Find the Least Common Denominator. Then, express each fraction using the Least Common Denominator.

The population P of a small town, measured in hundreds, is modeled by the inverse of the function P−1(t) = 10ln(50t − 1000), whe

AleksandrR [38]

Using the inverse function, it is found that the equation is:

$P(t) = \frac{e^{0.1t}}{50} + 20$

It's initial value is 20.

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We want to find the inverse of:

$y = P^{-1}(t) = 10\ln{50t - 1000}$

To do this, we <u>exchange y and t, and isolate y.</u>

Then:

$10\ln{50y - 1000} = t$

$\ln{50y - 1000} = \frac{t}{10}$

$e^{\ln{50y - 1000}} = e^{0.1t}$

$50y - 1000 = e^{0.1t}$

$50y = e^{0.1t} + 1000$

$y = \frac{e^{0.1t} + 1000}{50}$

$y = \frac{e^{0.1t}}{50} + \frac{1000}{50}$

$P(t) = \frac{e^{0.1t}}{50} + 20$

It's initial value is:

$P(0) = \frac{e^{0.1(0)}}{50} + 20 = 0.02 + 20 = 20.02$

Rounding, 20.

A similar problem is given at brainly.com/question/23950969

5 0

3 years ago

In the figure below, which term best describes point T?

Bezzdna [24]

The center of this triangle is created by intersection of altitudes of the triangle, so this point T is an orthocenter.

So, the answer is A.

5 0

3 years ago

Evaluate the surface integral. ??s (x2 y2 z2 ds s is the part of the cylinder x2 y2 = 4 that lies between the planes z = 0 and z

kondor19780726 [428]

The surface $S$ can be parameterized by

$\mathbf r(\theta,z)=(2\cos\theta,2\sin\theta,z)$

where $0\le\theta\le2\pi$ and $0\le z\le2$ . Then the surface integral can be computed with

$\displaystyle\iint_S(x^2+y^2+z^2)\,\mathrm dS$
$\displaystyle=\int_{\theta=0}^{\theta=2\pi}\int_{z=0}^{z=2}(4\cos^2\theta+4\sin^2\theta+z^2)\|\mathbf r_\theta\times\mathbf r_z\|\,\mathrm dz\,\mathrm d\theta=\dfrac{128\pi}3$

6 0

3 years ago

Determine the quadratic equation in standard form of a parabola with a zero at x=5 and vertex ar (-3, 32). start with factored f

elena-s [515]

Answer:

see image...

start with Graphing Form: y = a(x-h)²+ k

knowing that h is the x value (negative of it) of the vertex , and k is the y value of the vertex

Graphing Form Equation: y = a(x+3)²+32

you are also given that when the x value is 5 the y value has to be 0

0 = a(4)^2 + 32

a has to be - 1/2

Step-by-step explanation:

8 0

3 years ago

(1) a) 5270 cl= ? dal

Ivanshal [37]

Answer:

Check below

Step-by-step explanation:

1) These metric volume units can be easily converted by dividing or multiplying by 10 and its multiple. Like this: each step up on the ladder multiply by 10. Each step down divide by 10

$a)5270 \:cl=527\:dl\\b)kl=5.3 \times 10=530 hl\\c)58000ml=5.8 dal =(\frac{58000}{10000})\\d)0.39 dal=3.9 l\\e)7.8 dal=780 dl\\f)57.2 ml=5.72 cl$ .

2) When it comes to area, the "ladder scheme" remains valid but now we'll multiply or divide by

$10^3$

Bear in mind these useful relations:

$1litre =\frac{1}{10^3}m^{3}$

$1 cm^{3} =1 ml$

$a) 3.7 l=3700 cm^{3}\\b)29.6 dm^{3}\\29.6 dm^{3} \rightarrow 29.6\times10^{3} cm^3=29.6\times10^{3} ml = 29.6\times10^{2} cl \:or\:2960 cl\\c)8.1l=8100 cm^{3}\\d)5l=\frac{5}{10^{-3}} m^{3}\\e)5.2 cl=52ml=52 cm^{3}=52\times10^{3}=52000 \:mm^{3}\\f)375 ml=375 cm^{3}\\g) 1300 cm^{3}=1300 ml=13 dl\\h) 8.6 ml= 8.6 cm^{3}\times\: 10^{3}=8600 mm^{3}\\i) 51.8\times 10^{11} l \rightarrow 51.8\times 10^{-11}km^{3}$

6 0

3 years ago