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vovangra [49]
3 years ago
11

Suppose f and g are continuous functions such that g(6) = 6 and lim x → 6 [3f(x) + f(x)g(x)] = 45. Find f(6).

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
7 0
Since g(6)=6, and both functions are continuous, we have:

\lim_{x \to 6} [3f(x)+f(x)g(x)] = 45\\\\\lim_{x \to 6} [3f(x)+6f(x)] = 45\\\\lim_{x \to 6} [9f(x)] = 45\\\\9\cdot lim_{x \to 6} f(x) = 45\\\\lim_{x \to 6} f(x)=5


if a function is continuous at a point c, then lim_{x \to c} f(x)=f(c), 

that is, in a    c ∈  a continuous interval, f(c) and the limit of f as x approaches c are the same.


Thus, since lim_{x \to 6} f(x)=5, f(6) = 5


Answer: 5


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The projectile's horizontal and vertical positions at time t are given by

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where g=9.8\dfrac{\rm m}{\mathrm s^2}. Solve y=0 for the time t it takes for the projectile to reach the ground:

30+\dfrac{250}{\sqrt2}t-4.9t^2=0\implies t\approx36.2458\,\mathrm s

In this time, the projectile will have traveled horizontally a distance of

x=\dfrac{250\frac{\rm m}{\rm s}}{\sqrt2}(36.2458\,\mathrm s)\approx6400\,\mathrm m

The projectile's horizontal and vertical velocities are given by

v_x=\left(250\dfrac{\rm m}{\rm s}\right)\cos45^\circ

v_y=\left(250\dfrac{\rm m}{\rm s}\right)\sin45^\circ-gt

At the time the projectile hits the ground, its velocity vector has horizontal component approx. 176.77 m/s and vertical component approx. -178.43 m/s, which corresponds to a speed of about \sqrt{176.77^2+(-178.43)^2}\dfrac{\rm m}{\rm s}\approx250\dfrac{\rm m}{\rm s}.

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What is the mean absolute deviation of the following set of data?<br> 4<br> 6<br> 6<br> 2.
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Write an equation of the line below
gregori [183]

Answer:

The equation of the line is:

y = 4x + 3

Step-by-step explanation:

We know that the slope-intercept of line equation is

y = mx+b

Where m is the slope and b is the y-intercept

Given the two points on a line

  • (0, 3)
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Finding the slope between (0, 3) and (-2, -5)

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(0,\:3\right),\:\left(x_2,\:y_2\right)=\left(-2,\:-5\right)

m=\frac{-5-3}{-2-0}

m=4

We know that the y-intercept can be computed by setting x=0 and determining the corresponding y-value.

From the graph, it is clear:

at x = 0, y = 3

Thus, y-intercept = b = 3

Substituting m = 4 and b = 3 in the slope-intercept form of line equation

y = mx+b

y = 4x + 3

Therefore, the equation of the line is:

y = 4x + 3

8 0
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Anderson is a plumber and is paid a fixed amount just to make a house visit. The remainder of his fee, y, is determined by the n
Serhud [2]

Answer:

y=10x+50

Explanation:

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7 0
3 years ago
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