+2446 There are two interpretations of this problem, and they both result in different answers, so I will address both. They are:
I believe that you mean problem #1, but I'll solve both anyway. It's good practice:
| \(32m*\frac{3}{4}m^2\) | This is the original equation. To simplify, evaluate the coefficients and variables separately. I opted to deal with the variable first. We'll use this exponent rule: \(m^a*m^b=m^{a+b}\) |
| \(32m^3*\frac{3}{4}\) | Now, multiply 32 by 3/4 and simplify fully |
| \(\frac{32m^3*3}{4}\) | Do 32*3 first |
| \(\frac{96m^3}{4}\) | Do 96/4 |
| \(24m^3\) | This is your answer for interpretation #1 |
Now, let's do interpretation #2:
| \(32m*(\frac{3m}{4})^2\) | This is the original equation in scenario #2. First, square 3m/4. Remember that \((\frac{a}{b})^2=\frac{a^2}{b^2}\) |
| \(32m*\frac{(3m)^2}{4^2}\) | Simplify the numerator and denominator. |
| \(\frac{32m}{1}*\frac{9m^2}{16}\) | Instead of doing 32*9, let's notice that 32 and 16 can be canceled out! This simplifies matters a lot! |
| \(\frac{2m}{1}*\frac{9m^2}{1}={2m}*{9m^2}\) | Use the exponent rule that states that \(a^b*a^c=a^{b+c}\) |
| \(2m^3*9\) | Multiply 2*9, which is 18, of course |
| \(18m^3\) | This is your final answer for interpretation #2. |
+2446
Evaluating this requires knowledge of the fraction rules. Here it is step-by-step
| \(\frac{-5}{\frac{4}{3}}\) | This is the original expression. Let's apply a rule with fractions that says that \(\frac{a}{\frac{b}{c}}=\frac{ac}{b}\hspace{1mm},b\neq0,c\neq0\) |
| \(\frac{-5*3}{4}\) | Using the rule above, the problem becomes simpler to understand and solve |
| \(\frac{-15}{4}=-3.75\) | |
+2446 To figure out this problem, list the factors of both 20 and 150 and see which number appears twice in both lists. Ordering them from least to greatest makes it simpler:
| Number | Factors of Number |
| 20 | 1, 2, 4, 5, 10, 20 |
| 150 | 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 |
I have bolded the numbers that appear twice in the list. Those are the common factors. However, the question asks for the greatest one. Which one is greatest? 10! 10 is the greatest. That's your answer!
The GCF (greatest common factor) of 20 and 150 is 10!
+2446 Since it is a right triangle, we need not use the law of sines or cosines but rather trigonometric ratios! In this case, we must use tangent!
Here's an acronym that may or may not help you remember which relationship is which:
| S | Sine |
| O | Opposite |
| H | Hypotenuse |
| C | Cosine |
| A | Adjacent |
| H | Hypotenuse |
| T | Tangent |
| O | Opposite |
| A | Adjacent |
How do you know where the reference is? Your point of refence is where the angle is located. I know to use tangent because I need to find the opposite angle of the angle of reference, 56, and I can use 26ft as given info. Let's solve for x:
| \(\frac{\tan56}{1}=\frac{x}{26}\) | Solve by cross-multiplying |
| \(26\tan56=x\) | This is the exact value. To find a decimal approximation, use a calculator that has the trigonometric ratios! |
| \(x=26\tan56\approx38.5ft\) | Of course, do not forget to label your answer with a unit |
One last note before you go!
Be sure that your calculator is in degree mode when evaluating \(26\tan56\). If it isn't, then your answer will be wildly different. In fact, in radian mode \(26\tan56\approx-15.8931\). This answer is definitely wrong as a side length can never be negative.
