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2 years ago

Simplify the expression (sqrt3+i)(sqrt3-i) and write the result in the form a+bi

Mathematics

1 answer:

rjkz [21]2 years ago

7 0

Answer:

Step-by-step explanation:

This expression is a difference of squares.

(√3 + i)(√3 - i) = (√3)²-(i)², which is

3 - (-1)

= 3 + 1

= 4

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Factor by grouping 20p³+15p²+24p+18

ivolga24 [154]

(4p +3)(5p2 + 6) is your answer

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3 years ago

Jose's Bikes rents bikes for $14 plus $3 per hour. Heather paid $38 to rent a bike. For how many hours did she rent the bike?

Nady [450]

Answer:

8 hours

Step-by-step explanation:

14 + 3x =38

-14 -14

--------------------

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2 years ago

What is the next term of the geometric sequence?<br>375,75,15

Damm [24]

Answer:

Step-by-step explanation:

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2 years ago

Read 2 more answers

F(x) = 2x^2 - 3x, calculate f(x+h)-f(x) / h

kvasek [131]

First plug in (x+h) for x in the function.
f(x+h)= 2(x-h)^2-3(x-h) = 2(x^2-2xh+h^2)-3x-3h =
2x^2-4xh+2h^2-3x-3h - 2x^2 +3x =
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6 0

3 years ago

Element X decays radioactively with a half-life of eight minutes. If there are 800 g of element X, how long, to the nearest 10th

Harman [31]

Answer: 41.5 min

Step-by-step explanation:

This problem can be solved with the Radioactive Half Life Formula:

$A=A_{o}.2^{\frac{-t}{h}}$ (1)

Where:

$A=22 g$ is the final amount of the radioactive element

$A_{o}=800 g$ is the initial amount of the radioactive element

$t$ is the time elapsed

$h=8 min$ is the half life of the radioactive element

So, we need to substitute the given values and find $t$ from (1):

$22 g=(800 g) 2^{\frac{-t}{8 min}}$ (2)

$\frac{22 g}{800 g}=2^{\frac{-t}{8 min}}$ (3)

$\frac{11}{400}=2^{\frac{-t}{8 min}}$ (4)

Applying natural logarithm in both sides:

$ln(\frac{11}{400})=ln(2^{\frac{-t}{8 min}})$ (5)

$-3.593=-\frac{t}{8 min}ln(2)$ (6)

Clearing $t$ :

$t=41.46 min \approx 41.5 min$ This is the time elapsed

7 0

2 years ago