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That was a really good attempt anonymous. I like to see people 'having a go' 

When ever there is a negative or a negative number in front of a bracket you have to be really careful to expand the bracket properly BEFORE you collect like terms.  It is very easy to make  a mistake.

Sorry Rom, but your answer would imply that the function is defined for, say, x = -5, which it isn't.

This still isn't meaningful!

What does the expression log^(d/10) mean? You have to have the logarithm of something before you can start raising to a power.  

Perhaps you mean log(d^1/10) in which case your equation would be 1.08 = log(d^1/10), which is equivalent to 1.08 = (1/10)log(d), so log(d) = 10.8 so d = 10^10.8. 

or do you mean 1.08 = log(d/10) in which case 1.08 = log(d) - log(10) so 1.08 = log(d) - 1 so log(d) = 2.08 so d = 10^2.08. 

or do you mean 1.08 = (log(d))^1/10, in which case 1.08¹⁰ = log(d) so d = 10^{(1.08^10)}?

You could have log(m^d/10) or log(m)^d/10, but you would then need to specify the value of m in order to find d.

Just type this expression, exactly as you have written it, directly into the calculator on this site (go to Home to find it).

Yes, but you would have to type in the relevant equations yourself.  The calculator here doesn't have them built-in.

We can do this as follows: (Note: In copying the LaTeX from Tekmaker and pasting it here the third equation has been renumbered to (1)!!!. The third equation below should be numbered (3), of course.)

$$Let's first rewrite the two given equations as:
\begin{equation}
y1 = -\frac{3}{2}x+\frac{5}{2}
\end{equation}
\begin{equation}
y2 = -4x+5
\end{equation}$$

$$and the line perpendicular to the first of the above as:
\begin{equation}
y3 = mx+c
\end{equation}

where $m$ is its gradient and $c$ is its intersection with the y-axis.\\\\$$

$$The gradient, $m$, is given by -1/the gradient of the line to which it is perpendicular, so $m=\frac{2}{3}$\\\\

To find the point of intersection of lines (1) and (2) we need to equate them:
$$ -\frac{3}{2}x+\frac{5}{2}=-4x+5$$ and solve for $x$. This is straightforward and results in $x=1$. Plugging this back in either equation (1) or equation (2) we find that the value of y at the intersection point is also $y=1$\\\\
Now we put the known values of $x$ and $y$ at the intersection point, together with our value for $m$ into equation (3):
$$ 1=\frac{2}{3}*1+c$$

$$from which we get $c=\frac{1}{3}$; so, using equation (3), we get the equation of the perpendicular line as:
$$ y3=\frac{2}{3}x+\frac{1}{3}$$$$

Let's plot a graph to see if the result looks sensible:

Actually kitty, the general convention is that √9 is just 3 not -3.  If we have an equation like x² = 9 then there are two possible values of x, namely ±√9.  However, the √9 part is just 3 {otherwise we'd have the situation that x = ±(±3), or even worse the infinite regression: x = ±(±(±(±......(±√9)....))) !!!!!}

All of the problems have an answer of 1 pet.

Do you get it now mathcalc?

If it helps, the side measure must be less than 17.5 ft.

We need more information to solve this problem, i.e., at least one angle and its position in the triangle.

$$y=\dfrac{2x+1}{3x-2}$$

First off note that this isn't defined at x=2/3 but other than that it is one to one.

$$(3x-2)y=2x+1$$

$$3xy - 2y = 2x+1$$

$$x(3y-2)=1+2y$$

$$x=\dfrac {1+2y}{3y-2}$$

now just replace x by f^-1(x) and y by x to obtain

$$f^{-1}(x)=\dfrac{2x+1}{3x-2}~~\forall x \neq \dfrac 2 3$$

For real numbers log(x) function isn't defined for x<=0. So for this to be undefined

$$8x^2+26x-7<0$$

$$4x-1<0$$

and further division by 0 isn't permitted so

$$\log(4x-1)= 0 \Rightarrow (4x-1)= 1$$

Sorting through this we see

$$(2x+7)(4x-1)\leq 0 \Rightarrow \left[-\dfrac 7 2 \leq x \leq \dfrac 1 4 \right]$$

This also takes care of the second condition.

We also have

$$4x-1 = 1 \Rightarrow 4x = 2 \Rightarrow x = \dfrac 1 2$$

Combing these we have that the original function is undefined on

$$\left[-\dfrac 7 2 \leq x \leq \dfrac 1 4 \right] \bigcup \left\{\dfrac 1 2 \right\}$$

Please include angle measures, or how the sides are related to each other; are they opposite, adjacent?

Just subtract 7 squared (49) from 10.5 squared (110.25). X should equal 61.25

No, an ln function by itself is always equal to or greater than 0. Have a look at a graph for ln(x), you'll see it squashes right up against the y axis but never actually crosses it. This is because when you take a log, you're looking for the power to which you must raise the base of your logarithm to get the number in the brackets. Put more clearly:

log_a(b) = c if a^c = b. ln(x) = log_e(x), so if your b is negative, you're asking for the power to which you can raise e to get a negative number. Since e is positive, it doesn't matter what power you raise it to, it's always gonna be positive.

Either click the button with an "x" and a smaller "y" (just beneath the "e" button), or type (your equation)^(your power)

Type "acos(" in to the box, or hit "2nd" and then "acos"

The cosine only returns values from -1 to 1, inclusive......Since (1.83 / 1.2) > 1, this isn't defined for the cosine function.

Solve by substitution -8x+4y=20 y+6=(x+4)^2

---------------------------------------------------------------------------------------------------------------------------

OK...in the first equation, let's isolate y...we have

4y = 8x + 20   divide by 4 on both sides

y = 2x + 5    so, in the second equation, we have

(2x + 5) + 6 = (x + 4)^2       let's expand the right side and simplify the left

2x + 11 = x^2 + 8x + 16      now subtract the 2x + 11 from both sides

0 = x^2 + 6x +5    And this factors as

0 = (x+1) (x+5)    and setting each factor to 0, we get that x = -1 and x = -5

Using  y = 2x + 5  to find the y values, we have

y = 2(-1) + 5 = 3     and  y = 2(-5) + 5 = -5

So the solutions are (-1, 3)   and  (-5, 5)

BTW......this is the intersection in two points of a parabola (the second equation) and a line (the first equation)

Washington, D.C.

You're right about adding them together and then dividing by two. But when I redid this I got two 1's left and if you add them together and divide by two, you should get one. 00000000111111222333

x-10=√9

First add 10 to both sides.

x = 10 + √9

now √9 is equal to plus or minus 3, since (-3)² and (3)² both equal 9. However, positive 3 is called the principal (main) square root.

So technically there are two equations: x = 10 + 3  or  x = 10 + (-3)

So x = 13  or  x = 7

As Melody pointed out last night, Andre Massow recently installed a calculator for fractions on this site:

What I mean is 1.08= log with (d/10) as its exponent. I need to find the value of d. I pretty sure you could cancel the base 10 with the bottom 10 in its exponent. I hope the question is more comprehensible now. Please, can anyone help?

aren't we suppose to divide that 2 with 2 ? because I'm not getting one middle number, I'm getting pair of middle numbers. To find the value between them, add them together and divide by 2. This is the way i was taught in school. Please let me know. Thank you.