How do we draw graphs in those kinds of questions?
1 answer:
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The graph of is a horizontal line. So the area under
on [0, 8] is equal to the area of a rectangle with length 8 and height 2, or 16.
The graph of is the upper half of a circle with radius
. It's symmetric about
, so on the interval [0, 8], we're considering a quarter of the circle. The area of such a sector is
.
Then use the fact that the definite integral is distributive over sums, meaning
Answer:
(- 3, 37) and (- ,
)
Step-by-step explanation:
Given the 2 equations
2x² - y + 19 = 0 → (1)
y + 11x = 4 → (2) ← subtract 11x from both sides
y = 4 - 11x → (3)
Substitute y = 4 - 11x into (1)
2x² - (4 - 11x) + 19 = 0
2x² - 4 + 11x + 19 = 0
2x² + 11x + 15 = 0 ← in standard form
(2x + 5)(x + 3) = 0 ← in factored form
Equate each factor to zero and solve for x
2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = -
x + 3 = 0 ⇒ x = - 3
Substitute these values into (3) for corresponding values of y
x = - : y = 4 +
=
⇒ (-
,
)
x = - 3 : y = 4 + 33 = 37 ⇒ (- 3, 37 )