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4 years ago

Pls help asap !!

Mathematics

1 answer:

jekas [21]4 years ago

8 0

Answer:

Step-by-step explanation:

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What two-dimensional figure will result from slicing this rectangular pyramid parallel to the base?

andreev551 [17]

Answer: The answer is D. Trapezoid.

Step-by-step explanation: As shown in the attached figure, a rectangular pyramid ABCDE is drawn. We are slicing this rectangular pyramid parallel to the base BCDE at the points F, G, H and I.

We can clearly see from the figure that upper half of the sliced figure will be similar to the pyramid BCDE and the lower sliced figure will be a trapezoid. These are the three-dimensional figures.

Also, the sliced two-dimensional figure FGHI will be a rectangle, because

the pyramid is a rectangular one and so, FI=GH, FG=HI and all the angles are right angles.

Thus, the resulting two-dimensional figure will be a rectagle.

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3 years ago

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Sin t sin 3t sin 5t = 1/4(-sin t + sin 3t +sin 7t - sin 9t).

Pavlova-9 [17]

Recall that

cos(a + b) = cos(a) cos(b) - sin(a) sin(b)

cos(a - b) = cos(a) cos(b) + sin(a) sin(b)

and by subtracting the first equation from the second, we get

cos(a - b) - cos(a + b) = 2 sin(a) sin(b)

So, we can write

sin(t) sin(3t) = 1/2 (cos(2t) - cos(4t))

and expanding the left side in the original equation gives

sin(t) sin(3t) sin(5t) = 1/2 (cos(2t) - cos(4t)) sin(5t)

… = 1/2 cos(2t) sin(5t) - 1/2 cos(4t) sin(5t)

Similarly, recall that

sin(a + b) = sin(a) cos(b) + cos(a) sin(b)

sin(a - b) = sin(a) cos(b) - cos(a) sin(b)

===> sin(a + b) + sin(a - b) = 2 sin(a) cos(b)

Then

cos(2t) sin(5t) = 1/2 (sin(7t) + sin(3t))

and

cos(4t) sin(5t) = 1/2 (sin(9t) + sin(t))

So we have

sin(t) sin(3t) sin(5t) = 1/2 cos(2t) sin(5t) - 1/2 cos(4t) sin(5t)

… = 1/2 (1/2 (sin(7t) + sin(3t))) - 1/2 (1/2 (sin(9t) + sin(t)))

… = 1/4 sin(7t) + 1/4 sin(3t) - 1/4 sin(9t) - 1/4 sin(t)

… = 1/4 (-sin(t) + sin(3t) + sin(7t) - sin(9t))

as required.

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3 years ago

Can anyone by chance know how to do these geometry questions?

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4 ants are standing on a plane Ant A stands at (1,0) B at (0,1) C(-1,0) D at (0,-1) They all start walking to the next ant in al

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4 years ago

A parabola has a vertex at the origin. The equation of the directrix of the parabola is y = 3. What are the coordinates of its f

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Focus -
(0,-3)

let me know if explanation needed.

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3 years ago

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