MATHEMATICS COLLEGE

Find the real value of x,y if

(1/(x^2+y^2))+(1/(x+yi))=1

Answers

Answer 1

Answer:

It sounds like $x,y$ are supposed to be real numbers. If so, then we can do the following.

$\frac1{x^2+y^2}+\frac1{x+yi}=1$

Multiply the second term's numerator and denominator by the conjugate of the denominator:

$\frac1{x^2+y^2}+(x-yi)/((x+yi)(x-yi))=1$

$\frac1{x^2+y^2}+(x-yi)/(x^2+y^2)=1$

$(x+1-yi)/(x^2+y^2)=1$

Since the left hand side is equal to 1, this means it has no imaginary part, so that $y=0$ . Then the real parts of both sides of the equation give us

$(x+1)/(x^2)=1\implies x+1=x^2\implies x^2-x-1=0\implies x=\frac{1\pm\sqrt5}2$

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A high school soccer goalie blocked the ball from going into the goal 4 out of 5 times if the ball was kicked toward the goal 40 times how many blocks did the goalie make

Answers

Answer:

32 times

Step-by-step explanation:

4/5:x/40 ----x=32

Find the perimeter and area of the regular polygon. Round answers to the nearest tenth.

Answers

Answer: perimeter = 26.5

Area = 106

Step-by-step explanation:

The given polygon is an octagon. The apotherm which is the perpendicular line from the midpoint of the octagon is 8,

The formula for determining the area of a polygon is expressed as

Area = a² × n × tan 180/n

Where n represents the number of sides of the polygon.

n = 8

Therefore,

Area = 8² × 4 × tan(180/8)

Area = 256 × tan 22.5

Area = 106

The formula for determining the perimeter of a regular polygon is

P = 2 × area/apotherm

Perimeter = 2 × 106/8

Perimeter = 26.5

Given that r = ( 7, 3, 9) and v = ( 3, 7, -9), evaluate r + va. (-21,-21,81)
b. (10,10,0)
c. (21,21,-81)
d. (-10,-10,0)

Answers

Answer:

b. (10,10,0)

Step-by-step explanation:

r+v can be evaluated if the vectors/matrices have the same dimensions.

These do. They are both 1 by 3 vectors.

Just add first to first in each.

Just add second to second in each.

Just add third to third in each.

Example:

(5,-5,6)+(1,2,3)

=(5+1,-5+2,6+3)

=(6,-3,9)

Done!

In general, (a,b,c)+(r,s,t)=(a+r,b+s,c+t).

r+v

=(7,3,9)+(3,7,-9)

=(7+3,3+7,9+-9)

=(10,10,0)

Done!

Tyson and Ariana each invested $2,500 in separate accounts. Tyson’s interest rate is 5.75% and is compounded annually. Ariana’s simple interest rate is 5.75%. Neither will make any additional deposits or withdrawals. At the end of 6 years, how much more has Tyson earned? Round your answer to the nearest cent.

Answers

Answer:

Tyson's account will have $ 133.90 more than Ariana's account.

Step-by-step explanation:

In Tyson's case, he invests $ 2,500 in an account whose interest rate is 5.75% and is compounded annually. In turn, Ariana invests the same amount and for the same interest, but this is not compounded.

Thus, Ariana, at the end of her 6 years, will have a total amount in her account of $ 3,362.5 (((2,500 x 5.75 / 100) x 6) + 2,500), of which $ 862.5 will correspond to the interest generated.

Instead, Tyson's investment interests will be consolidated annually. Thus, in 6 years, this investment will evolve as follows:

-Year 1 --- 2,500 x 1.0575 = 2,643.75

-Year 2 --- 2,643.75 x 1.0575 = 2,795.76

-Year 3 --- 2,795.76 x 1.0575 = 2,956.52

-Year 4 --- 2,956.52 x 1.0575 = 3,126.52

-Year 5 --- 3,126.52 x 1.0575 = 3,306.29

-Year 6 --- 3,306.29 x 1.0575 = 3,496.40

Thus, at the end of the 6 years, Tyson will have $ 3,496.40 in his account. Thus, Tyson's account will have $ 133.90 more than Ariana's account.

George Mendel is examining peas to try to understand how traits are passed from parents to offspring. Today Gregor has 228 peas to examine . The pods have 6 peas per pod. How many pods of peas are there?

Answers

The answer is 38 peas per pod

228÷6 = 38

Glad to help you :)

Final answer:

By dividing the total number of peas (228) by the number of peas per pod (6), we find that Gregor Mendel has 38 pods of peas.

Explanation:

This question is asking how many pods of peas Gregor Mendel has if he has a total of 228 peas and each pod contains 6 peas. To find out this, you can divide the total number of peas by the number of peas per pod.

So, 228 peas ÷ 6 peas/pod = 38 pods.

Therefore, Gregor Mendel has 38 pods of peas that he is examining for his research.

Learn more about Division here:

brainly.com/question/33969335

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A small regional carrier accepted reservations for a particular flight with 17 seats. 14 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 52% chance.A. Find the probability that overbooking occurs. B. Find the probability that the flight has empty seats.