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Gwar [14]
3 years ago
7

The percent of concentration of a certain drug in the bloodstream x hours after the drug is administered is given by K(x) 5x/x^2

+ 9. a. Find the time at which the concentration is a maximum. b. Find the maximum concentration.
Mathematics
1 answer:
Olegator [25]3 years ago
5 0

Given :

The percent of concentration of a certain drug in the bloodstream x hours after the drug is administered is given by K(x) = \dfrac{5x}{x^2+9}.

To Find :

Find the time at which the concentration is a maximum. b. Find the maximum concentration.

Solution :

For maximum value of x, K'(x) = 0.

K'(x) = \dfrac{5(x^2+9)- 5x(2x)}{(x^2+9)^2}=0\\\\5x^2+45-10x^2=0\\\\5x^2 = 45\\\\x = \pm 3

Since, time cannot be negative, so ignoring x = -3 .

Putting value of x = 3, we get, K(3) = 15/( 9 + 9) = 5/6

Therefore, maximum value drug in bloodstream is 5/6 at time x = 3 units.

Hence, this is the required solution.

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GFC and BCF ??

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3 years ago
The equation of a line is y=-2x+1. What is the equation of the line that is parallel to the first line and passes through (2,2)?
Murrr4er [49]

Answer:

The equation in slope-intercept form is y=-2x+6.

The equation in standard form is 2x+y=6.

The equation in point-slope form is y-2=-2(x-2).

Step-by-step explanation:

The slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

Parallel lines will have the same slope and different y-intercept.

Anyways the slope of y=-2x+1 is -2.

So the equation of our line we are looking for is -2.

So we know our equation is in the form y=-2x+b.

We must inf b using y=-2x+b with (x,y)=(2,2).

y=-2x  +b  with (x,y)=(2,2)

2=-2(2)+b

2=-4+b

Add 4 on both sides:

2+4=b

Simplify:

6=b

The equation is y=-2x+6.

Now it didn't say what form it wanted.

There are some forms I can give you like standard and point-slope form.

There is also general form but it is not too much different from standard form.

Standard form is ax+by=c where a,b, and c are integers if possible.

Point-slope form is y-y1=m(x-x1) where (x1,y1) is a point on the line and m is the slope.

So let's go for standard form (ax+by=c) first:

y=-2x+6

add 2x on both sides:

2x+y=6

This is standard form because it is in the form

ax+by=c.

Ok we know point (2,2) is on our line and we also know we have slope,m, is -2.

Point-slope form is

y-y1=m(x-x1)

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8 0
3 years ago
Please help me answer this.
adoni [48]

Answer:

See explanation

Step-by-step explanation:

        Statements                         Reasons

1. \overline{AD}\parallel \overline{BC}                                        Given

2. \angle ADB\cong \angle CBD      As alternate interior angles when parallel lines AD and BC intersect by ltransversal BD

3. \overline{AD}\cong \overline{BC}                                     Given

4. \overline{BD}\cong \overline{DB}                     Reflexive property

5. \triangle ADB\cong \triangle CBD                  SAS postulate

6.  \angle ABD\cong \angle CDB              Corresponding parts of congruent triangles are congruent

7. \overline{AB}\parallel \overline{CD}            Inverse alternate interior angles theorem

8 0
3 years ago
The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle is 90 cm
svet-max [94.6K]
The sides of the triangle are 3x, 4x and 5x

3x + 4x + 5x = 90
12x = 90
x = 90/12
x = 7.5

first side = 3x = 3 * 7.5 = 22.5 cm
second side = 4x = 4 * 7.5 = 30 cm
third side = 5x = 5*7.5 = 37.5 cm
7 0
3 years ago
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
KiRa [710]

Answer:

1863 meters^{2}

Step-by-step explanation:

( 23 x 12 ) x 2 = 552

69 x 19 = 1311

 1311

<u>+552</u>

= 1863 meters^{2}

8 0
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