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2 years ago

How does Cavalieri’s Principle apply to two pyramids that have the same base area but different heights? Explain.

Mathematics

1 answer:

AysviL [449]2 years ago

6 0

Answer:

We know that the formula for the area of a rectangle is "base" times "height". The rectangle at the right has been sliced into 8 congruent sections. The sections have then been pushed to the right to form a slanted figure.

cavstacking1

The slanted figure has the same base, height and area as the rectangle, yet it is not a rectangle. The slanted figure resembles a parallelogram (except for all of the jagged edges). As we saw with the stacking technique, if we had sliced hundreds of very, very very thin sections, instead of 8 thick sections, we would see the parallelogram more clearly. The parallelogram will have the same area as the original rectangle.

Cavalieri described this relationship between figures using parallel lines.

Since parallel lines are everywhere equidistant, his figures ("regions") are of equal height.

Conditions:

• 2 parallel lines (p || q)

• two figures between the parallel lines

• every additional line parallel to p and q,

must cut equal widths on both figures

Conclusion:

• the areas of the two figures are equal

cacstacking2

Step-by-step explanation:

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Miss Watson runs a distance of 200 meters in 25 seconds. Workout the average speed of Mrs Watson in meters per second.

Readme [11.4K]

Hey there!

Divide 200 by 25.

200/25= 8

She is running an average of 8 m/s. (that's how we represent meters per second)

I hope this helps!
~kaikers

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2 years ago

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What values of c and d make the equation true? Assume x greater-than 0 and y greater-than-or-equal-to 0 StartRoot StartFraction

Maru [420]

Answer:

c = 1, d = 3

Step-by-step explanation:

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2 years ago

mrs sogiba is catering for her sons birthday party. she has invited some of her sons friends to the party. the number of friends

Alex

The only ones that would work are if the factor is composite and if 1 is added to it it can be divided into 48. So 15 would work. The factor 15 is composite, and if 1 is added it can be divided into 48.Therefore the son is 15.

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2 years ago

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An attempt to establish a video call via some social media app may fail with probability 0.1. If connection is established and i

xxMikexx [17]

Answer:

(1). y = x ~ Exp (1/3).

(2). Check attachment.

(3). EY = 3(1 - e^-2).

(4). Var[y] = 3(1 - e^-2) (1 -3 (1 - e^-2)) - 36e^-2.

Step-by-step explanation:

Kindly check the attachment to aid in understanding the solution to the question.

So, from the question, we given the following parameters or information or data;

(A). The probability in which attempt to establish a video call via some social media app may fail with = 0.1.

(B). " If connection is established and if no connection failure occurs thereafter, then the duration of a typical video call in minutes is an exponential random variable X with E[X] = 3. "

(C). "due to an unfortunate bug in the app all calls are disconnected after 6 minutes. Let random variable Y denote the overall call duration (i.e., Y = 0 in case of failure to connect, Y = 6 when a call gets disconnected due to the bug, and Y = X otherwise.)."

(1). Hence, for FY(y) = y = x ~ Exp (1/3) for the condition that zero is equal to y = x < 6.

(2). Check attachment.

(3). EY = 3(1 - e^-2).

(4). Var[y] = 3(1 - e^-2) (1 -3 (1 - e^-2)) - 36e^-2.

The condition to follow in order to solve this question is that y = 0 if x ≤ 0, y = x if 0 ≤ x ≤ 6 and y = 6 if x ≥ 6.