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Answer

The subtraction button also works as a negative sign.

Correct me if I'm wrong.

a=cos^-1(0,6)

i entered it into the web2 calc as      acos(0.6)=        and I set the calc to degrees

Inverse cos and arc cos are the same thing :)

acos(0.6) = 53.130102354156 degrees

Stacking   Thanks for this one  hectictar :)

\stackrel{?}{=}

\(\stackrel{?}{=}\)

Thanks hectictar

I've never seen your LaTex command before

\stackrel{?}{=}

I shall try and remember and I will add it to our LaTex thread :)

I was trying to work out how to put an arc over 2 letters, like for arc length... do you know how to do that?

I could not work it out. :/

Lol, 2052 views (currently) and no replies other than this.

LateX does not show % without a \ infront of it, I kinda forgot, anyways, thanks, gave u a liek.

13^(3x-1) = 91

(3x - 1)ln 13 = ln 91 

(3x - 1)ln 13 = ln 13 + ln 7

(3x - 2)ln 13 = ln 7

\(3x - 2 = \dfrac{\ln 7}{\ln13}=\log_{13}7\)

\(x = \dfrac{\log_{13}7+2}{3}\)

And then use ur calculator to get 0.919551471

(x + 2)(2x) = 54

2x^2 + 4x = 54

2x^2 + 4x - 54 = 0

x^2 + 2x - 27 = 0

(x + 1)^2 = 28

x + 1 = +- sqrt(28)

x = -1 +- 2sqrt(7)

x = 2sqrt7 - 1 OR -1 - 2sqrt7(rejected)

x = 2sqrt7 - 1

If it is included angle:

a, b are the given sides, theta is the included angle

Area = \(\dfrac{ab\sin \theta}{2}\)

James:

178.93805309734513"%"

I'll give it a go but it might be wrong.  I'm pretty confident on part b but less confident with part a.

Cost, revenue, and profit are in dollars and x is the number of units.

Suppose that the marginal revenue for a product is MR = 3600 and the marginal cost is MC = 120 sqrt(x + 4) with a fixed cost of $600.

(a) Find the profit or loss from the production and sale of 5 units.

Revenue for producing and selling 5 units = 3600*5 = $18000

\(\text{MC for 1st unit }= 120\sqrt{5}\\ \text{MC for 2nd unit }= 120\sqrt{6}\\ \text{MC for 3rd unit }= 120\sqrt{7}\\ \text{MC for 4th unit }= 120\sqrt{8}\\ \text{MC for 5th unit }= 120\sqrt{9}\\\)

Sum of marginal costs = 120*(sqr5+sqrt6+sqrt7+sqrt8+3) = $1579

marginal costs+FC = 1579+600 = $2179

Profit on 5 units = 18000-2179 = $15821

(b) How many units will result in a maximum profit?

\(\text{MProfit = marginal revenues - marginal costs} \\ MP=3600-120\sqrt{x+4}\\ \text{Profit is maximised when marginal profit =0}\\ 3600-120\sqrt{x+4}=0\\ 30-\sqrt{x+4}=0\\ \sqrt{x+4}=30\\ x+4=900\\ x=896\;units \)

1. Multiply 1.7893805309735 by 100 to convert to percent
\(1.7893805309735 × 100\)

Answer

\(178.93805309735 \%\)

Good answer! Though since the question asks for the complete factored form you might replace the \((x^2+25)\)  term by  \((x-5i)(x+5i)\)

y = 1500*1.023^t

.

\(f(x)= ?\)

There is a zero at 2 with multiplicity 3

\(f(x) = (x-2)^3 (?)\)

 A zero at 6 with multiplicity 1

\(f(x)= (x-2)^3(x-6)(?)\)

A zero of 5i

\(f(x)=(x-2)^3(x-6)(x^2+25)\)

It is good to note that complex factors come in pairs so by adding a complex factor you essentially solve for two complex zeroes                                                                         

Now we have a polynomial with a degree of 6. However, we need the leading coefficient to be 10. To do this we just include a ten as a subset of the function like this. \(f(x)=10(x-2)^3(x-6)(x^2+25)\)  Now you have a polynomial f(x) that satisfies all the given conditions. 

Is the angle that you are given between the two given sides, or is the angle not "included"?

Using Desmos graphing calculator

0.4166666666666667. You divide the top number by the bottom number.

So your GP is

3, 3r, 3r^2 ....

where

\(3+3r+3r^2=21\\ 3r^2+3r+3=21\\ r^2+r+1=7\\ r^2+r-6=0\\ (r+3)(r-2)=0\\ r=-3\quad or \quad r=2\\ so\\ 3,-9, 27 \qquad sum=21\\ 3,6, 12 \qquad sum=21\\\)

so the common ratio could be  -3 or  +2

It will affect your answers if you use any of these buttons:

sin, cos, tan, sinh, cosh, tanh, cot, sec, csc  (and their inverses)

Subtract 29 from 30 (30-29=x). To be nice, I'll just give you the answer: 1.

The answer is 0.041875294788348

This is one way of doing it.

We want to get the function into vertex form.

y = x² - 4x + 2                  Subtract 2 from both sides.

y - 2 = x² - 4x                   Add (-4/2)² , or 4, to both sides.

y - 2 + 4 = x² - 4x + 4       Now that the right hand side is a perfect square trinomial, factor it.

y + 2 = (x - 2)(x - 2)          

y + 2 = (x - 2)²                  Subtract 2 from both sides.

y = (x - 2)² - 2

When the equation is in this form, we can see that this is the graph of y = x² shifted to the right 2 units and shifted down 2 units. The vertex is at (2, -2). So plot the first point at (2, -2) and go up just like a basic parabola from there. :)

ya thats right

no it is a very well designed website.