The concentration C (in mg/cc) of a drug in a patient's bloodstream is related to the time t (in hours) after injection in such a way that as t changes from 0 to 12, C changes from 0.7 to 0.1. Find the average rate of change of C with respect to t.
I have a calculus question similar to this one and I am unsure of how to begin working on this problem.

Answer:

R (t) = 60 - 60 cos (6t)

Step-by-step explanation:

Given that:

R(t) = acos (bt) + d

at t= 0

R(0) = 0

0 = acos (0) + d

a + d = 0 ----- (1)

After [tex]\dfrac{\pi}{12}[/tex] seconds it reaches a height of 60 cm from the ground.

i.e

[tex]R ( \dfrac{\pi}{12}) = 60[/tex]

[tex]60 = acos (\dfrac{b \pi}{12}) +d --- (2)[/tex]

Recall from the question that:

At t = 0, R(0) = 0 which is the minimum

as such it is only  when a is  negative can acos (bt ) + d can get to minimum at t= 0

Similarly; 60 × 2 = maximum

R'(t) = -ab sin (bt) =0

bt = k π

here;

k  is the integer

making t the subject of the formula, we have:

[tex]t = \dfrac{k \pi}{b}[/tex]

replacing the derived equation of k into R(t) = acos (bt) + d

[tex]R (\dfrac{k \pi}{b}) = d+a cos (k \pi)[/tex] [tex]= \left \{ {{a+d \ for \ k \ odd} \atop {-a+d \ for k \ even}} \right.[/tex]

Since we known a < 0 (negative)

then d-a will be maximum

d-a = 60  × 2

d-a = 120 ----- (3)

Relating to equation (1) and (3)

a = -60 and d = 60

∴ R(t) = 60 - 60 cos (bt)

Similarly;

For [tex]R ( \dfrac{\pi}{12})[/tex]

[tex]R ( \dfrac{\pi}{12}) = 60 -60 \ cos (\dfrac{\pi b}{12}) =60[/tex]

where ;

[tex]cos (\dfrac{\pi b}{12}) =0[/tex]

Then b = 6

∴

R (t) = 60 - 60 cos (6t)

Answer:

B

Step-by-step explanation:

B because if it's 1000 then the number will be greater then the fraction.

Answer:

Hey there!

-6-(-12)

-6+12

6

Hope this helps :)

Answer:

[tex]6[/tex]

Step-by-step explanation:

[tex]-6-(-12)[/tex]

[tex]-6+12[/tex]

Since 12 - 6 is equal to 6, -6 + 12 would be 6.

[tex]=6[/tex]

Now you have your answer!

Hope this helps!

Answer:

x = ± sqrt(k)

x = ± 8 by the square root property

Step-by-step explanation:

x^2 = k

K is a real number

Take the square root of each side

sqrt(x^2) = ± sqrt(k)

x = ± sqrt(k)

Letting k = 64

x = ± sqrt(64)

x = ± 8 by the square root property

Answer:

x = ± √k

x = ± √8 by the square root property

Step-by-step explanation:

x² = k

where k is a real number

square root of each side

√x² = ± √k

x = ± √k

let k = 64

x = ± √64

therefore

x = ± 8 by the square root property

Answer:

38.38 miles per gallon

Step-by-step explanation:

16.3 km/L to miles per gallon

1 mile = 1.609 km

16.3 km = 16.3/1.609 = 10.13 miles

1 gallon = 3.788 L

1 L = 1/3.788 = 0.2639 gallon

therefore,

16.3 km/L = 10.13/0.2639 = 38.38 miles per gallon

Replace x in the equation with 3

6(3) -8 = 18 -8 = 10

The answer is 10

Answer:

10

Step-by-step explanation:

To find f(3), substitute 3 in the function

f(3) = 6*3 - 8

     = 10

Answer:

(3,-1)

Step-by-step explanation:

(2+4)/2. (5-7)/2

6/2. - 2/2

3,-1

Answer:

the sum would be located 2 notches to the right from 0.

Step-by-step explanation:

since the notches are already split up into 5, you just count 2 notches to the left (since its negative) and then count 4 notches to the right and then you land on your sum :) btw I like your profile picture

Answer:

x + 13

Step-by-step explanation:

5x + 2(3 - 2x) +7

Distribute the 2 into (3 - 2x)

5x + 6 - 4x + 7

Combine like terms

x + 13

PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. The given expression 5x+2(3−2x)+7 when simplified will be equal to x+13.

PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. PEMDAS is an acronym that stands for P-Parenthesis, E-Exponents, M-Multiplication, D-Division, A-Addition, and S-Subtraction.

The given expression 5x+2(3−2x)+7 can be simplified as shown below.

5x + 2(3−2x) + 7

Open the parenthesis,

= 5x + 6 − 4x + 7

Bring the like terms together,

= 5x − 4x + 7 + 6

Add the like terms,

= x + 13

Hence, The given expression 5x+2(3−2x)+7 when simplified will be equal to x+13.

Learn more about PEMDAS here:

https://brainly.com/question/36185

#SPJ2

Answer: no solution or zero solutions.

Step-by-step explanation:

Given System of equations

2x+2y = 5

3x + 3y = 7

have No solution

Given :

2x+2y = 5

3x + 3y = 7

We write the given equation in y=mx+b form and then we compare the slope 'm'

Solve each equation for y

[tex]2x+2y=5\\2y=-2x+5\\Divide \; by 2\\y=-1x+\frac{5}{2}[/tex]

Slope of first equation is -1

[tex]3x+3y=7\\3y=-3x+7\\Divide \; by \; 3\\y=-1x+\frac{7}{3}[/tex]

Slope of second equation is -1

Slope of both the equations are equal . So the lines are parallel to each other.

Hence , No solution

Learn more :    brainly.com/question/17705616

Answer: [tex]\sqrt[5]{27}[/tex], fifthroot(27) [according to your picture, I think there will be no space between fifth and root]  

Step-by-step explanation:

concept to know: any exponent that is performed in fraction, the numerator will be the real exponent for the base, while the denominator will be the root

-------------------------------------

[tex]27^{\frac{1}{5}[/tex]

This has 1 as the numerator and 5 as the denominator.

1 can be ignored because any number to the 1 power is equal to itself.

5 is the root for 27

[tex]\sqrt[5]{27}[/tex]

Hope this helps!! :)

Please let me know if you have any question

Answer:

Domain: [-4, 4]

Range: [-3, 5]

Function? No

Step-by-step explanation:

Domain is all x-values that can be inputted in the graph that returns an output.

Range is all y-values that are outputted when x is inputted.

A function has to pass the Vertical Line Test.

Answer:

12/32, 3/8, or 37.5%

Step-by-step explanation:

Add the candies in the bag together

13+7+12=32

12 out of the thirty-two are orange

12/32

After dividing by 4 to simplify, you get

3/8

3÷8 will give us the decimal which we can then turn into a percentage

37.5%

12/32, 3/8, or 37.5%

Hope this helps :-)

Answer: 3/5

Step-by-step explanation:

concept to know: the slope of perpendicular line is always opposite reciprocal

----------------------

Step 1. Find the slope of line t

 (y2-y1)/(x2-x1)

=(4-9)/(10-7)

=-5/3

-------------------

Step 2. Apply the concept

Opposite reciprocal of (-5/3)=3/5

Hope this helps!! :)

Please let me know if you have any question

Answer:

the second option 5 2/3

Step-by-step explanation:

since 0.3 with a line over it is equal to 2/3 and 3+2 is 5 our answer would be 5 2/3

Answer:

6

Step-by-step explanation:

Answer: he gave up so he wasn’t able to do it

Step-by-step explanation:

Answer:

$87

The slope is .3

The y-intercept is 42

Step-by-step explanation:

150(.3)=45  

45+42=87

Answer:

[tex]\boxed{\bold 4.651 \times {10}^{5}}}[/tex]

Step-by-step explanation:

[tex]400000 + 60000 + 5000 + 100 \\ = 465100[/tex]

Now write it in standard form.

[tex]465100 \\ = 4.651 \times {10}^{5} [/tex]

hope this helps you.

will give the brainliest!

follow~Hi1315~

Step-by-step explanation:

Lunar eclipses can only happen when the Moon is opposite the Sun in the sky, a monthly occurrence we know as a full Moon.

Answer:

  k = 1/9

Step-by-step explanation:

In order for the function to be continuous at x=9, the values of the two expressions must be the same at x=9.

The first expression evaluates to ...

  [tex]\dfrac{\sqrt{9}-3}{-9}=-\dfrac{3-3}{9}=0[/tex]

The second expression needs to have the same value:

  [tex]1 -k(9) = 0\\\\1 = 9k\\\\\boxed{k=\dfrac{1}{9}}[/tex]

Answer:

[tex]k=1/9[/tex]

Step-by-step explanation:

A function is continuous at a point if and only if:

[tex]\lim_{x \to n} f(x)=f(n)[/tex]

So, we have the piecewise function:

[tex]f(x) = \left\{ \begin{array}{lI} \frac{\sqrt{x} -3}{-9} & \quad0< x <9 \\ 1-kx & \quad x\geq 9 \end{array} \right.$$[/tex]

And we want to find the value of k such that the function is continuous.

First, find the left hand limit of f(x):

[tex]\lim_{x\to9^-} f(x)[/tex]

Since we're coming from the left, we'll use the first equation. Thus:

[tex]=\lim_{x\to9^-} \frac{\sqrt{x}-3}{-9}[/tex]

Direct substitution:

[tex]=\frac{\sqrt{9}-3}{-9}[/tex]

Simplify:

[tex]=\frac{3-3}{-9}[/tex]

Subtract and divide:

[tex]=\frac{0}{-9}=0[/tex]

So, what this tells us is that for the function to be continuous, the right hand limit as  f(x) approaches 9 from the right must also be equal to 0.

Therefore:

[tex]\lim_{n \to 9^+} 1-kx=0[/tex]

Direct substitution:

[tex]1-9k=0[/tex]

Subtract 1 from both sides:

[tex]-9k=-1[/tex]

Divide both sides by -9:

[tex]k=1/9[/tex]

Therefore, the value of k is 1/9.

So, our equation in the end is:

[tex]f(x) = \left\{ \begin{array}{lI} \frac{\sqrt{x} -3}{-9} & \quad0< x <9 \\ 1-\frac{1}{9}x & \quad x\geq 9 \end{array} \right.$$[/tex]

Answer:

[tex]4\frac{3}{8}[/tex] yards of wood

Step-by-step explanation:

The correct question is Hakim is making birdhouses. Each birdhouse uses  7 /8 yard of wood. What is the total length of wood Hakim will need to build 5 birdhouses?

Answer: Given that the amount of wood need to produce one bird house is 7/8 yard, for 5 birdhouse, the amount of wood needed would be 5 times the number needed for one birdhouse. It is given by:

Amount of wood needed for 5 birdhouse = 5 × amount of wood for 1 birdhouse

Amount of wood needed for 5 birdhouse = 5 × 7/8 yards = 35/8 = [tex]4\frac{3}{8}[/tex] yards of wood

Answer:

The answer is three halves why proof is in the step by step explanation.

Step-by-step explanation:

Answer:

The answer is

3

_

2

Because y is over x

y

_

x

Step-by-step explanation:

Step-by-step explanation:

Remember: the origin is at the very center of the graph: (0,0). Not (0,1), (1,0), or 0. The first two options are not at the center. (0,1) takes us one unit above the middle, and (1,0) takes us one unite to the right of the origin. The number 0 is not used to find a point. So, our final answer is: (0,0).

Answer:

1144.18 e-12 chips

Step-by-step explanation:

Conversation rate of nanometers

1 nanometers =1* 10^-12 km

35 nanometers= 35 *10^-12

Radius of earth= 6371 km

Circumference of earth = 2πr

Circumference= 2*22/7*6371

Circumference=40046.29 km

The number of chips to be used to circle the earth

= 40046.29/35 *10^-12

=1144.18 *10^-12

= 1144.18 e-12 chips

Answer:

10

Step-by-step explanation:

Solving $4x=3y$ for $x$ gives $x = \frac{3}{4}y$. Substituting this into the desired expression gives\begin{align*}\frac{2x+y}{3x-2y} &= \frac{2\left(\frac34\right)y + y}{3\left(\frac34y\right) - 2y}\\

&=

\frac{\frac32y + y}{\frac94y - 2y} = \frac{\frac52y}{\frac{y}{4}} \\

&=\frac{5}{2}\cdot 4 = \boxed{10}.\end{align*}

Answer:

10

Step-by-step explanation:

Substitution and simplification

Answer:

Yes  dog owners in the country spend more time walking their dogs than do dog owners in the city

Step-by-step explanation:

From the question we are told that

    The sample size from country is [tex]n_1 = 21[/tex]

     The  sample  size from city is  [tex]n_2 = 23[/tex]

     The  sample  mean for  country is   [tex]\= x_1 =  15 [/tex]

      The  Sample  mean for  city is  [tex]\= x_2 =  10[/tex]

       The  standard deviation for country  is [tex]\sigma _1 =  4[/tex]

        The standard deviation for  city is  [tex]\sigma _2 =  3[/tex]

Let the level of significance is  [tex]\alpha = 0.05[/tex]

The null hypothesis is  [tex]H_o : \mu_1 = \mu_2[/tex]

The  alternative hypothesis is  [tex]H_a : \mu_1 > \mu_2[/tex]

 The  pooled standard deviation is  mathematically represented as

       [tex]s =  \sqrt{ \frac{s_1 ^2  *  (n_1 - 1 ) + s_2 ^2 *  (n_2 - 1 )}{ df} }[/tex]

Here  df is the degree of freedom which is mathematically represented as

          [tex]df =  n_1 + n_2  - 2[/tex]

         [tex]df =  21 + 23 -2 [/tex]

        [tex]df =  42[/tex]

So

    [tex]s =  \sqrt{ \frac{4 ^2  *  (15.0 - 1 ) + 3 ^2 *  (10 - 1 )}{ 42} }[/tex]  

    [tex]s =  3.5[/tex]

Generally the test statistics is mathematically represented

        [tex]t =  \frac{\= x_1 - \= x_2 }{ s *  \sqrt{\frac{1}{n_1} +\frac{1}{n_2}  } }[/tex]

          [tex]t =  \frac{ 15 -10 }{ 3.5 * \sqrt{\frac{1}{ 21 } + \frac{1}{23} } }[/tex]

[tex]t =  4.733[/tex]

Generally the p-value  is obtained from the student t-distribution table   table , the value  is  

         [tex]P(T >   4.733)=  t_{4.733,  42 } = 0.000013  [/tex]

From the calculation we see that

         [tex]p-value  < \alpha[/tex]

So we reject the null hypothesis

Hence we can conclude that there is  sufficient evidence to support the claim that dog owners in the country spend more time walking their dogs than do dog owners in the city

Answer:

the largest square tile is 35cmx35 cm

Step-by-step explanation:

1. Factorize 105 = 5*7*3=35*3

Factorize 280=10*7*4=2*5*7*4=35*8

The common factor is 35.

So Matt can tile 3 tiles 35x35 along the side 105 and 8 tiles along the side 280.

Total 24 pieces 35x35 are necessary to tile the area 105x 280 cm

( However the question is only about the largest tile that Matt could use and not about the quantity of the tiles)

(- 1 - 2√3)²

applicating (a - b)² = a² + b² - 2ab

a = - 1

b = 2√3

so:

(- 1 - 2√3)² =

(- 1)² + (2√3)² - 2(- 1)(2√3) =

1 + (2² * √3²) + 2(2√3) =

1 + (4 * 3) + 4√3

1 + 12 + 4√3 = 13 + 4√3