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Thank you for this answer. I've done further research and found this pdf which was pretty helpful as well:

Note that 2*67.5 = 135, and that cos 135 = -cos 45, and that cos 45 = 1/sqrt(2)

So set A = 67.5 and use your formula (noting that cos 67.5 will be positive).

This graph should answer that question:

Hi NinjaDragons98,

Here are the graphs.  I have also included a colour coded line at the centre of the temperature limits.

Red         Los Angeles

Green     Osaka

Blue        Buenos Aires

4, -6   would be the center

A cube has all sides equal

Volume of a cube is H X W X D    (height     width   depth)

H & W  & D   are all the same

so   H X H X H = 512       H^3 = 512    H = Cuberoot(512) =  8 cm

Area = H x W   = 8 x8 = 64 cm^2

Surface area : there are SIX sides to a cube     so   6  x 64 = 384 cm^2

If side length is doubled to 16    volume = 16 x 16 x 16 =  4096 cm^3         (2x 2 x 2 x 512= 4096)

Wow.....you left out some critical information.

What are the sizes of the planks....what shape of structure did she build ?     Etc

Since he is making: 1.2/1.4 =6/7% less because of his "yardstick" being too long, and since a yard = 36 inches, it therefore follows that his yardstick must be: 36 / (6/7) =36 x 7/6 = 42 inches.

Do the PARENTHESES first   then the multiplication

6/2 ( 1+2) =   6/2 (3) = (6x3) / 2 = 18/2 = 9

Well, if a gallon of paint costs $3 and a gallon of paint thinner costs 1/3 of a dollar, then a gallon of each costs: $3 + $1/3 =$3 1/3. Therefore, the number of gallons of each equals:

$10 / $3 1/3 = 3 gallons. 

120 degrees is 1/3 of a circle. Therefore the perimeter of the fence is 1/3 of

the circumfrence (2 pi r/ 3). Set 300m = 2 pi r / 3. Solving for r gives 143m.

Well, I don't blame you. For instance, here is a technical definition of a "tensor", if you can understand it. Good luck to you.

An nth-rank tensor in m-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules. Each index of a tensor ranges over the number of dimensions of space. However, the dimension of the space is largely irrelevant in most tensor equations (with the notable exception of the contracted Kronecker delta). Tensors are generalizations of scalars (that have no indices), vectors (that have exactly one index), and matrices (that have exactly two indices) to an arbitrary number of indices.
Tensors provide a natural and concise mathematical framework for formulating and solving problems in areas of physics such as elasticity, fluid mechanics, and general relativity.
The notation for a tensor is similar to that of a matrix (i.e., A = (a_(ij))), except that a tensor a_(ijk...), a^(ijk...), a_i ^(jk) ..., etc., may have an arbitrary number of indices. In addition, a tensor with rank r + s may be of mixed type (r, s), consisting of r so-called "contravariant" (upper) indices and s "covariant" (lower) indices. Note that the positions of the slots in which contravariant and covariant indices are placed are significant so, for example, a_μν ^λ is distinct from a_μ ^νλ.
While the distinction between covariant and contravariant indices must be made for general tensors, the two are equivalent for tensors in three-dimensional Euclidean space, and such tensors are known as Cartesian tensors.

LCM is equal to 38*72/gcd (38,72). So, 2,736 / 2 = 1,368.

What is the L.C.M. of 38 and 72?

factor(38) = 2*19         = 2   *19

factor(72) = 2^3*3^2    =2    *2*2*3*3

Lowest common multple is    2 (only needs to be included once because it is a factor of both) * 19*2*2*3*3

2*19*2*2*3*3 = 1368

Solve for x:
3 x^2 - 2 x - 8 = 0

Divide both sides by 3:
x^2 - (2 x)/3 - 8/3 = 0

Add 8/3 to both sides:
x^2 - (2 x)/3 = 8/3

Add 1/9 to both sides:
x^2 - (2 x)/3 + 1/9 = 25/9

Write the left hand side as a square:
(x - 1/3)^2 = 25/9

Take the square root of both sides:
x - 1/3 = 5/3 or x - 1/3 = -5/3

Add 1/3 to both sides:
x = 2 or x - 1/3 = -5/3

Add 1/3 to both sides:
Answer: |x = 2         or          x = -4/3

L.C.M. of 38 and 72?

Find the least common multiple:
lcm(38, 72)
Find the prime factorization of each integer:
The prime factorization of 38 is:
38 = 2×19
The prime factorization of 72 is:
72 = 2^3×3^2
Find the largest power of each prime factor.
The largest power of 2 that appears in the prime factorizations is 2^3.
The largest power of 3 that appears in the prime factorizations is 3^2.
The largest power of 19 that appears in the prime factorizations is 19^1.
Therefore lcm(38, 72) = 2^3×3^2×19^1:
Answer: |lcm(38, 72) = 1368

Solve for x over the real numbers:
log(x^2) = log^2(x)

Subtract log^2(x) from both sides:
log(x^2) - log^2(x) = 0

Transform log(x^2) - log^2(x) into a polynomial with respect to log(x):
2 log(x) - log^2(x) = 0

Factor log(x) and constant terms from the left hand side:
-log(x) (log(x) - 2) = 0

Multiply both sides by -1:
log(x) (log(x) - 2) = 0

Split into two equations:
log(x) - 2 = 0 or log(x) = 0

Add 2 to both sides:
log(x) = 2 or log(x) = 0

Cancel logarithms by taking exp of both sides:
x = e^2 or log(x) = 0

Cancel logarithms by taking exp of both sides:
Answer: |x = e^2                        or                              x = 1

First, this how I interpreted your equaton.
2*4sqrt(5x^2 - 8x + 1) + 4 =33*2sqrt(5x^2 - 8x), solve for x
Second, this is a very long and complicated solution, but it is ACCURATE!

Solve for x:
4 + 8 sqrt(5 x^2 - 8 x + 1) = 66 sqrt(5 x^2 - 8 x)

Subtract 4 from both sides:
8 sqrt(5 x^2 - 8 x + 1) = 66 sqrt(5 x^2 - 8 x) - 4

Raise both sides to the power of two:
64 (5 x^2 - 8 x + 1) = (66 sqrt(5 x^2 - 8 x) - 4)^2

Expand out terms of the left hand side:
320 x^2 - 512 x + 64 = (66 sqrt(5 x^2 - 8 x) - 4)^2

(66 sqrt(5 x^2 - 8 x) - 4)^2 = 16 - 34848 x + 21780 x^2 - 528 sqrt(5 x^2 - 8 x):
320 x^2 - 512 x + 64 = 16 - 34848 x + 21780 x^2 - 528 sqrt(5 x^2 - 8 x)

Subtract 64 - 512 x + 320 x^2 - 528 sqrt(5 x^2 - 8 x) from both sides:
528 sqrt(5 x^2 - 8 x) = 21460 x^2 - 34336 x - 48

Raise both sides to the power of two:
278784 (5 x^2 - 8 x) = (21460 x^2 - 34336 x - 48)^2

Expand out terms of the left hand side:
1393920 x^2 - 2230272 x = (21460 x^2 - 34336 x - 48)^2

Expand out terms of the right hand side:
1393920 x^2 - 2230272 x = 460531600 x^4 - 1473701120 x^3 + 1176900736 x^2 + 3296256 x + 2304

Subtract 460531600 x^4 - 1473701120 x^3 + 1176900736 x^2 + 3296256 x + 2304 from both sides:
-460531600 x^4 + 1473701120 x^3 - 1175506816 x^2 - 5526528 x - 2304 = 0

Factor constant terms from the left hand side:
-16 (28783225 x^4 - 92106320 x^3 + 73469176 x^2 + 345408 x + 144) = 0

Divide both sides by -16:
28783225 x^4 - 92106320 x^3 + 73469176 x^2 + 345408 x + 144 = 0

Eliminate the cubic term by substituting y = x - 4/5:
144 + 345408 (y + 4/5) + 73469176 (y + 4/5)^2 - 92106320 (y + 4/5)^3 + 28783225 (y + 4/5)^4 = 0

Expand out terms of the left hand side:
28783225 y^4 - 37058408 y^2 + 298197904/25 = 0

Substitute z = y^2:
28783225 z^2 - 37058408 z + 298197904/25 = 0

Divide both sides by 28783225:
z^2 - (37058408 z)/28783225 + 298197904/719580625 = 0

Subtract 298197904/719580625 from both sides:
z^2 - (37058408 z)/28783225 = -298197904/719580625

Add 343331400873616/828474041400625 to both sides:
z^2 - (37058408 z)/28783225 + 343331400873616/828474041400625 = 300250368/33138961656025

Write the left hand side as a square:
(z - 18529204/28783225)^2 = 300250368/33138961656025

Take the square root of both sides:
z - 18529204/28783225 = (528 sqrt(1077))/5756645 or z - 18529204/28783225 = -(528 sqrt(1077))/5756645

Add 18529204/28783225 to both sides:
z = 18529204/28783225 + (528 sqrt(1077))/5756645 or z - 18529204/28783225 = -(528 sqrt(1077))/5756645

Substitute back for z = y^2:
y^2 = 18529204/28783225 + (528 sqrt(1077))/5756645 or z - 18529204/28783225 = -(528 sqrt(1077))/5756645

Take the square root of both sides:
y = sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or y = -sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or z - 18529204/28783225 = -(528 sqrt(1077))/5756645

Substitute back for y = x - 4/5:
x - 4/5 = sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or y = -sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or z - 18529204/28783225 = -(528 sqrt(1077))/5756645

Add 4/5 to both sides:
x = 4/5 + sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or y = -sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or z - 18529204/28783225 = -(528 sqrt(1077))/5756645

Substitute back for y = x - 4/5:
x = 4/5 + sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or x - 4/5 = -sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or z - 18529204/28783225 = -(528 sqrt(1077))/5756645

Add 4/5 to both sides:
x = 4/5 + sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or x = 4/5 - sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or z - 18529204/28783225 = -(528 sqrt(1077))/5756645

Add 18529204/28783225 to both sides:
x = 4/5 + sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or x = 4/5 - sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or z = 18529204/28783225 - (528 sqrt(1077))/5756645

Substitute back for z = y^2:
x = 4/5 + sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or x = 4/5 - sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or y^2 = 18529204/28783225 - (528 sqrt(1077))/5756645

Take the square root of both sides:
x = 4/5 + sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or x = 4/5 - sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or y = sqrt(18529204/28783225 - (528 sqrt(1077))/5756645) or y = -sqrt(18529204/28783225 - (528 sqrt(1077))/5756645)

Substitute back for y = x - 4/5:
x = 4/5 + sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or x = 4/5 - sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or x - 4/5 = sqrt(18529204/28783225 - (528 sqrt(1077))/5756645) or y = -sqrt(18529204/28783225 - (528 sqrt(1077))/5756645)

Add 4/5 to both sides:
x = 4/5 + sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or x = 4/5 - sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or x = 4/5 + sqrt(18529204/28783225 - (528 sqrt(1077))/5756645) or y = -sqrt(18529204/28783225 - (528 sqrt(1077))/5756645)

Substitute back for y = x - 4/5:
x = 4/5 + sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or x = 4/5 - sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or x = 4/5 + sqrt(18529204/28783225 - (528 sqrt(1077))/5756645) or x - 4/5 = -sqrt(18529204/28783225 - (528 sqrt(1077))/5756645)

Add 4/5 to both sides:
x = 4/5 + sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or x = 4/5 - sqrt(18529204/28783225 + (528 sqrt(1077))/5756645) or x = 4/5 + sqrt(18529204/28783225 - (528 sqrt(1077))/5756645) or x = 4/5 - sqrt(18529204/28783225 - (528 sqrt(1077))/5756645)

4 + 8 sqrt(5 x^2 - 8 x + 1) ≈ 12.0148
66 sqrt(5 x^2 - 8 x) ≈ 4.01479:
So this solution is incorrect

4 + 8 sqrt(5 x^2 - 8 x + 1) ⇒ 4 + 8 sqrt(1 - 8 (4/5 + sqrt(18529204/28783225 - (528 sqrt(1077))/5756645)) + 5 (4/5 + sqrt(18529204/28783225 - (528 sqrt(1077))/5756645))^2) = 4 + (8 sqrt(1172917 - 528 sqrt(1077)))/1073 ≈ 12.0148
66 sqrt(5 x^2 - 8 x) ⇒ 66 sqrt(5 (4/5 + sqrt(18529204/28783225 - (528 sqrt(1077))/5756645))^2 - 8 (4/5 + sqrt(18529204/28783225 - (528 sqrt(1077))/5756645))) = (132 sqrt(5397 - 132 sqrt(1077)))/1073 ≈ 4.01479:
So this solution is incorrect

4 + 8 sqrt(5 x^2 - 8 x + 1) ≈ 12.1341
66 sqrt(5 x^2 - 8 x) ≈ 12.1341:
So this solution is correct

4 + 8 sqrt(5 x^2 - 8 x + 1) ⇒ 4 + 8 sqrt(1 - 8 (4/5 + sqrt(18529204/28783225 + (528 sqrt(1077))/5756645)) + 5 (4/5 + sqrt(18529204/28783225 + (528 sqrt(1077))/5756645))^2) = 4 + (8 sqrt(1172917 + 528 sqrt(1077)))/1073 ≈ 12.1341
66 sqrt(5 x^2 - 8 x) ⇒ 66 sqrt(5 (4/5 + sqrt(18529204/28783225 + (528 sqrt(1077))/5756645))^2 - 8 (4/5 + sqrt(18529204/28783225 + (528 sqrt(1077))/5756645))) = (132 sqrt(5397 + 132 sqrt(1077)))/1073 ≈ 12.1341:
So this solution is correct

The solutions are:
Answer: |x = 4/5 + sqrt(18529204/28783225 + (528 sqr(1077))/5756645                                              or x = 4/5 - sqrt(18529204/28783225 + (528 sqrt(1077))/5756645)

You are given   m/h     and m    and want  h  

so if we    DIVIDE m   BY  m/h

we get

m  /   m/h   =   m x h/m   = h   (because the m's cancel)

So your answer is

3.8m / (285 m/h)  =  3.8  /   285/1  =  3.8  x   1/285  =  3.8/285 = 0.0133333333333333  hr    or   48 seconds

My guess is, you are looking for the pOH of the solution

pOH = -log[OH-]  = -log [3.46 x 10^-3 ]   =  -log(0.00346) =  2.46

The new volume would be (2x2x2) times the original volume, thus 2^3 x old volume = 8x112 cm3 = 896 cm3

The scale factor 2 works in each of the 3 directions, so (2 to the power 3) overall.

Unit rate in this instance is miles per hour   or   m/h    so just divide miles by hours

270/6 =  ??    mph    (use the calculator)

They are all between -518 and -324.

They are all negative integers.

This is not an equation EP a can represent any number.  :)