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3 years ago

The volume formula of a right pyramid is V= 1/3 Bh. What does B represent?

Mathematics

2 answers:

Jobisdone [24]3 years ago

6 0

Answer:

The Base Area

Step-by-step explanation:

B represents the Base Area of a pyramid. The Volume is one third times base times height. Because the Volume of Pyramid occupies 1/3 of a prism-like in the picture below.

This is valid not only for the right pyramids but also for every other cases: Regular Pyramid, Oblique Pyramid.

tino4ka555 [31]3 years ago

4 0

Answer:

B is the area of the base

Step-by-step explanation:

V= 1/3 Bh

V is the volume

B is the area of the base

h is the height of the pyramid

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A car is traveling at a rate of 50 miles per hour, while a motorcycle is traveling at 70 miles per hour. The car takes 4 hours l

solmaris [256]

Answer:

C,DB

Step-by-step explanation:

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4 years ago

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In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 3.0 m/s up a 22.0° inclined track

Aloiza [94]

Answer:

Approximately $0.31\; \rm m$ , assuming that $g = 9.81\; \rm N \cdot kg^{-1}$ .

Step-by-step explanation:

Initial kinetic energy of the sled and its passenger:

$\begin{aligned}\text{KE} &= \frac{1}{2}\, m \cdot v^{2} \\ &= \frac{1}{2} \times 14\; \rm kg \times (3.0\; \rm m\cdot s^{-1})^{2} \\ &= 63\; \rm J\end{aligned}$ .

Weight of the slide:

$\begin{aligned}W &= m \cdot g \\ &= 14\; \rm kg \times 9.81\; \rm N \cdot kg^{-1} \\ &\approx 137\; \rm N\end{aligned}$ .

Normal force between the sled and the slope:

$\begin{aligned}F_{\rm N} &= W\cdot \cos(22^{\circ}) \\ &\approx 137\; \rm N \times \cos(22^{\circ}) \\ &\approx 127\; \rm N\end{aligned}$ .

Calculate the kinetic friction between the sled and the slope:

$\begin{aligned} f &= \mu_{k} \cdot F_{\rm N} \\ &\approx 0.20\times 127\; \rm N \\ &\approx 25.5\; \rm N\end{aligned}$ .

Assume that the sled and its passenger has reached a height of $h$ meters relative to the base of the slope.

Gain in gravitational potential energy:

$\begin{aligned}\text{GPE} &= m \cdot g \cdot (h\; {\rm m}) \\ &\approx 14\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \times h\; {\rm m} \\ & \approx (137\, h)\; {\rm J} \end{aligned}$ .

Distance travelled along the slope:

$\begin{aligned}x &= \frac{h}{\sin(22^{\circ})} \\ &\approx \frac{h\; \rm m}{0.375}\end{aligned}$ .

The energy lost to friction (same as the opposite of the amount of work that friction did on this sled) would be:

$\begin{aligned} & - (-x)\, f \\ = \; & x \cdot f \\ \approx \; & \frac{h\; {\rm m}}{0.375}\times 25.5\; {\rm N} \\ \approx\; & (68.1\, h)\; {\rm J}\end{aligned}$ .

In other words, the sled and its passenger would have lost (approximately) $((137 + 68.1)\, h)\; {\rm J}$ of energy when it is at a height of $h\; {\rm m}$ .

The initial amount of energy that the sled and its passenger possessed was $\text{KE} = 63\; {\rm J}$ . All that much energy would have been converted when the sled is at its maximum height. Therefore, when $h\; {\rm m}$ is the maximum height of the sled, the following equation would hold.

$((137 + 68.1)\, h)\; {\rm J} = 63\; {\rm J}$ .

Solve for $h$ :

$(137 + 68.1)\, h = 63$ .

$\begin{aligned} h &= \frac{63}{137 + 68.1} \approx 0.31\; \rm m\end{aligned}$ .

Therefore, the maximum height that this sled would reach would be approximately $0.31\; \rm m$ .

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3 years ago

How many solutions does the following equation have? ln(x2 + 4x − 5) = 0

lisov135 [29]

Alrighty
remember
$log_a(b)=c$ means $a^c=b$
and
$ln(x)=log_e(x)$
and
$x^0=1$ for all real values of x
so

$ln(x^2+4x-5)=0$ means
$log_e(x^2+4x-5)=0$ means
$e^0=x^2+4x-5$ which simplifies to
1=x²+4x-5
minus 1 both sides
0=x²+4x-6
use quadratic formula or complete the square
$x=-2+\sqrt{10}$ and $x=-2-\sqrt{10}$
2 solutions

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3 years ago

A rubber band ball weighed some amount. Fatima added two rubber bands to the ball, and now the ball weighed 88 grams. Fatima add

earnstyle [38]

Answer:

Step-by-step explanation:

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3 years ago

First, find the volume for each bottle. Use 3.14 for pie or the pie button and round to the nearest hundredth. Volume of cylinde

marshall27 [118]

the volume of the cylinder is 572.27 cm³

Explanation:

Given:

radius of the cylinder = 4.5cm

height = 9cm

To get the volume of the cylinder, we will use the formula:

$\begin{gathered} Volume\text{ = \pi r^^b2h} \\ where\text{ \pi= 3.14} \\ r\text{ = radius, h = height} \end{gathered}$ $\begin{gathered} Volume\text{ of the cylinder = 3.14 }\times\text{ 4.5}^2\text{ }\times\text{ 9} \\ Volume\text{ of the cylinder = 3.14 }\times\text{ 182.25} \\ \\ Volume\text{ of the cylinder = 572.265 cm}^3 \end{gathered}$

To the nearest hundredth, the volume of the cylinder is 572.27 cm³

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1 year ago