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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The value of x is 3.
Solution:
Length of the top rectangle = x ft
Width of the top rectangle = x ft
Height of the top rectangle = 3x ft
Volume of the top rectangle
Volume of the top rectangle cubic feet
Length of the bottom rectangle = ft
Width of the bottom rectangle = ft
Height of the bottom rectangle = 0.5 ft
Volume of the bottom rectangle
Volume of the bottom rectangle cubic feet
Total concrete for both pieces = 90 cubic feet.
Volume of top + volume of bottom = 90 cubic feet
Solve by factoring.
x = 3,
Solve using quadratic formula,
Ignore the complex roots.
The value of x is 3.