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3 years ago

Simplify i3 a. -I b. -1 c. I d. 1

Mathematics

2 answers:

Sholpan [36]3 years ago

6 0

i3 simplified is c. I

Fantom [35]3 years ago

5 0

Answer:

a. -i.

Step-by-step explanation:

i^2 = -1 so

i^3 = i^2 * i

= -1 * i

= -i.

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3 years ago

There are 16 students playing kickball. Two students leave to go play hopscotch. How do you write the fraction of children left

olga55 [171]

Answer:

7/8

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3 years ago

Factor: 9t^2-16u^2 ?

liq [111]

Answer:

Step-by-step explanation:

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3 years ago

Leah practices dance for 2 hours each week. Her younger sister Sonia practices dance for 0.8 the amount of time Leah practices.

galben [10]

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2 years ago

Read 2 more answers

A circle has centre (3,0) and radius 5. The line y = 2x + k intersects the circle in two points. Find the set

lara [203]

A circle with center $(3,0)$ and radius $5$ has equation

$(x-3)^2+y^2=25 \iff x^2 + y^2- 6 x = 16$

If we substitute $y=2x+k$ in this equation, we have

$x^2+(2x+k)^2-6x=16 \iff 5x^2+(4k-6)x+k^2-16=0$

This equation has two solutions (i.e. the line intersects the circle in two points) if and only if the determinant is greater than zero:

$\Delta=b^2-4ac=(4k-6)^2-4\cdot 5\cdot (k^2-16)>0$

The expression simplifies to

$-4 (k^2 + 12 k - 89)>0 \iff k^2 + 12 k - 89$

The solutions to the associated equation are

$k^2 + 12 k - 89=0 \iff k=-6\pm 5\sqrt{5}$

So, the parabola is negative between the two solutions:

$-6-5\sqrt{5}$

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3 years ago