Approximate the solution of the system to the nearest thousandth.

Mathematics

1 answer:

Sonja [21]3 years ago

4 0

Answer:

(-0.283, -0.733)

Step-by-step explanation:

There are various ways in which to approximate the solution. One is to use a graphing calculator and graph the two functions separately, then determine the point of intersection. The first function has a parabolic graph that opens down, whereas the second function has an exponential graph which heads downward as x increases.

At first try I found that the two graphs intersect in Quadrant III, at approximately (-1/2, -3/4).

Next I used my calculator's CALC tools, specifically that which finds the coordinates of the intersection of two graphs, ending up with these coordinates: (-0.283, -0.733). These coordinates are to the nearest thousandths.

If and when you take Calculus, you'll learn Newton's Method for Finding Roots, which doesn't require a graphing calculator.

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Given:
Equilateral Triangular Prism
Each side of the triangular face has a length of 196cm
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I have attached an image of the tent. Since the height of the tent is also the height of the triangle, I will solve for the height of the triangle using Pythagorean theorem.

I divided the equilateral triangle into 2 right triangle. The height then becomes the long leg of the triangle. The hypotenuse is 196cm and the short leg is 98cm, half of one side of the triangle.

a² + b² = c²
a² = c² - b²
a² = (196cm)² - (98cm)²
a² = 38,416cm² - 9,604cm²
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a = √28,812cm²
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The height of the tent is 169.74 centimeters.