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If you are the trig person, that is okay.

You will know for next time.     

$$\frac{5n^2}{4}-28n-\frac{3n^2}{3}-18n\\\\
=\frac{5n^2}{4}-28n-n^2-18n\\\\
=\frac{5n^2}{4}-n^2-18n-28n\\\\
=\frac{5n^2}{4}-\frac{4n^2}{4}-46n\\\\
=\frac{n^2}{4}-46n\\\\$$

I don't quite understand. Do you mean the third root of (8+1/3)-16? If so, then it's not a real number, because roots of negatives are weird that way.

I assume that by HCF you mean highest common factor. I also assume that "C is divisible by e" means c/e is an integer. In this case, since e is a factor of c, and the fighest factor of itself, e is the HCF.

As SckSniper stated earlier, it would certainly help if you made your question more specific. 

SckSniper explained the Pythagorean Theorem, which is related to trigonometry and triangles, but good try:)

The Quadratic Formula is  and helps solve for x with a quadratic equation in the standard form: $${{\mathtt{ax}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{bx}}{\mathtt{\,\small\textbf+\,}}{\mathtt{c}} = {\mathtt{0}}$$

You can read about it here: http://www.purplemath.com/modules/quadform.htm

It is . . . currently around 75 degrees outside.

But seriously, if you want a specific answer, please make your question more specific, such as posting the picture of the triangle with the angle in question. Since a triangle has 180 degrees total for its three angles, an angle A could be anywhere from 1  to 178 degrees.

Lateral surface area is the surface area of an object, excluding the area of the base(s).

So the formula for the lateral surface area of a cylinder would be: $${\mathtt{A}} = {\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{r}}{\mathtt{\,\times\,}}{\mathtt{h}}$$ where r is radius of the circular base and h is the height.

Start by substituting in the values for r and h. And for this problem, pi will be the approximate value of 3.14

$${\mathtt{A}} = {\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{3.14}}{\mathtt{\,\times\,}}{\mathtt{9.6}}{\mathtt{\,\times\,}}{\mathtt{7}} \Rightarrow {\mathtt{A}} = {\mathtt{422.016}}$$

The lateral S.A. of the cylinder would be  about 422 meters².

Another way would be to think of the lateral surface area of the cylinder as the circumference of the base circle, multiplied by the height of the cylinder.

A cylinder is like stacking a bunch of circles together, so the surface area of the cylinder would be the circumferences of all the circles added together. Adding the circumferences together multiple times would be equivalent to multiplying them by the height of the cylinder.

So another way to find the lateral surface area of a cylinder would be:

$${\mathtt{A}} = {\mathtt{C}}{\mathtt{\,\times\,}}{\mathtt{h}}$$ where C is the circumference of the base and h is the height:)

For this question, you can use the Pythagorean Theorem: $${{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{b}}}^{{\mathtt{2}}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$ since this is a right triangle. A and b are the legs (shorter sides) of the triangle and c is the hypotenuse (longest side, diagonal side).

a  and b are 8 and 5 since the length of the wire is the diagonal side of the right triangle. So set up the equation:

$${{\mathtt{8}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{5}}}^{{\mathtt{2}}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$

Simplify the left side:

64 + 25 = c²

89 = c²

Now take the square root of both sides:

$${\sqrt{{\mathtt{89}}}} = {\mathtt{9.433\: \!981\: \!132\: \!056\: \!603\: \!8}}$$ = c

So the wire is about 9.434 or 9.4 feet long.

If you mean finding the cosine of a specific angle, use the cosine button. Starting from the left, it is in the first column.The cos( ) button is in the third row down.

It works for angles in both radians and degrees, but you will need to select radians if you are using that, since the calculator defaults to degrees.

You can also directly type in cos(   ) to the calculator:)

40.5 / sin(35)

70.6095952226601444 ft.

thank you very much :)

depends on the conditions, e can be eulers constant. 

or on some calculators E5 for example means $${{\mathtt{10}}}^{{\mathtt{5}}}$$

$${\mathtt{degrees}} = {\frac{{\mathtt{rad}}{\mathtt{\,\times\,}}{\mathtt{180}}}{{\mathtt{\pi}}}}$$

so

$${\frac{{\frac{{\sqrt{{\mathtt{3}}}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\mathtt{180}}}{{\mathtt{\pi}}}} = {\mathtt{49.619\: \!600\: \!587\: \!961\: \!284\: \!5}}$$

about 50 degrees

could you be more specific? or do you mean $${{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{b}}}^{{\mathtt{2}}} = {{\mathtt{c}}}^{{\mathtt{2}}}$$ in a rectangle, where a and b are the sides along de 90° corner, and c is the long side

0.3333333333333....

$${\frac{{\mathtt{1.5}}{\mathtt{\,\times\,}}{\mathtt{0.6}}}{{\mathtt{0.4}}}} = {\frac{{\mathtt{9}}}{{\mathtt{4}}}} = {\mathtt{2.25}}$$

Do you mean in the calculator here?  For what purpose: plotting a graph (yes, but graphing here isn't very good)?; finding the roots of the equation (yes, but might depend on the nature of the equation!)?

First rewrite this to isolate y.

7y = 3x - 9

y = (3/7)x - (9/7)

In this form the slope is given by the number multiplying the x, so the slope is 3/7

If there are eight "wheels", four of which have the letters A to Z and four of which have the digits 0 to 9, then there are 26⁴*10⁴ possible combinations, so the probability that a random guess will get the right combination is:

$${\mathtt{p}} = {\frac{{\mathtt{1}}}{\left({{\mathtt{26}}}^{{\mathtt{4}}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{4}}}\right)}} \Rightarrow {\mathtt{p}} = {\mathtt{0.000\: \!000\: \!000\: \!218\: \!829\: \!9}}$$

or about 2*10^-10

Of course if a different alphabet is used that has a different number of letters, the probability will be different!

Turn both sides upside down and the equation is still balanced

$$$\frac{x}{50}=\frac{256000}{1350}$$$

Multiply both sides by 50

$$$x=\frac{50*256000}{1350}$$$

$${\mathtt{x}} = {\frac{{\mathtt{50}}{\mathtt{\,\times\,}}{\mathtt{256\,000}}}{{\mathtt{1\,350}}}} \Rightarrow {\mathtt{x}} = {\mathtt{9\,481.481\: \!481\: \!481\: \!481\: \!481\: \!5}}$$

 This can also be written as

 $$$x = 9481\frac{13}{27}$$$

If this is y = (1/4)*sin(x-3) then the derivative is just dy/dx = (1/4)*cos(x-3)

$$$$\frac{c}{\sqrt{2x}}+\frac{y}{2\sqrt{x}}$$\\
Multiply top and bottom of 1st term by $\sqrt2$\\
$$\frac{c}{\sqrt{2x}}+\frac{y}{2\sqrt{x}}=\frac{\sqrt2c}{\sqrt2\sqrt{2x}}+\frac{y}{2\sqrt{x}}$$\\
The denominator of the first term can be rewritten as $\sqrt2\sqrt{2x}=2\sqrt{x}$ so
$$ \frac{c}{\sqrt{2x}}+\frac{y}{2\sqrt{x}}=\frac{\sqrt2c}{2\sqrt{x}}+\frac{y}{2\sqrt{x}}$$\\
Both terms now have a common denominator so:
$$\frac{c}{\sqrt{2x}}+\frac{y}{2\sqrt{x}}=\frac{\sqrt2c+y}{2\sqrt{x}}$$

Mr. Tanaka = T

Son = S

years = y

$$\\T+y=(S+y)*3\\
T+y= 3S+3y \quad | \quad -3S\\
T+y-3S=3y \quad | \quad -y\\
T-3S=2y \quad | \quad :2 \\
y=\dfrac{T-3S}{2}\\
y=\dfrac{35-3*5}{2}\\
y=\dfrac{35-15}{2}\\
y=\dfrac{20}{2}\\
\boxed{y=10}$$

In 10 years: Mr Tanaka is 45 and his son is 15.

15 * 3 = 45

$$\\4x^2-4x-27 \\
=4(x^2-x)-27\\
=4\left(x^2-x+\left(\frac{1}{2}\right)^2-\left(\frac{1}{2}\right)^2\right) -27\\
=4\left( \left( x-\frac{1}{2}\right)^2-\frac{1}{4}\right) -27\\
=4\left(x-\frac{1}{2}\right)^2 - \frac{4}{4}-27\\
=4\left(x-\frac{1}{2}\right)^2 - 1-27\\
=4\left(x-\frac{1}{2}\right)^2 -28\\$$

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