Assuming no air resistance and the projextile is fired from ground level, you can use the kinematic equation applied to the vertical component of motion:

s = ut + (1/2)at²  where s is the net distance travelled in time t; u is the initial velocity and a is acceleration.

Here: s = 0  (because it starts and ends at ground level)

         u = 200*sin(53°) m/s    (the vertical component of the initial velocity)

         a = -9.8 m/s²    (acceleration due to gravity - acting downwards)

This results in a quadratic equation for t

0 = ut + (1/2)at²

or

0 = t(u + (1/2)at)

so t = 0 (start time) or

t = -2u/a

$${\mathtt{t}} = {\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{200}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{53}}^\circ\right)}}{{\mathtt{9.8}}}} \Rightarrow {\mathtt{t}} = {\mathtt{32.597\: \!367\: \!757\: \!020\: \!408\: \!2}}$$

t ≈  32.6 seconds

.

$${\frac{{\mathtt{58\,765\,432\,098}}}{{\mathtt{100\,000\,000\,000}}}} = {\frac{{\mathtt{238}}}{{\mathtt{405}}}} = {\mathtt{0.587\: \!654\: \!320\: \!98}}$$

Do you mean x is decreased by 10% and you want to know the decrease for x²?

If so x_decreased = 0.9*x  so  x_decreased² = 0.9²x² = 0.81x²  

This means x_decreased² is 81% of x²,  which means the decrease is 19%

.

-(3z+4z)-(6z-2) = - 7z -6z +2 =-13z +2

gradient = (y2 - y1)/x2 - x1)

$${\mathtt{gradient}} = {\frac{\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0}}\right)}{\left({\mathtt{6}}{\mathtt{\,-\,}}{\mathtt{5}}\right)}} \Rightarrow {\mathtt{gradient}} = {\mathtt{3}}$$

Volume of a pyramid is given by one third of the base area multiplied by the height

$${\mathtt{Volume}} = \left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right){\mathtt{\,\times\,}}{{\mathtt{16}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{15}} \Rightarrow {\mathtt{Volume}} = {\mathtt{1\,280}}$$

Volume = 1280 m³

.

arcsine is the same as asin which is the same as sin^-1

Press 2nd then asin on the calculator

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{10}}}{{\mathtt{20}}}}\right)} = {\mathtt{30^{\circ}}}$$

.

0.4 recurring can be expressed as a fraction in the following way:

Let x = 0.44444.....

Multiply by 10

10x = 4.44444....

Subtract x from 10x

9x = 4

So x = 4/9

Now multiply this by 4 to get 16/9

If you want this as a decimal:

$${\frac{{\mathtt{16}}}{{\mathtt{9}}}} = {\mathtt{1.777\: \!777\: \!777\: \!777\: \!777\: \!8}}$$

or 1.77777777....   (i.e. the 7's recurr).

.

y is the seventh root of 8, so y = 8^1/7

$${\mathtt{y}} = {{\mathtt{8}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{7}}}}\right)} \Rightarrow {\mathtt{y}} = {\mathtt{1.345\: \!900\: \!192\: \!632\: \!356\: \!2}}$$

.

The angles can be anything so long as the 5 altogether they add up to (5-2)*180 = 540 degrees

There is not one equation Mathcad, there are 2.

When simplified Alan found them to be the equations of parallel lines.

That is why there can be no solutions.  The lines will never cross one another.  

It's "/".

This is used for fractions too.

Sorry, too much Latex!

divide by 1000.

20% =0.20

The total (1) - (20%) =0.80

4299*0.8=34392

=$34.39

I think..?

$${{\mathtt{8}}}^{\left({\frac{{\mathtt{5}}}{{\mathtt{6}}}}\right)} = {\mathtt{5.656\: \!854\: \!249\: \!492\: \!381}}$$

Thanks Mathcad

There is often more than one way to answer a question.

We like to see how you would do it but do not be quick to criticize other peoples answers.

Even when your method is correct, it does NOT mean that someone elses method is wrong.   

CONGRATULATIONS ZEGROES  

Ok then,

please do this one - you have not done it yet.

Do it with the most allowed canceling so that you do not need to multiply big numbers any more than necessary.  Also, keep it all together please like I do.  I would like you to use Latex please.   

$$\\34\frac{1}{8}\times \frac{14}{51}\div 1\frac{30}{68}$$

First we're going to want to factor these out.

f(x)=x^3+x^2-42x

f(x) = (x)(x^2+x-42)   ---this second part can be factored

f(x) = (x)(x+6)(x-7)    

Now that this is factored completely, we can find the zeros. The "zeros" of a polynomial funtion like we have here are the numbers you could put in for x to make f(x) = 0. 

For instance, if we put in -6 for x, we would get this:

f(x)=(-6)(-6+6)(-6-7)

f(x)=(-6)(0)(-13)       ---anything and everything multiplied by zero is zero.

f(x) = 0

Basically you find the opposites of the numbers next to x.

So the zeros are 0, -6, and 7.

Why don't you try this on the website's calculator my friend?

I'm thinking you mean 

$$log_3(2x-1) = 2$$

To do this, we need to rewirte this is exponential form!

What $$log_3(2x-1) = 2$$ is saying, is that $$3^2 = 2x-1$$

Now that we have it like this its pretty easy to solve.

3^2 = 2x-1

9 = 2x-1

10=2x

x=5

Neighbor Malia has 126 inches of lumber, but the problem is we need to know how many feet of lumber this is!

To do this, we need to know how many inches are in a foot.

It turns out there are 12 inches in a foot, so $$126\div12$$ will tell us how many feet of lumber Malia has.

$$126\div12=10\frac{1}{2}$$

add this to the lumber Jim gave her, which is 8 feet.

$$10\frac{1}{2}+8 = 18\frac{1}{2}$$

So...Jenna won't have enough for her fence yet, but she does have $$18\frac{1}{2}$$ feet of lumber so far.

Well, the area of the known side is height*length, 7.5*9, and thus 67.5.

Well, since there are two of these sides on a rectangle, we can do 67.5*2 = 135

Now subtract this from the total surface area: 399-135 = 264

Now this is where it'll be a little tricky. We know there's four sides left and 264 more surface area left...but not all of these sides are necessarily the same area.

If you think about it, one of the sides lengths of two of these squares will have to be 7.5, and one of the side lengths of the other two squares will be 9. Also, the other side legnth for all four of these squares will be the width (or x, because we don't know this yet)

So what we can do is set up an equation! Woohoo!

We'll end up with something like

2(7.5*x) + 2(9*x) = 264      (x = width)

2(7.5x)+2(9x)=264

15x+18x=264

33x=264

x = 264/33

x = 8

Nice! The width is 8 cm!