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4 years ago

What is the product of 6+5i and 4+7i?

Mathematics

2 answers:

kirill [66]4 years ago

4 0

The answer to this question is the product is 12i

3241004551 [841]4 years ago

3 0

Answer: The required product is $-11+62i.$

Step-by-step explanation: We are given to find the product of the following two complex numbers :

$z_1=6+5i,~~~z_2=4+7i.$

We will be using the following property :

$(a+b)(c+d)=a(c+d)+b(c+d).$

Also, we will use the fact that $i=\sqrt{-1},~~i^2=-1.$

The product of the given complex numbers is

$z_1z_2\\\\=(6+5i)(4+7i)\\\\=6(4+7i)+5i(4+7i)\\\\=24+42i+20i+35i^2\\\\=24+62i-35\\\\=-11+62i.$

Thus, the required product is $-11+62i.$

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A spherical snowball is melting. The radius after t hours is 1-t meters. [Volume of a sphere of radius R is 4R3π/3] (a) What fra

MrMuchimi

Answer:

$0,52m^{3}$

Step-by-step explanation:

r=(1-tm) $Vs=\frac{4\pi r^{3} }{3} =\frac{4\pi (1-t)^{3}}{3}=4,18(0,5)^{3} = 0,52m^{3}$

7 0

4 years ago

The cost for a ticket at the movie theater is $13. Students get a 9% discount taken off the price of a ticket. How much does the

inn [45]

So 9% of 13 is 1.17
so then you go $13 - $1.17 and your answer is $11.83

5 0

3 years ago

15, 11, 7, 3, -1, ... explicit formula and recursive formula

monitta

Recursive formula is: $a_n = a_{n-1} -4$

Explicit formula is: $a_n = 19-4n$

Step-by-step explanation:

Given sequence is:

15,11,7,3,-1

Here

$a_1 = 15\\a_2 = 11\\a_3 = 7$

First of all, we have to find the common difference

Common difference is the difference between consecutive terms of an arithmetic sequence

So,

$d = a_2-a_1 = 11-15 = -4\\d = a_3-a_2 = 7-11 = -4$

<u>Recursive Formula:</u>

A recursive formula is used to find the next term of an arithmetic sequence using previous term and common difference

General form of recursive formula for a given common difference d is:

$a_n = a_{n-1} + d$

Putting the value of d

$a_n = a_{n-1} -4$

<u>Explicit Formula:</u>

The explicit formula is given by:

$a_n = a_1 + (n-1)d$

Putting the first term and common difference

$a_n = 15 + (n-1)(-4)\\a_n = 15 -4n+4\\a_n = 19-4n$

Hence,

Recursive formula is: $a_n = a_{n-1} -4$

Explicit formula is: $a_n = 19-4n$

Keywords: Arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

4 0

4 years ago

Write -0.65 as a fraction.

dolphi86 [110]

Answer:

-13/20

Step-by-step explanation:

-0.65 = -65/100

gcd(65,100) = 5

-0.65 = -(65/5)/(100/5) = -13/20

6 0

3 years ago

If $450 is invested at 6% compounded A (annually), B (quarterly), C (monthly), what is the amount after 7 years? How much intere

ss7ja [257]

Answer:

Step-by-step explanation:

Here's the gameplan for this. First of all we need a general formula, then we will define the variables for each.

The general formula for all of these is the same:

$A(t)=P(1+\frac{r}{n})^{nt}$

where A(t) is the amount after the compounding, P is the initial investment, n is the number of compoundings per year, r is the interest rate in decimal form, and t is time in years.

Then after we find the amount after the compounding, we will subtract the initial amount from that, because the amount at the end of the compounding is greater than the initial amount. It's greater because it represents the initial amount PLUS the interest earned. The difference between the initial amount and the amount at the end is the interest earned.

For A:

A(t) = ?

P = 450

n = 1

r = .06

t = 7

$A(t)=450(1+\frac{.06}{1})^{(1)(7)}$

Simplifying gives us

$A(t)=450(1.06)^7$

Raise 1.06 to the 7th power and then multiply in the 450 to get that

A(t) = 676.63 and

I = 676.63 - 450

I = 226.63

For B:

A(t) = ?

P = 450

n = 4 (there are 4 quarters in a year)

r = .06

t = 7

$A(t)=450(1+\frac{.06}{4})^{(4)(7)}$

Simplifying inside the parenthesis and multiplying the exponents together gives us

$A(t)=450(1.015)^{28}$

Raising 1.015 to the 28th power and then multiplying in the 450 gives us that

A(t) = 682.45

I = 682.45 - 450

I = 232.75

For C:

A(t) = ?

P = 450

n = 12 (there are 12 months in a year)

r = .06

t = 7

$A(t)=450(1+\frac{.06}{12})^{(12)(7)}$

Simplifying the parenthesis and the exponents:

$A(t)=450(1+.005)^{84}$

Adding inside the parenthesis and raising to the 84th power and multiplying in 450 gives you that

A(t) = 684.17

I = 684.17 - 450

I = 234.17

4 0

3 years ago