The product of two consecutive even integers is 360. find the integers.

1 answer:

7 0

Let the integers be x and x + 2, provided x is even.

x(x + 2) = 360
x² + 2x = 360
x² + 2x - 360 = 0
(x - 18)(x + 20) = 0

x = 18, or x = -20
Thus, the integers are: 18 and 20, or -20 and -18

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The tallest tree in the world is reputed to be a giant redwood named Hyperion located in Redwood National Park in California, US

dlinn [17]

Answer:

114.02 meters

Step-by-step explanation:

The information you're given about the tree will form a triangle, with the three corners being the top of the tree, the point where the tree meets the ground, and the specified point 41.5 meters from the tree. The angle of elevation (70°) is the angle made where the line representing the ground and the line connecting the top of the tree to the ground at the specified point connect.

The angle where the tree meets the ground is 90°, so the triangle a right triangle.

So this all means you know one angle of a right triangle (70°) and the side adjacent to this angle (41.5 meters). You're solving for the height of the tree, which is the side opposite of the angle you know. You can solve using either Sine, Cosine, or Tangent.

Use the acronym SOHCAHTOA to figure out which of those three functions to use. Feel free to look this up for more information if you haven't heard of it before. In this case, we're using Tangent (TOA = Tangent, Opposite side, Adjacent side)

To solve using any of those three functions, you'll need a scientific calculator. On your calculator, you'll see the buttons SIN, COS, andTAN. For this problem, press TAN and you'll see something appear that says tan (___). You'll need to input a number to get your answer, and here's how to find that number:

Again referencing SOHCAHTOA, the "TOA" part lists Opposite first and then Adjacent. This is because you're going to write a fraction with those two numbers, and since Opposite is first, it's the numerator. That means that Adjacent is the denominator. We don't know the value of the opposite side, so it'll be represented by x, and we do know the value of the adjacent side, 41.5. This means the fraction is $\frac{x}{41.5}$ .