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Akimi4 [234]
3 years ago
14

Solve i=Prt for t, if i=105, P=700, and r=0.05

Mathematics
1 answer:
hram777 [196]3 years ago
3 0
If you are supposed to round up then your answer should be 2.91 because 700x0.05= 35. 35x2.91=101.85 which rounded up is then 102.
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Prove that if $w,z$ are complex numbers such that $|w|=|z|=1$ and $wz\ne -1$, then $\frac{w+z}{1+wz}$ is a real number.
mr_godi [17]

Answer:

See proof below

Step-by-step explanation:

Let r=\frac{w+z}{1+wz}. If w=-z, then r=0 and r is real. Suppose that w≠-z, that is, r≠0.

Remember this useful identity: if x is a complex number then x\bar{x}=|x|^2 where \bar{x} is the conjugate of x.

Now, using the properties of the conjugate (the conjugate of the sum(product) of two numbers is the sum(product) of the conjugates):

\frac{r}{\bar{r}}=\frac{w+z}{1+wz} \left(\frac{1+\bar{w}\bar{z}}{\bar{w}+\bar{z}}{\right)

=\frac{(w+z)(1+\bar{w}\bar{z})}{(1+wz)(\bar{w}+\bar{z})}=\frac{w+z+w\bar{w}\bar{z}+z\bar{z}\bar{w}}{\bar{w}+\bar{z}+\bar{w}wz+\bar{z}zw}=\frac{w+z+w+|w|^2\bar{z}+|z|^2\bar{w}}{\bar{w}+\bar{z}+|w|^2z+|z|^2w}=\frac{w+z+\bar{z}+\bar{w}}{\bar{w}+\bar{z}+z+w}=1

Thus \frac{r}{\bar{r}}=1. From this, r=\bar{r}. A complex number is real if and only if it is equal to its conjugate, therefore r is real.

3 0
3 years ago
Six groups of students sell 162 balloons at the school carnival there are 3 students in each group if each student sells the sam
Kitty [74]
Each student sells 9 balloons because 162 balloons divided by 6 groups of students is 27, and 27 divided by 3 students is 9 balloons. 
5 0
3 years ago
Read 2 more answers
Is my answer correct
nikklg [1K]
I strongly believe your answer is correct
8 0
3 years ago
Which list is ordered from least to greatest?
olga55 [171]
It would be A. It is A because 5 is negative, 2.1 is negative, 0.3 and 3.1 are positive. Also 5 is greater than 2.1, so in this case -5 would be before -2.1.
4 0
3 years ago
i think of a number. if i divide the sum of 6 and the number by 3, the result is 4 more than one quarter of the number. find the
slega [8]

Answer:

-12

Step-by-step explanation:

Let the number be A

Given if you divide the sum of six and the number A by 3 , the result is 4 more than 1/4 of A

That’s

6+A/3 = 4+1/4 of A

6+A/3 = 4+1/4 x A

6+A/3 = 4+A/4

Cross multiply

4(6 + A) = 3(4 + A)

Distribute

4 x 6 + 4 x A = 3 x 4 + 3 x A

24 + 4A = 12 + 3A

Subtract 24 from both sides to eliminate 24 on the left side

24 - 24 + 4A = 12 - 24 + 3A

4A = -12 + 3A

Subtract 3A from both sides so the unknown can be on one side

4A - 3A = -12 + 3A - 3A

A = -12

Check

6+(-12)/3 = 4 +(-12)/4

6 -12/3 = 4 -12/4

-6/3 = -8/4

-2 = -2

6 0
3 years ago
Read 2 more answers
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