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daser333 [38]
3 years ago
8

This is similar to a problem in the textbook. After a foreign substance is introduced into the blood, the rate at which antibodi

es are made is modeled by f(t)=19t3t2+7 where f(t) is in thousands of antibodies per minute, and t is measured in minutes with 0≤t≤10. Assuming that there are no antibodies present at time t=0, find the total number of antibodies in the blood at the end of 10 minutes. Round your answer to two decimal places.
Mathematics
1 answer:
BartSMP [9]3 years ago
7 0

Answer:

We will find the number of antibodies by integrating the function:

∫

f

0

f

′

(

t

)

=

∫

60

0

27

t

8

t

2

+

3

d

t

Integrating both sides we get:

f

=

27

16

ln

(

8

t

2

+

3

)

Now let us plug-in the bounds we get:

Step-by-step explanation:

You might be interested in
Find the sum. Enter your answer in the box below as a fraction, using the slash mark ( / ) for the fraction bar.
Rom4ik [11]

Answer:

5/7

Step-by-step explanation:

2/7 + 3/7

Denominator are equal so adding numerator,

(2+3)/7 = 5/7

5 0
2 years ago
Which of the following describes the image of a figure after a dilation that has a scale factor between zero and one?
g100num [7]

Answer:

When a figure or shape is dilated , the size of the figure either enlarges or shrank without changing its actual shape.

Shape or figure after dilation is similar to original figure.

If the scale or factor of dilation is greater than 1 the shape enlarges.

If the scale factor lies between 0<scale factor<1, then the figure shrinks i.e size reduces.

So out of all the options given →It has the same shape as the original and is smaller than the original figure.




7 0
2 years ago
2. Suppose you pay $21 for a pair of shoes that was originally $30. What was the percent of decrease in price for the shoes? Set
boyakko [2]
30$ originally - 21$ paid = 9$ discount

> divide the discount by the original price, multiply by 100 to get the percent decrease.

100 x (9$ / 30$) = 30% discount
> So the shoes where on sale for 30% off the original price.

for the equation:
100 x (30-21)/30 = % decrease
8 0
3 years ago
I need help The point (1, –5) is reflected across the y-axis.
Paladinen [302]

Answer:

Step-by-step explanation:

Then the x part of the point takes on the opposite sign that it currently has.

  • Right now it is 1. If it takes on the opposite sign, it becomes - 1
  • So the new point is (-1,-5).
  • Nothing happens to the - 5 when reflected across the y axis.

4 0
2 years ago
HELP ME PLEASE LIKE PLEASE I DONT UNDERSTAND THIS MATH
mafiozo [28]

Given that:

- A race car game takes 6 points each time the player hits a cone.

- You must find the integer that represents the change in total points if the player hits 10 cones.

It is important to remember that the Set of Integers contains the negative numbers, the positive numbers, and zero.

Then, by analyzing the data given in the exercise, you can identify two integers that must be multiplied, in order to calculate the total points if the player hits 10 cones. These are:

\begin{gathered} 10\text{ } \\ -6 \end{gathered}

Since the game takes 6 points from the player each time this hits a cone, the integer that represents the points taken from the player must be negative.

In order to multiply the integers, you need to remember the Sign Rules for Multiplication:

\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ +\cdot-=- \\ -\cdot+=- \end{gathered}

Therefore, you get this result:

(10)(-6)=-60

Hence, the answer is:

8 0
1 year ago
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