# Hard Problems To Solve

If you develop your math skills, however, then these questions won’t be that much more difficult for you.Note: This is a two-part question, but we left out the first part to focus on the second one.We’ve also included how many questions fall under each category, so if you’re self-studying, you can prioritize the types of questions that appear more often.

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For our fluid moving at a velocity of \(1\), we have \(q=\fracn(1)v^2\).

We can thus see that the dynamic pressure of the faster fluid will be \(2.25\) times that of the slower fluid. If you’re given a word problem that involves geometry or trigonometry and no diagram, you should draw yourself a diagram and label the information.

Most students find grid-in questions harder than the multiple-choice because some test tactics—like substituting answer choices into the problem—don’t work.

You’ll need to find the correct solution without any help from answer choices.

The first question asked for the value of \(x\) in the expression.

Because her bank account earns \(2\%\) interest compounded annually, we can convert \(2\%\) to a decimal, giving us \(.02\).This is similar to the earlier problem where there are only variables, but if we proceed step-by-step and manipulate the equation carefully, we can find the solution.In this problem, we have two fluids, and one of them is moving at a velocity of \(1\) and the other at \(1.5\).We then add \(1\) to this so that we don’t lose the initial deposit.The answer is \(x=1.02\), which you need to know to solve the question above. Since the roots of the above quadratic will give us the solution to the system of equations above, we can use the discriminant of the quadratic formula to find out how many solutions there are.Rewriting word problems to include words like equal to, less than, more than, sum, and so on can help you easily translate the problem into equations and inequalities.2.We’re told that Roberto wanted to sell \(57\) insurance policies but he didn’t meet his goal, which means that he sold less than \(57\) insurance policies. Next, we’re told that the value of all the policies sold was more than \(\$3,000,000\).A larger standard deviation means that the points in the data set are more spread out from the mean value, and a smaller one means that the points in the data set are close to the mean value. The discriminant is the part of the quadratic formula under the radical, or \(b^2-4ac\).Likewise, you’ll need to know what is meant by range. Let’s first determine the standard deviations of each data set relative to each other. If the discriminant is positive, there are 2 solutions; if the discriminant is 0, there is 1 real solution (or a repeated solution); if the discriminant is negative, there are no real solutions.In the first data set, most of the data points are clustered around each other, which makes it likely that the mean is somewhere around \(72\) (even though there are two outliers, they are equidistant from \(72\) so they will balance each other out when determining the mean). We can subtract the highest and lowest values for each set to find the range. Substituting the numbers from the equation into the discriminant formula gives us \(29^2-4(4)(49)=841-784=57\).In contrast, the second data set is more spread out, so we can conclude that the standard deviation of the first set is smaller than the standard deviation of the second. This is a positive number, which means there are 2 solutions to the system of equations.1.

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