Draw a vector representing the course of a ship that goes 75 miles on a
1 answer:
Answer:
The answer is below
Step-by-step explanation:
We have a vector with a magnitude of 75 miles and a direction of 300 °.
To draw it, the first thing is to make a Cartesian plane, the first thing is to know in which quadrant it would be, 300 ° is in the fourth quadrant (270 ° - 360 °), that is, it would be 30 ° (300 ° - 270 °) with respect to to the y axis negative.
Knowing this angle, we calculate the value of x and y, knowing that the magnitude of the vector is 75 miles, that is, this value would be the hypotenuse.
The value on the x-axis can be calculated using the sine of the angle, like this:
sin 30 ° = x / 75
x = sin 30 ° * 75
x = 37.5
Now to calculate the value on the y-axis it would be by means of Pythagoras and it would be:
y ^ 2 = 75 ^ 2 - 37.5 ^ 2
y ^ 2 = 4218.75
y = 64.95, -64.95 because it must be located in the fourth quadrant
Which means that to draw the vector that we are asked to do, we must draw a point from origin (0,0) to (37.5, -64.95).
Then I leave a sketch of what it would be:
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Answer:
The value of the single logarithm is -11 ⇒ answer B
Step-by-step explanation:
* Lets revise the rule of the logarithmic functions
# ㏒ a + ㏒ b = ㏒ ab
# ㏒ a - ㏒ b = ㏒ a/b
# ㏒ a^n = n ㏒ a
# ㏒ 1 = 0
* Now lets solve the problem
∵
- Change the single logarithm to an expression by change the
multiplication to addition and the division to subtraction
∵
∵
∵
∴ The single logarithm =
* Now lets substitute the values
∵
- Substitute the values into the expression
∴ The value = 5(3) + 2(2) - 6(5) = 15 + 4 - 30 = -11
* The value of the single logarithm is -11