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3 years ago

Find the average velocity of the function over the given interval.

Mathematics

1 answer:

snow_lady [41]3 years ago

6 0

Answer:

Average velocity of the function over the given interval

= $log(\frac{7}{4} ) -2$

Step-by-step explanation:

Explanation:-

Given function y = 3/x -2 ...(i)

The average velocity of the function over the given interval

Average velocity = $\frac{1}{b-a} \int\limits^b_a {(\frac{3}{x} -2)} \, dx$

= $\frac{1}{7-4} \int\limits^7_4 {(\frac{3}{x} -2)} \, dx$

now integrating

= $\frac{1}{3}( \int\limits^7_4 {(\frac{3}{x} )} \, dx-2\int\limits^7_4 {1} \, dx )$

= $\frac{1}{3} (3 (log x) - 2 x )_{4} ^{7}$

= $\frac{1}{3}( (3 (log 7) - 14 )-(3 log 4 -8))$

by using formulas

log a-log b = log(a/b)

on simplification , we get

= $\frac{1}{3}( (3 (log 7) -3 log 4 ) - \frac{1}{3} (6)$

= $log(\frac{7}{4} ) -2$

Average velocity of the function over the given interval

= $log(\frac{7}{4} ) -2$

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Andreas93 [3]

Answer:

Step-by-step explanation:

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3 years ago

When temperature is zero degree Celsius, the Fahrenheit temperature is 32. When the Celsius temperature is 100, the correspondin

7nadin3 [17]

Answer:

$\\ y = 1.8(x) + 32$ or $\\ y = \frac{9}{5}(x) + 32$

or equivalently:

$\\ F = 1.8(C) + 32$ or $\\ F = \frac{9}{5}(C) + 32$

Step-by-step explanation:

To express the Fahrenheit temperature as a linear function of the Celsius temperature, F(c), we can proceed as follows.

We can use here the two-point form equation of a line:

$\\ y-y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x-x_1)$ [1]

We are asked to express the Fahrenheit temperature as a function of Celsius temperature, so the independent variable, in this case, is x (Celsius temperature) and the dependent variable is y (Fahrenheit temperature).

When temperature is zero degree Celsius ( $\\x_1 = 0$ ), the Fahrenheit temperature is 32 ( $\\y_1 = 32$ ).

When the Celsius temperature is 100 ( $\\x_2 = 100$ ), the corresponding Fahrenheit temperature is 212 ( $\\y_2 = 212$ ).

Then, using [1], we have:

$\\ y-32 = \frac{212 - 32}{100 - 0}(x-0)$

$\\ y-32 = \frac{180}{100}(x)$

$\\ y-32 = 1.8(x)$ .

It could be also be written as:

$\\ y-32 = \frac{18}{10}(x)$ = $\\ y-32 = \frac{9}{5}(x)$ , as it commonly appears in books.

Then the Fahrenheit temperature express as a linear function of the Celsius temperature, F(c) is ( solving the equation for y ) :

$\\ y = 1.8(x) + 32$ or $\\ y = \frac{9}{5}(x) + 32$ .

Or equivalently:

$\\ F = 1.8(C) + 32$ or $\\ F = \frac{9}{5}(C) + 32$

We can check this using the given values from the question:

For 0 Celsius degrees, the Fahrenheit temperature is:

$\\ y = 1.8(0) + 32$ = 32 Fahrenheit degrees.

For 100 Celsius degrees, the Fahrenheit temperature is:

$\\ y = 1.8(100) + 32 = 180 + 32$ = 212 Fahrenheit degrees.

5 0

3 years ago

The city planning commission has been given a budget of 300,000 if the density of concrete is 150 lbs/ft3 determine if the cpc c

Romashka [77]

Answer:

Check Explanation

Step-by-step explanation:

The volume of concrete required to build the bridge is missing and should be provided.

In its absence, let us assign a letter to it.

Let the volume of concrete required to build the bridge be V ft³.

And we further assume that the concrete is the only major material needed to build the bridge for the sake of our question.

Density = (mass/volume)

Density = 150 lb/ft³

Mass = ?

Volume = V ft³

Mass = (Density) × (Volume)

Mass of concrete required = 150 × V = (150V) lb

Cost of concrete is 0.80 per lb

1 lb of concrete costs 0.80

150V of concrete will cost 150V × 0.80 = (120V) currency amount.

Now, depending on the value of V, we can now determine if the city planning commission (cpc) can afford the bridge.

If 120V > 300,000 budget, the cpc cannot afford the bridge, but if 300,000 budget > 120V, then the cpc can afford the bridge.

Hope this Helps!!!

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3 years ago

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mafiozo [28]

D. Robert E. Lee if I'm not mistaken

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3 years ago

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statuscvo [17]

Answer:

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2 years ago

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