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statuscvo [17]
3 years ago
8

use vectors to decide whether the triangle with vertices p(1,-3,-2), Q(2,0,4), R(6,-2,-5) is right-angled.

Mathematics
1 answer:
kupik [55]3 years ago
4 0
The direction vectors for the three sides are given by the differences in the vertices, not the vertices themselves. So consider the vectors
P−Q,P−R,Q−RP−Q,P−R,Q−Rand see whether any of these are orthogonal.
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How do you find a volume of a cone?
Dennis_Churaev [7]

Answer:

  V = (1/3)πr²h

Step-by-step explanation:

The volume of a cone is 1/3 the volume of a cylinder with the same radius and height.

  Cylinder Volume = πr²h

  Cone Volume = (1/3)πr²h

where r is the radius (of the base), and h is the height perpendicular to the circular base.

_____

<em>Comment on area and volume in general</em>

You will note the presence of the factor πr² in these formulas. This is the area of the circular base of the object. That is, the volume is the product of the area of the base and the height. In general terms, ...

  V = Bh . . . . . for an object with congruent parallel "bases"

  V = (1/3)Bh . . . . . for a pointed object with base area B.

This is the case for any cylinder or prism, even if the parallel bases are not aligned with each other. (That is, it works for oblique prisms, too.)

Note that the cone, a pointed version of a cylinder, has 1/3 the volume. This is true also of any pointed objects in which the horizontal dimensions are proportional to the vertical dimensions*. (That is, this formula (1/3Bh), works for any right- or oblique pyramid-like object.)

__

* in this discussion, we have assumed the base is in a horizontal plane, and the height is measured vertically from that plane. Of course, any orientation is possible.

4 0
3 years ago
What are the coordinates of A and Q?
Ad libitum [116K]

Answer:

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Step-by-step explanation:

8 0
3 years ago
Given z1 = 2 + sqrt 3i and z2 = 1 – sqrt 3i, what is the sum of z1 and z2?
icang [17]

Answer:

its B. 3

^-^

Step-by-step explanation:

7 0
3 years ago
Need some help please
katovenus [111]

Answer:

the answer is 40.1 cm

Step-by-step explanation:

\cos( \alpha )  = adjacent \div hypotenuse

The adjacent in the triangle is 23cm and the Alpha is 55 degrees, so just insert the formula to find the adjacent which is x .

Tq

8 0
3 years ago
Can someone help me turn these two word problems into algebraic expressions?
Dima020 [189]
1. N=x+3
    S=2(x+3), or Sam=2x+6
5 0
3 years ago
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