1. (x^2+1)*(x^3+2*x)*(x^2-64)
=(x^2+1)*x*(x^2+2)*(x+8)(x-8)
Solving for each factor in turn, for example,
x^2+1=0 => x^2=-1 => x=+i, x=-i
x=0 => x=0
x^2+2=0 => x^2=2 => x=+sqrt(2)i, -sqrt(2)i
x+8=0 => x=-8
x-8=0 => x=+8
we have solution set
S, whereS={+i, -i, 0, +sqrt(2)i, -sqrt(2)i, -8, +8)
2. A.
x^4-81=0 => x^4=81 => x^2=+9 or x^2=-9
x^2=+9 => x=+3, -3
x^2=-9 => x=+3i, -3i
S={+3i, -3i, +3, -3}
B.
x^4+10x^2+25=0 => (x^2+5)^2=0 => ± (x^2+5)=0 => x^2=-5
=> x=+sqrt(5)i (multiplicity 2 and x=-sqrt(5)i (multiplicity 2)
S={+sqrt(5)i (multiplicity 2) -sqrt(5)i (multiplicity 2)}
C.
x^4-x^2-6=0 => (x^2-3)(x^2+2)=0 => x^2=3 or x^2=-2
S={+sqrt(2)i,-sqrt(2)i, +sqrt(3), -sqrt(3) }
3.
x^4+3x^2-4=0 = (x^2-1)(x^2+4) => x^2=1 or x^2=-4
S={+2i, -2i, +1, -1}
Answer:
-2i+8
Step-by-step explanation:
(1+i)(3-5i)
3+3i-5i-5i^2
3-2i-5(-1), because i^2=-1,
3-2i+5
-2i+3+5
-2i+8
The Hypotenuse is the Longest side of right triangle; side Opposite from the right angle.
According to the statement
we have given that the property of the hypotenuse of the triangle and we have to complete it.
So, For this purpose, we know that the
A hypotenuse is the longest side of a right-angled triangle, and The length of the hypotenuse can be found using the Pythagorean theorem.
Now we discuss about the properties of the hypotenuse;
- The hypotenuse is the longest side in a right angled triangle.
- The hypotenuse is opposite the right angle.
- The midpoint of the hypotenuse is the circumference.
And from these properties we have to complete the given property.
So, The Hypotenuse is the Longest side of right triangle; side Opposite from the right angle.
Learn more about hypotenuse here
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5ft 4in= 64 inches
3yd 5in= 113 inches
5yd 2ft= 204 inches/ 17 feet
9ft 6in= 114 inches
$9890 + $8250 + $680 = $18,820 for one year
Since she is going for four years, we need to multiply that number by four.
$18820 * 4 = $75,280
Total: $75,280