# Hard Math Problem We multiply by the common ratio to change any one term into its successor.

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This is a useful trick for problems like this on the ACT.

What’s important is that you visualize what an ellipse like this looks like: If we put a circle inside this shape, it can only have a diameter that is as wide as the ellipse is wide, otherwise it wouldn’t fit. Back to the ellipse equation: , or 9, in our answer choice for the radius of the circle, making our answer C. ANSWER: A Probably the most elegant way to solve this problem is to remember the Factor Theorem.

The bus then stopped for lunch in a suburb before continuing on a 3 hour tour of countryside at a constant speed of 10mph. The ACT will never expect you to do that, so there must be a better way. As soon as we get to √4, we have something that can be simplified to an integer. Something like √5 gets really messy because there are not two equal fractions that can be multiplied together to equal 5.

Students at Thomas Jefferson High School boarded the bus for a field trip that went 15mph through a 30 mile section of the city. Since we know one of the other angles of the triangle is 90°, we can find the measure of the remaining angle, angle B, by subtracting the two known angles from 180° (since the angles in a triangle always add up to 180°). And for some bonus fun (particularly if you got tripped up on finding the area of the sector), check out this cool animated video we made on this topic! Rational numbers can be expressed as a fraction; irrational numbers cannot. Do you really have to go through every number from 1 to 50? The perfect squares are the only square roots that are rational numbers.

What would s have to be so that is divisible by (x 2)? If it is taller than it is wide, it looks like the second one.

## Writing An Essay Steps - Hard Math Problem

So let’s get started with the equation for an ellipse: = 1 = 1 If an ellipse is wider than it is tall, our equation looks like the first one. In other words, x = -2 must be a root of the equation. If we want polynomial P(x) to be divisible by (x 2), it must be true that P(– 2) = 0. The radius is the key to unlocking other important circle things, such as the area, circumference, sector area, or arc length. Here’s another important tip: Whenever you are dealing with circles, and you aren’t given the radius, your first step should be to the radius. To master these problems, you’ll need to refresh your understanding of the concepts, then put them into practice. Check out the twelve ACT math challenge problems we’ve put together for you below. Point D is the midpoint of AC, which is 22 cm long. a=5 r=√5 Because every term is positive, we don’t have to consider the negative square root. 40 miles 30 miles so the Total Distance was 70 miles. The average speed in this problem is 14 mph, which is different from simply taking the mean of the two speeds. This option is in QII and QIII, so the part in QIII might go down low enough to contain the angle. Technically, this ray isn’t even included, because it’s the endpoint of an inequality, but we will just use this value. As shown in the figure below, A is the center of the circle, and right triangle ABC intersects the circle at D and E. Here, we don’t know the common ratio, so let it be r. ANSWER: D Average Speed = Total Distance / Total Time. Notice how the test-maker has made this problem tricky!If you want to refer to sections of Survey of integrating methods while working the exercises, you can click here and it will appear in a separate full-size window. If you’re wondering why hard ACT Math problems are so difficult, know that it’s not because they test crazy advanced topics like multivariable calculus or anything like that. For the first part of the field trip: 30 miles = 15mph x T, so we know that T = 2 hours. First of all, notice that the angle must be in QIII or QIV, since the sine is negative. The first three choices are all in QI and QII, so the angle can’t possibly be in any of those. As we rise from this bottom, we get negative values of smaller and smaller absolute value, until it equals zero at the positive x-axis. Because every circle has 360 degrees: = Solving this proportion to find angle A gives us x = 32.727272 repeating, or approximately 33°. First of all, we need to remember what rational and irrational numbers are. If sin = – , which of the following could be true about ? Which of the following best describes the graph of y = p(x) in the standard (x,y) coordinate plane? Because a sector is a fraction of a circle, we can use the proportion of the area of the sector to the area of entire circle to find the degree measure of the central angle.

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