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3 years ago

What is the length of a segment in the complex plane with endpoints at 4 + 2i and 7 – 2i?

Mathematics

2 answers:

ira [324]3 years ago

6 0

Answer:

Step-by-step explanation:

The complex number 4 + 2i on the complex plane has coordinates (4,2) and the complex number 7 - 2i has coordinates (7,-2). Thus, the length of a segment in the complex plane with endpoints at 4 + 2i and 7 – 2i is

$\sqrt{(4-7)^2+(2-(-2))^2}=\sqrt{(-3)^2+4^2}=\sqrt{9+16}=\sqrt{25}=5.$

8_murik_8 [283]3 years ago

3 0

Answer:

Step-by-step explanation:

From question statement , we observe that

Two end points of a line segment are given we have to calculate the length of the line segment.

On complex plane,we represent 4+2i as coordinate (4,2) and 7-2i as coordinate (7,-2).

We use distance formula to calculate the length of a line segment.

length = √(x₂-x₁)²+(y₂-y₁)²

Putting given values in above formula , we get

length = √(7-4)²+(-2-2)² = √(3)²+(-4)²

length = √9+16 = √25 = 5

Hence, the length of a segment with end points at 4+2i and 7-2i is 5.

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Use the number line below to find a fraction that is equivalent to 1/2

Yuliya22 [10]

Answer:

4/8

Step-by-step explanation:

There are an infinite number of fractions equal to 1/2, but the number line in the question has 8 spaces, and shows 1 divided into 8 pieces. Therefore, the answer to this question is likely 4/8.

(may I ask why exactly this is put as a college level problem?)

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2 years ago

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A quantity with an initial value of 6200 decays continuously at a rate of 5.5% per month. What is the value of the quantity afte

ELEN [110]

Answer:

410.32

Step-by-step explanation:

Given that the initial quantity, Q= 6200

Decay rate, r = 5.5% per month

So, the value of quantity after 1 month, $q_1 = Q- r \times Q$

$q_1 = Q(1-r)\cdots(i)$

The value of quantity after 2 months, $q_2 = q_1- r \times q_1$

$q_2 = q_1(1-r)$

From equation (i)

$q_2=Q(1-r)(1-r) \\\\q_2=Q(1-r)^2\cdots(ii)$

The value of quantity after 3 months, $q_3 = q_2- r \times q_2$

$q_3 = q_2(1-r)$

From equation (ii)

$q_3=Q(1-r)^2(1-r)$

$q_3=Q(1-r)^3$

Similarly, the value of quantity after n months,

$q_n= Q(1- r)^n$

As 4 years = 48 months, so puttion n=48 to get the value of quantity after 4 years, we have,

$q_{48}=Q(1-r)^{48}$

Putting Q=6200 and r=5.5%=0.055, we have

$q_{48}=6200(1-0.055)^{48} \\\\q_{48}=410.32$

Hence, the value of quantity after 4 years is 410.32.

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2 years ago

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Patrick’s luck had changed over night – but not his skill at mathematical reasoning. The day after graduating from college he us

Verdich [7]

Answer:

I assume Josh and Peyton are his friends and both gave him advice on what to do with half of the money from the big lottery win.

Let's say Josh said "save it or invest it for your retirement" and Peyton said "use it to keep playing the lottery.

We will now look at the sense in each piece of advice!

Step-by-step explanation:

JOSH

By investing the $250,000 (half of the money won), Patrick will be sure that the money is available for him anytime and would even have gotten interest, by the time he's ready to use it.

PEYTON

By playing the lottery continuously, Patrick could get lucky once in a while and win big again. How big though?

Analyzing with the figures given,

$20 gets Patrick a lottery ticket.

$250,000 will get him 12,500 lottery tickets!

Whether he's buying the tickets at once or he'll play the lottery once in a while, I'll say he has good chances of winning big again.

So if the probability of winning big after purchasing up to 12,500 tickets is close to 1, Patrick should play the lottery with the $250,000

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3 years ago

A building 84 ft high casts a 46 ft shadow. How tall is a building that casts a 110 ft shadow at the same time of the day? (to t

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The ratio of building heights will be the same as the ratio of shadow lengths.
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The appropriate selection is
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2 years ago

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Dally has a discount card that reduces the price of her grocery bill in a certain grocery store by 5%. If c represents the cost

creativ13 [48]

C is the cost of groceries.

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= (95/100) * c

= 0.95c

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