2 sdev away from 84 and the...

CL/1 / L / L + 1/C
= ((CL/1)/L) + 1/C
= CL/L + 1/C
= C + 1/C

1lb = 0.453kg
Work = Force x Distance
= [ 0.453kg x 9.80m/s^2 ] * 50m
= 221.97 J

Work = Force x Distance
= (400 lb) x (30 feet)
= 12000 ft-ib

G(1) = 3
G(2) = 3 + 2(1)
G(3) = 3 + 2(2)
G(4) = 3 + 2(3)
.
.
.
G(n) = 3 + 2(n-1)
hence,
G(100) = 3 + 2(100-1) = 201

The Ruie is when you have two similar numbers (same base), each raised to a power, the product of these (base) numbers raised to their power is the base raised to the sum of e powers.
i.e. (ax)*(ay) = a(x+y)

Be sure to keep your significant figures. There's a huge difference between answers but all with the right approach. My answer came to 19.2 minutes.

3ft = 1 yrd
(45 + 2/3)yards * (3 feet /1 yard) = (45(3) + 2) feet
= 137 feet

9c - 4x = 7
9c -4x +4x = 7 + 4x => 9c = 7 + 4x
9c -7 = 7 + 4x -7 => 9c - 7 = 4x
(1/4)(9c - 7) = (1/4)*4x => x = (9c-7)/4

1cc (cubic centimeter) = 1 mL
V = Pi* r2 * h [cc]
convert from [cc] to [L] => [cc] x[1 mL/ 1cc] x [1L/ 1000mL] => [L]
V = 471 L,
(1/2) V = 235.6 L
t = [(1 min) / 12.3 L ] x 235.6 L = 19.2minutes
&nbs...

Since multiplying and dividng are equal in order...from left to right:
[x8 / (2y)]*[(5y2)] / [x3]
= (x5 5y)/2

If you mean (3/5)^x = 2^(1-x). Then take the natural log of both sides.
Rule: if y = ax, then ln(y) = x ln(a)
x ln(3/5) = (1-x) ln 2
x ln (3/5) = ln 2 - x ln 2
x (ln (3/5) + ln 2) = ln 2
x = ln 2 / [ln (3/5) +...

Y=x^2 is centered around origin.
Assuming your coordinates are traditional (+ to the right and - to the left of the origin)
Analyze y=x^2 - 4x:
To bring y back to the origin, we have to add (move 4x units to the right).
This...

Sum of the forces in the vertical direction Fy = FN + (-mg) = ma
(a) At rest, ma= 0.
Scale reading is equal to FN and is equal to (mg)
FN = 55kg *(9.8m/s) = 539 N = 121 lbs
(b) at a=1.5m/s2,
FN = mg + ma = (55kg)(9.8m/s2) + (55kg)(1...

9h to the -2 power = (9h)-2 = 1/(9h)2 = 1/(92h2) = 1/81h2
Rule: a-n = 1/(an)
5h to the 10th power = (5h)10 = 510h10
Rule: (ab)n = anbn
(1/81h2) x (510h10)
= [(510) (h10)] / [(81) (h2)]
Rule:...

The key word is "of" which should tell you to multiply
so half of 2/3 is
(1/2) * (2/3) = 2/6 = 1/3
essentially you're right when you say you're dividing by 2 because you're multiplying by 1/2

45 - 50 - (-12)
-(-) is the same as -1*(-1). So multiply first.
= 45 - 50 + 12
To avoid confusion in the Order of operation:
45 - 50 + 12
= 45 + (-50) + 12
= 7
...