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2 years ago

8

Find the volume (in cubic yards) of a cylinder with radius 1.2 yards and height 2.9 yards. (Round your answer to one decimal pla

ce.)

1 answer:

Dvinal [7]2 years ago

5 0

Answer:

11.8 yd³

Step-by-step explanation:

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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.

4 0

2 years ago

Q4) Kiarah collects data throughout the basketball season and uses these 1 point

Jobisdone [24]

Answer:

C. Bulldogs

Step-by-step explanation:

In this question, we want to compare several numbers with different denominators and find out which number is the least. To compare this number, we have to change the denominator into the same number by finding the least common multiple (LCM) of the 4 numbers. The factor of each number will be:

3= 3 ^1

5= 5^1

8= 2 * 2 * 2 = 2^3

2= 2^1

We can find the LCM by multiplying a higher exponent of each prime number. The LCM will be:3^1 * 5^1 * 2^3 = 120

Each number will be:

Tiger= 2/3 * 40/40= 80/120

Redbird = 4/5 * 24/24= 96/120

Bulldogs = 3/8 * 15/15 = 45/120

Titans = 1/2 * 60/60 = 60/120

As you can see, the team with the lowest chance to play is Bulldogs = 45/120

6 0

2 years ago

Find the surface area of the rectangular prism.<br> 8 m<br> 4 m<br> 1 m

Dmitry_Shevchenko [17]

Answer:

A=2(wl+hl+hw)

Step-by-step explanation:

5 0

1 year ago

Laura borrowed $1,990 at 5% for 2 years. what was the total interest?

Gnom [1K]

Answer:

$199

Step-by-step explanation:

I = Prt

I = (1990)(0.05)(2)

I = 199

7 0

2 years ago

Number A3 part 2 show that x is sufficiently small for x⁴

Dahasolnce [82]

Lopo d’oro es qua la

4 0

2 years ago