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3 years ago

What is the base of the exponential function f(x)=0.5x−2 ?

Mathematics

1 answer:

Scilla [17]3 years ago

5 0

Answer:

0.5

Step-by-step explanation:

The base of the exponential function is the number which the exponent is touching. If it is exponential then the exponent must be x. This means 0.5 is the base.

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A curve passes through the point (0,7) and has the property that the slope of the curve at every point P is five times the y-coo

iren [92.7K]

Answer:

y(x) = 7e^(5x)

Step-by-step explanation:

The question says that the slope of the curve at every point P is five times the y-coordinate of P. This means that

dy/dx = 5y

Refer to solutions of differential equations, dy/dt = ky, being in the form of y(t) = y(0) e^(kt)

Using the above stated law now, we can relate to our equation, saying that

y(x) = y(0) e^(5x)

The point given from the question is, (0, 7). This also means that y(0) = 7. So finally, we can have

y(x) = 7e^(5x)

And that is our needed equation of the curve

8 0

3 years ago

For what value of x is the rational expression below equal to zero?

pentagon [3]

Answer:

A.-10 should be the answer to the question..

6 0

3 years ago

1. What is the slope of the line that passes through the given points? <br> (2, 12) and (6, 11)

Y_Kistochka [10]

Answer:

-1/4x

Step-by-step explanation:

11-12/6-2 = -1/4

8 0

3 years ago

The curves y = √x and y=(2-x) and the Cartesian axes form two distinct regions in the first quadrant. Find the volumes of rotati

makkiz [27]

Answer:

Step-by-step explanation:

If you graph there would be two different regions. The first one would be

$y = \sqrt{x} \,\,\,\,, 0\leq x \leq 1 \\$

And the second one would be

$y = 2-x \,\,\,\,\,, 1 \leq x \leq 2$ .

If you rotate the first region around the "y" axis you get that

$A_1 = 2\pi \int\limits_{0}^{1} x\sqrt{x} dx = \frac{4\pi}{5} = 2.51$

And if you rotate the second region around the "y" axis you get that

$A_2 = 2\pi \int\limits_{1}^{2} x(2-x) dx = \frac{4\pi}{3} = 4.188$

And the sum would be 2.51+4.188 = 6.698

If you revolve just the outer curve you get

If you rotate the first region around the x axis you get that

$A_1 =\pi \int\limits_{0}^{1} ( \sqrt{x})^2 dx = \frac{\pi}{2} = 1.5708$

And if you rotate the second region around the x axis you get that

$A_2 = \pi \int\limits_{1}^{2} (2-x)^2 dx = \frac{\pi}{3} = 1.0472$

And the sum would be 1.5708+1.0472 = 2.618

7 0

3 years ago

HELLPP!!!!!!!!!!!!!!!!!!!!!!!!!

Genrish500 [490]

$\left\{\begin{array}{ccc}2x-3y=-27&|\cdot3\\-3x+2y=23&|\cdot2\end{array}\right\\\underline{\left\{\begin{array}{ccc}6x-9y=-81\\-6x+4y=46\end{array}\right}\ \ \ \ |\text{add both sides}\\.\ \ \ \ \ \ -5y=-35\ \ \ \ \ |:(-5)\\.\ \ \ \ \ \ \ \ y=7\\\\\text{put the value of y to the first equation}\\\\2x-3(7)=-27\\\\2x-21=-27\ \ \ \ |+21\\\\2x=-6\ \ \ \ |:2\\\\x=-3\\\\\text{Answer:}\ x=-3,\ y=7\to\boxed{(-3,\ 7)}$

6 0

3 years ago