Answer:
see below
Step-by-step explanation:
x⁵ - 8x⁴ + 22x³ - 26x² + 21x - 18 = 0
x = 2, x = ± i, x=3 with multiplicity 2
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x⁴ - 5x³ + 7x² - 5x + 6 = 0
x = 2, x=3, x = ± i
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<u>-1 + 4i</u> = 4 + i
i
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x³ - 26x² + 21x - 18 = 0
x = ± 2i, x = 3/2
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(1 + i) (-3 - 4i)
= 1 - 7i
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6.
(-5 + 2i) + (3 - 6i)
= -2 -4i
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7.
x⁴ + 5x² + 4 = 0
x = ± i , x = ± 2i
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8.
(7 - i) - (-5 + 6i)
= 12 - 7i
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9.
(4 - i) (4 + i)
= 17
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10.
(3 + 8i) (4 - 3i)
= 36 + 23i
Answer:
AB = 75
BC = 60
AC = 45
m∠A = 53°
m∠B = 37°
m∠C = 90°
Step-by-step explanation:
<u>Trigonometric ratios</u>
where:
is the angle- O is the side opposite the angle
- A is the side adjacent the angle
- H is the hypotenuse (the side opposite the right angle)
Given:
Therefore:
- side opposite angle A = BC = 60
- side adjacent angle A = AC = 45
To find the length of AB (the hypotenuse), use Pythagoras’ Theorem:
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
⇒ AC² + BC² = AB²
⇒ 45² + 60² = AB²
⇒ AB² = 5625
⇒ AB = √5625
⇒ AB = 75
To find m∠A:
m∠C = 90° (as it is a right angle)
The interior angles of a triangle sum to 180°
⇒ m∠A + m∠B + m∠C = 180°
⇒ 53° + m∠B + 90° = 180°
⇒ m∠B = 180° - 53° - 90°
⇒ m∠B = 37°
No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true. :)
Answer:
Step-by-step explanation:
Let length be x and breadth be y .
Along the river no fencing is required so total boundary line of the rectangular land = x + y + y = x + 2y
add divider to it so total length
= x + 2y + y = x + 3y
x + 3y = 2400
area A = xy
y ( 2400 - 3y ) = A
2400y - 3y² = A
For maximum area dA / dy = 0
2400 - 6y = 0
y = 400 yards.
x = 1200 yards
largest area = xy
= 48000 sq yards.
Divide the numerical coefficients and write the quotation in simplest form
