Tutor profile: Aiden H.
An inquisitive math student is standing 25 feet from the base of the Washington Monument. The angle of elevation from her horizontal line of sight is 87.4∘. If her “eye height” is 5ft, how tall is the monument?
We can find the height of the monument by using the tangent ratio and then adding the eye height of the student. tan87.4∘h=h25=25⋅tan87.4∘=550.54 Adding 5 ft, the total height of the Washington Monument is 555.54 ft. According to Wikipedia, the actual height of the monument is 555.427 ft.
A cube has a surface area of fifty-four square centimeters. What is the volume of the cube?
The formula for the volume V of a cube with edge-length e is: V = e3 To find the volume, I need the edge-length. Can I use the surface-area information to get what I need? Let's see... A cube has six sides, each of which is a square; and the edges of the cube's faces are the sides of those squares. The formula for the area of a square with side-length e is A = e2. There are six faces so there are six squares, and the cube's total surface area SA must be: SA = 6e2 Plugging in the value they gave me, I get: 54 = 6e2 54 / 6 = (6e2) / 6 9 = e2 3 = e Since the volume is the cube of the edge-length, and since the units on this cube are centimeters, then: the volume is 27 cubic centimeters, or 27 cc, or 27 mL
One number is 10 more than another. The sum of twice the smaller plus three times the larger, is 55. What are the two numbers?
Let x be the smaller number. Then the larger number is 10 more: x + 10. The problem states: 2x + 3(x + 10) = 55. That implies 2x + 3x + 30 = 55. 5x = 55 − 30 = 25. x = 5. That's the smaller number. The larger number is 10 more: 15.
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