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bija089 [108]
3 years ago
13

√45 is the distance between which of the following complex numbers?

Mathematics
1 answer:
Schach [20]3 years ago
3 0

Step-by-step explanation:

we don't see the complex numbers.

so, we cannot check their distances.

a suspicion, though.

sqrt(45) a distance between 2 complex numbers is

sqrt(a² + b²).

so,

a² + b² = 45

a nice combination of whole square numbers would be 6 and 3.

6² + 3² = 36 + 9 = 45

if that is the case, then that would mean one of the following committed numbers

6 + 3i

3 + 6i

-6 + 3i

6 - 3i

-6 - 3i

-3 + 6i

3 - 6i

-3 - 6i

one of these numbers must be the result of the subtraction of the 2 provided complex numbers.

remember

(a + bi) - (c + di) = a-c + (b-d)i

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Runners race around a rectangular park during the city marathon. The length of the park is 6 miles. The width of the park is 7 m
Otrada [13]
Hi there! The answer is A. miles

We can find the miles someone would run during the marathon, by using the formula for the perimeter. This is:
2 × width + 2 x length.

Filling in this formula learns us that the distance that is run is measured in miles. The answer is A.
8 0
3 years ago
A carpenter has a piece of wood that is 78 inches long. He wants to cut it so that one piece is five times as long as the other
Lyrx [107]

Answer:

13 and 65

Step-by-step explanation:

x + 5x = 78

(because u want a piece (x) and a piece that's five times longer than x- so 5x. and they should come from a 78 inch piece)

6x = 78

x = 78 / 6

x= 13

(to counter check:  13 * 5 = 65.  

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7 0
3 years ago
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At the beginning of the week, a puppy weighed 5 1/4 pounds. During the week, the puppy gains 8 ounces.
lys-0071 [83]

Answer:

5 3/4

Step-by-step explanation:

8 ounces is half (1/2) of a pound

1/2 is equivalent to 2/4

So I added 5 1/4 and 2/4

Which gives us 5 3/4

5 0
3 years ago
Researchers recorded that a certain bacteria population declined from 800,000 to 500,000 in 6 hours after the administration of
kupik [55]

Answer:

We can assume that the decline in the population is an exponential decay.

An exponential decay can be written as:

P(t) = A*b^t

Where A is the initial population, b is the base and t is the variable, in this case, number of hours.

We know that: A = 800,000.

P(t) = 800,000*b^t

And we know that after 6 hours, the popuation was 500,000:

p(6h) = 500,000 = 800,000*b^6

then we have that:

b^6 = 500,000/800,000 = 5/8

b = (5/8)^(1/6) = 0.925

Then our equation is:

P(t) = 800,000*0.925^t

Now, the population after 24 hours will be:

P(24) = 800,000*0.925^24 = 123,166

5 0
3 years ago
A cone and a triangular pyramid have a height of 9.3 m
Otrada [13]

Answer:

x=17.1\ in

Step-by-step explanation:

<u><em>The complete question is</em></u>

A cone and a triangular pyramid have a height of 9.3 m  and their cross-sectional areas are equal at every level  parallel to their respective bases. The radius of the base of the cone is 3 in and the other leg (not x) of the triangle base of the triangular pyramid is 3.3 in

What is the height, x, of the triangle base of the  pyramid? Round to the nearest tenth

The picture of the question in the attached figure

we know that

If their cross-sectional areas are equal at every level  parallel to their respective bases and the height is the same, then their volumes are equal

Equate the volume of the cone and the volume of the triangular pyramid

\frac{1}{3}\pi r^{2}H=\frac{1}{3}[\frac{1}{2}(b)(h)H]

simplify

\pi r^{2}=\frac{1}{2}(b)(h)

we have

r=3\ in\\b=3.3\ in\\h=x\ in\\pi=3.14

substitute the given values

(3.14)(3)^{2}=\frac{1}{2}(3.3)(x)

solve for x

28.26=\frac{1}{2}(3.3)(x)

x=28.26(2)/3.3\\x=17.1\ in

7 0
3 years ago
Read 2 more answers
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