9514 1404 393
Answer:
15
Step-by-step explanation:
||3v|| = ||(-9, 12)|| = √((-9)² +12²) = √225
||3v|| = 15
_____
<em>Additional comment</em>
The (3, 4, 5) Pythagorean triple shows up in numerous algebra, geometry, and trigonometry problems. This is one of them. Once you identify the magnitude of v as the hypotenuse of a triangle with legs 3 and 4, you know immediately that ||v|| = 5 and ||3v|| = 15.
This is the concept of volume of solid figures, the volume of a given figure is given by:
volume=(base area)*(height)
In our case the base area will be given by the area of the trapezoid. Which is:
Area=1/2*h*(a+b)
height,h=x
a=x
b=2x
thus;
Area=1/2*x*(2x+x)=3/2x^2
Given that the height of the prism is 20 units, the volume will be:
V=(3/2 x^2*20)
V=30x^2 cubic units
The answer is 30x^2 cubic units
Answer:
she put 9 cars in each pile since 9times 5 equals 45.
Step-by-step explanation:
De Moivre's Theorem states that if a complex number is written in the polar coordinate form [ r (cosθ +
sinθ)] and you raise it to the power n, then this can be evaluated by raising the modulus (r) to the power and multiply the argument (θ) by the power. This therefore would give r ⁿ [cos (nθ) +
sin (nθ)].
let A = ∛ <span>(8 cos (4π / 5) + 8 i sin (4π / 5))
</span>⇒ A = ∛ <span>(8 [cos (4π / 5) + i sin (4π / 5)])
</span>
Now by applying De Moivre's Theorem,
⇒ A =
[cos (
×
) +
sin (
×
)
⇒ A = 2 [ cos (
) +
sin (
)
⇒ A = 2 [0.0117 +
0.01297 ] rads