Given the graph of the system of equations f(x) = x +2 and g(x) = 3x - 2, determine the solution

Mathematics

1 answer:

umka21 [38]3 years ago

3 0

Answer:

Step-by-step explanation:

If you were given graphs of the equations, then the solution is the (x,y) where the lines intersect.

The lines intersect at (2,4).

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Paladinen [302]

The solid shape is a cone and a half sphere. So the equation would be (cone volume) + (1/2 sphere volume):
$cone = \frac{1}{3} \pi {r}^{2} h \\ sphere = \frac{4}{3} \pi {r}^{3} \\ object = ( \frac{1}{3} \pi {r}^{2} h) + \frac{1}{2} ( \frac{4}{3} \pi {r}^{3} )$
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$270\pi = \frac{1}{3} \pi {r}^{2} (10) \\ 27 = \frac{1}{3} {r}^{2} \\ 80 = {r}^{2} \\ r = 9$
The radius of the object is 9 cm. Therefore, we can plug into the formula for the total volume:
$object = 270\pi + \frac{1}{2} ( \frac{4}{3} \pi {(9)}^{3} ) \\ = 270\pi + \frac{2}{3} (729\pi) \\ = 270\pi \: + 243\pi \\ = 513\pi$
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Without solving determine the character of the solutions of the equation x^2+2x+5=0

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★ QUADRATIC RESOLUTION ★

Roots of the given equation will be imaginary because it's discriminant is less than 0 and hence it'll yield imaginary solutions

D < 0

b² - 4ac < 0

4² - 4 ( 5 ) < 0

16 - 20 < 0

-4 < 0

Hence it's character is stated above

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Given the graph of the system of equations f(x) = x +2 and g(x) = 3x - 2, determine the solution​

Given the graph of the system of equations f(x) = x +2 and g(x) = 3x - 2, determine the solution