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1 year ago

A square pyramid has sides of 8 m. Each face is an equilateral triangle. What is the lateral area of the pyramid?

Mathematics

1 answer:

tia_tia [17]1 year ago

3 0

Answer:

The lateral area is equal to

$LA=64\sqrt{3}\ m^{2}$

Step-by-step explanation:

In this problem the lateral area is equal to the area of one equilateral triangle multiplied by $4$

To find the area of one equilateral triangle calculate the height

The area of the triangle is equal to

$A=\frac{1}{2}bh$

we have

$b=8\ m$

Applying the Pythagoras theorem

$h^{2}=8^{2} -4^{2} \\h^{2}=64-16\\ h=\sqrt{48} \\ h=4\sqrt{3}\ m$

The area of one triangle is equal to

$A=\frac{1}{2}(8)(4\sqrt{3})\ m^{2}$

The lateral area is equal to

$LA=4\frac{1}{2}(8)(4\sqrt{3})=64\sqrt{3}\ m^{2}$

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PLEASE HELP ASAP: A particle is moving with velocity v(t) = t2 – 9t + 18 with distance, s measured in meters, left or right of z

dimaraw [331]

1) $\frac{v(8)-v(0)}{8 - 0} = \frac{10-18}{8} = -1\frac{m}{s}$ .
2) $v(5) = 5^2-9*5+18 = 25-45+18 = -2\frac{m}{s}$ .
3) The particle is moving right when the velocity function is positive: $0\ \textless \ t\ \textless \ 3$ or $6\ \textless \ t\ \textless \ 8$ .
4) When $0\ \textless \ t\ \textless \ \frac{9}{2}$ the particle is slowing down because the acceleration is close to zero $\Rightarrow$ the particle is speeding up when acceleration is increasing away from zero: $\frac{9}{2}\ \textless \ t\ \textless \ 8$ .
5) $(\frac{1}{8})* \int\limits^8_0 {t^2-9t+18dt}=\frac{1}{8}*(\frac{t^3}{3}-(\frac{9}{2}*t^2+18t)_{0}^{8}= \\=(\frac{1}{8})*(\frac{8^3}{3}-(\frac{9}{2})*8^2+18*8)=\frac{8^2}{3}-(\frac{9}{2})*8+18=3\frac{1}{3} \frac{m}{s}$ .

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2 years ago

A theatre has the capacity to seat people across two levels, the Circle and

andriy [413]

Answer: $76.19\%$

Step-by-step explanation:

<h3> The complete exercise is: " A theatre has the capacity to seat people across two levels, the Circle, and the stalls. The ratio of the number of seats in the circle to a number of seats in the stalls is 2:5. Last Friday, the audience occupied all the 528 seats in the circle and $\frac{2}{3}$ of the seats in the stalls. What is the percentage of occupancy of the theatre last Friday?"</h3>

Let be "s" the total number of seats in the Stalls.

The problem says that the ratio of the number of seats in the Circle to the number of seats in the Stalls is $2:5$ .

Since the number of seats that were occupied last Friday was 528 seats, we can set up the following proportion:

$\frac{2}{5}=\frac{528}{s}$

Solving for "s", we get:

$s*\frac{2}{5}=528\\\\s=528*\frac{5}{2}\\\\s=1,320$

So the sum of the number of seats in the Circle and the number of seats in the Stalls, is:

$Total=1,320\ seats+528\ seats=1,848\ seats$

We know that $\frac{2}{3}$ of the seats in the Stalls were occupied. Then, the number of seat in the Stalls that were occupied is:

$(1,320)(\frac{2}{3})=880$

Therefore, the total number of seats that were occupied las Friday is:

$Total\ occupied=880\ seats+528\ seats=1,408\ seats$

Knowing this, we can set up the following proportion, where "p" is the the percentage of occupancy of the theatre last Friday:

$\frac{100}{1,848}=\frac{p}{1,408}$

Solving for "p", we get:

$(1,408)(\frac{100}{1,848})=p\\\\p=76.19\%$

8 0

1 year ago

A bicycle is traveling at 20 feet per minute. What is the bicycle's speed expressed in inches per second?

Vikentia [17]

Answer:

4 inches per second

Step-by-step explanation:

Speed = distance/time

Given

Distance = 20 feet

12 inches = 1 foot

X inches = 20 feet

X = 20 x 12 = 240 inches

Time = 1 minute = 60 secs

Therefore

Speed = 240/60

= 4 inches per second

7 0

2 years ago

A box has 6 beads of the same size, but all are different colors. Tania draws a bead randomly from the box, notes its color, and

kirill [66]

6 total beads

1 is yellow

1 is blue

1/6 of getting a yellow

1/6 of getting a blue and

1/6 of getting a yellow again

1/6 * 1/6 * 1/6 = 1/216 probability

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1 year ago

PLEASE HELP I HAVE NO IDEA

Agata [3.3K]

Part 1:

The table showing the decreasing debt is shown as follows:

$\begin{tabular}
{|c|c|c|c|}
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\end{tabular}$

The column for interest accrued is obtained by the folmular

$I=P(1+0.155)^{\frac{1}{12}}$

where P is the month's starting balance.

Part 2:

From the table, the last payment is $138.51

Part 3:

The total amount paid by the time the credit card is payed of is the summation of the "payment" column of the table.

Thus, the total amount is given by:

$Payment\ total=2(400)+5(200)+138.51=\$1,938.51$

Part 4:

The debt ratio is given by

$Debt\ ratio= \frac{debt}{limit} = \frac{1,853.42}{3,000} \approx0.62$

4 0

1 year ago

Read 2 more answers