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2 years ago

How can you find the magnitude of a vector v→=

Mathematics

1 answer:

dalvyx [7]2 years ago

4 0

Answer:

The magnitude of a vector is its length.

To calculate the magnitude of a vector in any number of dimensions, square root the sum of the squares of each dimension.

Therefore, if $\vec v=(x,y)$ then its magnitude is:

$|v|=\sqrt{x^2+y^2}$

Similarly, if $\vec v=(x,y,z)$ then its magnitude is:

$|v|=\sqrt{x^2+y^2+z^2}$

You might be interested in

A certain region currently has wind farms capable of generating a total of 2200 megawatts (2.2 gigawatts) of power. Assuming win

sveta [45]

Answer:

The correct answer is A. 4,818'000,000 kilowatt-hours per year and B. 481,800 households.

Step-by-step explanation:

1. Let's review the information provided to us for solving the questions:

Power capacity of the wind farms = 2,200 Megawatts or 2.2 Gigawatts

2. Let's resolve the questions A and B:

Part A

Assuming wind farms typically generate 25% of their capacity, how much energy, in kilowatt-hours, can the region's wind farms generate in one year?

2,200 * 0.25 = 550 Megawatts

550 Megawatts = 550 * 1,000 Kilowatts = 550,000 Kilowatts

Now we calculate the amount of Kilowatts per hour, per day and per year:

550,000 Kw generated by the farms means that are capable of produce 550,000 kw per hour of energy

550,000 * 24 = 13'200,000 kilowatt-hours per day

13'200,000 * 365 = 4,818'000,000 kilowatt-hours per year

Part B

Given that the average household in the region uses about 10,000 kilowatt-hours of energy each year, how many households can be powered by these wind farms?

For calculating the amount of households we divide the total amount of energy the wind farms can generate (4,818'000,000 kilowatt-hours) and we divide it by the average household consumption (10,000 kilowatt-hours)

Amount of households = 4,818'000,000/10,000 = 481,800

8 0

3 years ago

Find the slope of the tangent line to the curve f(x)=e^(x) at (0.4,1.49)

almond37 [142]

Answer:

1.49

Step-by-step explanation:

In order to find the slope of the tangent line to a given equation, and in a given point, we need to:

1. Find the first derivative of the given function.

2. Evaluate the first derivative function in the given point.

1. Let's find the first derivative of the given function:

The original function is $f(x)=e^{x}$

But remeber that the derivative of $e^{x}$ is $e^{x}$

so, $f'(x)=e^{x}$

2. Let's evaluate the first derivative function in the given point

The given point is (0.4,1.49) so:

$f'(x)=e^{x}$

$f'(0.4)=e^{0.4}$

$f'(x)=1.49$

Notice that the calculated slope of the tangent line is equal to the y-coordinate of the given point because f'(x)=f(x). In conclusion, the slope of the tangent line is equal to 1.49.

8 0

3 years ago

Suppose the function y = 30,000(1.06)x models the annual profit for a small business x years after 2000. Find the profit at the

goldfiish [28.3K]

From 2000 to 2011, there are 11 years. From the given function, we can calculate the profit for a small business at the end of 2011 by substituting 11 to the x of the given equation.
y = (30,000)(1.06)(11)
y = 349,800
Thus, the profit at the end of 2011 is approximately $349,800.

4 0

3 years ago

harriet is cultivating a strain of bacteria has doubled by the end of every second hour. how many bacteria will harriet have in

Black_prince [1.1K]

Answer:

n2^3 bacteria, n being the initial population.

Step-by-step explanation:

compound growth equation: P=n2^t

P is total population

n is initial population

t is time

since it doubles every second hour, and there are 6 hours

6hours/2hours= doubles 3 times, thats why t=3.

7 0

3 years ago

The sum of two numbers is equal to 63, and their difference is equal to 12. Find the numbers

Ainat [17]

Answer:

25.5 and 37.5

Step-by-step explanation:

x+y=63

x-y = 12 then x = 12 + y sub this into the first equation

(12+y) + y = 63

12 + 2y = 63

2y = 51

y = 25.5 then x = 37.5

6 0

2 years ago