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3 years ago

The Great Pyramid at Giza, Egypt, is 147 meters tall,

Mathematics

2 answers:

charle [14.2K]3 years ago

5 0

Answer:

The formula for the volume of a pyramid is V = (1/3)·(Area of the Base)·(Height)

Since the base of the pyramid is a square, 240 meters on each side, the area of the base is:

A = 240 m x 240 m = 57,600 square meters

The volume of the pyramid is: V = (1/3)·(57,600 m2)·(147 m) = 2,822,400 m³.

Step-by-step explanation:

klemol [59]3 years ago

4 0

Answer:

V = (1/3) x (57,600 m^2) x (147 m) = 2,822,400 m^3

Step-by-step explanation:

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If n represents a number then write an expression for two less than one fourth of n

Ne4ueva [31]

Answer: $\frac{1}{4}n-2$

This is the same as $\frac{n}{4} - 2$ and it is also equivalent to $0.25n-2$

=====================================================

Explanation:

n is some placeholder for a number

one fourth of that number is $\frac{1}{4}n$ which is the same as $\frac{n}{4}$ or $0.25n$ since 1/4 = 0.25

From here, we subtract off 2 to get $\frac{1}{4}n-2$ as one possible final answer.

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3 years ago

A 100 gallon tank initially contains 100 gallons of sugar water at a concentration of 0.25 pounds of sugar per gallon suppose th

Vsevolod [243]

At the start, the tank contains

(0.25 lb/gal) * (100 gal) = 25 lb

of sugar. Let $S(t)$ be the amount of sugar in the tank at time $t$ . Then $S(0)=25$ .

Sugar is added to the tank at a rate of P lb/min, and removed at a rate of

$\left(1\frac{\rm gal}{\rm min}\right)\left(\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm gal}\right)=\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm min}$

and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

$\dfrac{\mathrm dS}{\mathrm dt}=P-\dfrac S{100}$

Separate variables, integrate, and solve for S.

$\dfrac{\mathrm dS}{P-\frac S{100}}=\mathrm dt$

$\displaystyle\int\dfrac{\mathrm dS}{P-\frac S{100}}=\int\mathrm dt$

$-100\ln\left|P-\dfrac S{100}\right|=t+C$

$\ln\left|P-\dfrac S{100}\right|=-100t-100C=C-100t$

$P-\dfrac S{100}=e^{C-100t}=e^Ce^{-100t}=Ce^{-100t}$

$\dfrac S{100}=P-Ce^{-100t}$

$S(t)=100P-100Ce^{-100t}=100P-Ce^{-100t}$

Use the initial value to solve for C :

$S(0)=25\implies 25=100P-C\implies C=100P-25$

$\implies S(t)=100P-(100P-25)e^{-100t}$

The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

$1000\,\mathrm{gal}+\left(-1\dfrac{\rm gal}{\rm min}\right)t=5\,\mathrm{gal}\implies t=995\,\mathrm{min}$

has passed. At this time, we want the tank to contain

(0.5 lb/gal) * (5 gal) = 2.5 lb

of sugar, so we pick P such that

$S(995)=100P-(100P-25)e^{-99,500}=2.5\implies\boxed{P\approx0.025}$

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3 years ago

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OleMash [197]

Two triangles are similar if and only if all corresponding angles are equal (congruence), even if the corresponding sides are equal or not, therefore the answer is true because ΔJKL and ΔRST are similar and the statement above demands that "it must be", namely, this is a sufficient condition.

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3 years ago

Solve the equation by completing the square. 3x^2 -6+9=0

Debora [2.8K]

The factored form would be (3x-9)(x-1)
The picture should help a bit

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3 years ago

Read 2 more answers

A certain electronics manufacturer found that the average cost C to produce x DVD/Blu- ray players can be found using the equati

Marina CMI [18]

Answer:

Minimum average cost = 743.75

Number of dvds to achieve the cost = 62.5

Step-by-step explanation:

Given the cost equation

C = 0.04x² − 5x + 900

To Obtian the minimum average cost ;

Find dc/dx = 0

Diffentiate cost, c it ith respect to x

dc/dx = 2(0.04x) - 5

dc/dx = 0.08x - 5 = 0

0.08x = 5

x = 5 / 0.08

x = 62.5

Substitute the value of x into C to obtain the minimum average cost

C = 0.04(62.5)² - 5(62.5) + 900

C = 743.75

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2 years ago