MATHEMATICS HIGH SCHOOL

A quadrilateral regular pyramid, the area of any of its lateral faces equal the area of its base, if the sidelength of the base of the pyramid is = 6 cm, then the volume of the pyramid =..........cm3
a) 36
b) 673
c) 36/15
d) 216V15

Answers

Answer 1
Answer:

Answer:

  c)  36√15 cm³

Step-by-step explanation:

We can compute the volume of the pyramid if we know the area of its base, and its height.

__

A regular quadrilateral is a square. If one side of the square is 6 cm, its area will be ...

  A = s² = (6 cm)² = 36 cm² . . . . area of the pyramid base

__

Each triangular face will have a slant height that makes its area the same as that of the base.

  A = 1/2bh

  36 cm² = (1/2)(6 cm)h

  (36 cm²)/(3 cm) = h = 12 cm  . . . . .  divide by the coefficient of h

The slant height of a face is the hypotenuse of a right triangle whose short leg is half the side length, and whose long leg is the height of the pyramid. If that height is represented by h, the Pythagorean theorem tells us ...

  (6 cm/2)² +h² = (12 cm)²

  h² = (144 -9) cm²

  h = 3√15 cm . . . . . height of the pyramid

__

The volume of the pyramid is given by ...

  V = 1/3Bh . . . . . . base area B, height h

Using the values we found above, we compute the volume to be ...

  V = (1/3)(36 cm²)(3√15 cm) = 36√15 cm³

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Mike recently increased the size of his Jeep tires from the original 29 inch diameter to the larger 33.73 inch diameter. If Mike didn't recalibrate his speedometer, how fast is he really going on the new tires when his speedometer shows he is traveling 60 mph?a. 54.5 mph
b. 62.1 mph
c. 66.1 mph
d. 69.8 mph

Answers

Answer:

d. 69.8 mph

Step-by-step explanation:

Since, the ratio of the diameter of the tyre of a vehicle and its speed must be constant,

Given,

The original diameter of the tyre = 29 inch,

Original speed = 60 mph,

Thus, the ratio of diameter and the speed of the vehicle = (29)/(60)

New diameter of the tyre = 33.73 inch,

Let x be the new speed of the vehicle = (33.73)/(x)

\implies (29)/(60)=(33.73)/(x)

\implies x=(33.73* 60)/(29)=69.79\approx 69.8\text{ mph}

Hence, the actual speed of the vehicle would be 69.8 mph.

OPTION D is correct.

In the game of pool, the fifteen balls are packed tightly into a triangular rack. The diameter of all the balls are the same. If the height of the rack is BC = 33 cm. Find the diameter of a ball.

Answers

(264(3^1/2)-198)/39 = approximately 6.648 cm.
Let x be the diameter of the ball. Stacking the balls will create a kite. From there it can be derived that the height of the kite is x(3^1/2).
There will be 2 kites in the stack, and 2 half balls + increment between the ball and tip of triangle which is x/2.
Adding these altogether = 33, we get x as stated above. 
Hello there.

In the game of pool, the fifteen balls are packed tightly into a triangular rack. The diameter of all the balls are the same. If the height of the rack is BC = 33 cm. Find the diameter of a ball.

6.648 cm.

Do you think making a table is the best way to find the total area of the rooms

Answers

Well it depends on how many tables you are using and if all the sides of the table are equal lengths....you can it will not hurt anything just make sure you right down all of the area length/width that you cover that way you get the amount you need :) remember to hit that thanks button please:)

The distance between each base on a baseball field is 90 feet. what is the approximate distance from second base to home plate 90 ft

127.3 ft

140.2

180 ft

Answers

Answer:

Option B. 127.3 ft.

Step-by-step explanation:

In the diagram attached, we can see the locations of 1st base, 2nd base, 3rd base and Home plate.

Since these four points form a square of which diagonals are equal in size.

So if we find the distance between 1st and 3rd base that will be equal to the distance between Home plate to the second base.

By applying "Pythagoras Theorem"

Distance between 2nd base and Home plate =

\sqrt{(90)^(2) }+(90)^(2)=90√(2)

= 90 × 1.414 = 127.3 ft.

The distance from second base to home plate is 127.3 ft.

The answer is 127.3 feet

The graph of a system of equations with the same slope and the same y-intercepts will have no solutions.A. Always
B. Sometimes
C. Never

Answers

I think the correct answer from the choices listed above is option C. The graph of a system of equations with the same slope and the same y-intercepts will never have no solutions. Rather, it has an infinite number of solutions since all points of the lines intersects.

Suppose that you want to model the height of a rider on a Ferris wheel as a function of time. The amplitude of the function you use as a model should be equal to which of the following?A) the area of the Ferris wheel
B) the circumference of the Ferris wheel
C) the diameter of the Ferris wheel
D) the radius of the Ferris wheel

Answers

D
The maximum vertical displacement of the rider from the center will be when he is at the top or bottom of the Ferris wheel. The distance from the center to the top (or bottom) of the Ferris is its radius.

Answer:

the answer is in the picture below :)

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