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3 years ago

ABCD is a rhombus. Fill in the missing steps in the two column proof to explain why ABC is congruent to CDA.

Mathematics

1 answer:

White raven [17]3 years ago

8 0

1)Opposite sides of a rhombus are have the same length.
2)Same thing as statement 1: Opposite sides of a rhombus have the same length.
3) The side AC is common to the two triangles ABC and CDA.
4)The two angles ABC and CDA are congruent by the SSS theorem of
congruent triangles

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After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is modelled by the function C(t)=8(e

Alexxx [7]

Answer:

the maximum concentration of the antibiotic during the first 12 hours is 1.185 $\mu g/mL$ at t= 2 hours.

Step-by-step explanation:

We are given the following information:

After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is modeled by the function where the time t is measured in hours and C is measured in $\mu g/mL$

$C(t) = 8(e^{(-0.4t)}-e^{(-0.6t)})$

Thus, we are given the time interval [0,12] for t.

We can apply the first derivative test, to know the absolute maximum value because we have a closed interval for t.
The first derivative test focusing on a particular point. If the function switches or changes from increasing to decreasing at the point, then the function will achieve a highest value at that point.

First, we differentiate C(t) with respect to t, to get,

$\frac{d(C(t))}{dt} = 8(-0.4e^{(-0.4t)}+ 0.6e^{(-0.6t)})$

Equating the first derivative to zero, we get,

$\frac{d(C(t))}{dt} = 0\\\\8(-0.4e^{(-0.4t)}+ 0.6e^{(-0.6t)}) = 0$

Solving, we get,

$8(-0.4e^{(-0.4t)}+ 0.6e^{(-0.6t)}) = 0\\\displaystyle\frac{e^{-0.4}}{e^{-0.6}} = \frac{0.6}{0.4}\\\\e^{0.2t} = 1.5\\\\t = \frac{ln(1.5)}{0.2}\\\\t \approx 2$

At t = 0

$C(0) = 8(e^{(0)}-e^{(0)}) = 0$

At t = 2

$C(2) = 8(e^{(-0.8)}-e^{(-1.2)}) = 1.185$

At t = 12

$C(12) = 8(e^{(-4.8)}-e^{(-7.2)}) = 0.059$

Thus, the maximum concentration of the antibiotic during the first 12 hours is 1.185 $\mu g/mL$ at t= 2 hours.

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2 years ago

How to make 2700 and 600 a fraction

devlian [24]

I think I may be missing something ... I don't completely understand your question.
All you need to make a fraction is two numbers and a bar. The bar can be either
horizontal or slanty. Then you write one number on top and the other number on
the bottom, and bada-bing, you have a fraction.

You can make fractions like

   2700 / 600
   27 / 6
   9 / 2    (all 3 of these have the same value)

   600 / 2700
   6 / 27
   2 / 9 (all 3 of these have the same value)

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