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2 years ago

Complete the statements about these similar pyramids.

Mathematics

1 answer:

baherus [9]2 years ago

7 0

A ratio shows us the number of times a number contains another number. The ratio of the sides, base area, and volume are equal to 3:1, 9:1, and 27:1, respectively.

<h3>What is a Ratio?</h3>

A ratio shows us the number of times a number contains another number.

Given the two lateral sides of the pyramids, therefore, the ratio of the sides of the pyramid can be written as,

Length of pyramid A: Length of pyramid B = 15:5 = 3:1

Let the length of the base of the pyramid is represented by a.

The ratio of the base area can be written as,

Area of Base of A: Area of base of B = (3a)²:a² = 9:1

The ratio of the volume can be written as,

Volume of A: Volume of B = (3l×3b×3h)/3 : (lbh)/3 = 27:1

Hence, the ratio of the sides, base area, and volume are equal to 3:1, 9:1, and 27:1, respectively.

Learn more about Ratios:

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You might be interested in

In the figure above, point O is the center of the circle,

snow_tiger [21]

Answer:

16.67 or 16 2/3

Step-by-step explanation:

so, as BC is a tangent, it means the angle OBC is 90 degrees.

therefore, the angle BOC is 180 - 90 - 30 = 60 degrees.

that means the angle AOB is 180 - 60 = 120 degrees.

the triangle ABO must be an isosceles triangle, as the sides are both the radius of the circle. so, both remaining angles are the same : half of 180 - 120 = 60 = 30 degrees.

and so, we know that ABC is an isosceles triangle, because both "side angles" are equal = 30 degrees.

so, AB = BC.

and we know the circumference of the circle (50) and can calculate the radius

50 = 2×pi×r

25 = pi×r

r = 25/pi ≈ 7.96

now we have multiple ways to calculate AB.

AB = BC = tan(60) × r

AB = sqrt(r² + r² - 2×r×r×cos(120))

or ...

the first one might be easiest.

AB = tan(60) × 7.96 ≈ 13.78

oh, I just recognized, we need the arc AB (not the straight line).

even easier.

50 is the full "arc" of the circle for all 360 degrees.

but we only need the part of the angle AOB = 120 degrees.

so, this is then only the 120/360 part of the full circle circumference.

ABarc = 50 × 120/360 = 50 / 3 ≈ 16.67 or 16 2/3

8 0

3 years ago

Help picture below problem 10

DedPeter [7]

Solution :-

Here, we have been given that lines f and g are parallel. Thus, the angle measuring 135° and ∠2 are vertically opposite angles.

And we know that vertically opposite angles measure same. Thus,

∠2 = 135°

And,

∠2 + ∠6 = 180° ( Co - interior angles sum up to 180° )

135° + ∠6 = 180°

∠6 = 180° - 135°

∠6 = 45°

Hope that helps :)

4 0

3 years ago

Two vertical poles of heights 60 ft and 80 ft stand on level ground, with their bases 100 ft apart. A cable that is stretched fr

Andreyy89

Answer:

Step-by-step explanation:

Given

height of two Poles are 60 and 80 ft

Distance between them is 100 ft

Let x be the distance of Pole of ht 80 ft from Point of stretch

thus length of rope is given by

$L=L_1+L_2$

$L_1=\sqrt{80^2+x^2}$

$L_2=\sqrt{60^2+(100-x)^2}$

$L=\sqrt{80^2+x^2}+\sqrt{60^2+(100-x)^2}$

differentiate w.r.t x we get

$\frac{\mathrm{d} L}{\mathrm{d} x}=\frac{2x}{2\sqrt{80^2+x^2}}-\frac{2\left ( 100-x\right )}{\sqrt{60^2+\left ( 100-2x\right )^2}}$

Put $\frac{\mathrm{d} L}{\mathrm{d} x}=0$ to get minimum value

$\frac{2x}{2\sqrt{80^2+x^2}}=\frac{2\left ( 100-x\right )}{\sqrt{60^2+\left ( 100-2x\right )^2}}$

squaring

$x^2\left ( (100-x)^2+60^2\right )=(100-x)^2(80^2+x^2)$

Rearranging

$28x^2-1800x+640000=0$

$x=\frac{400}{7}$

thus $L_1=98.312 ft$

$L_2=73.73 ft$

$L=172.04 ft$

7 0

3 years ago

Given the linear equation 4x +6y - 9 =0, another linear equation in two variables such that the geometrical representation of th

Kisachek [45]

Answer:

Step-by-step explanation:

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7 0

3 years ago

Determine the first four terms of the sequence in which the nth term is

Licemer1 [7]

Answer:

The correct answer option is: $\frac{1}{3} ,\frac{1}{4} ,\frac{1}{5} ,\frac{1}{6}$ .

Step-by-step explanation:

We know that the $nth$ term $a_n$ for an arithmetic sequence is given by:

$a_n=\frac{(n+1)!}{(n+2)!}$

where $n$ is the number of the position of the term.

We are supposed to find the first four terms of the sequence so we will substitute the values of $n$ from 1 to 4 in the given formula to get:

1st term:

$a_1=\frac{(1+1)!}{(1+2)!}=\frac{1}{3}$

2nd term:

$a_2=\frac{(2+1)!}{(2+2)!}=\frac{1}{4}$

3rd term:

$a_3=\frac{(3+1)!}{(3+2)!}=\frac{1}{5}$

4th term:

$a_4=\frac{(4+1)!}{(4+2)!}=\frac{1}{6}$

8 0

4 years ago