Answer: -36
Step-by-step explanation: a negative and a negative give a positive so -36/-3=12
(to check your answer you can also always just multiply the two numbers ex: 12 x -3= -36)
The spread of a virus is modeled by V (t) = −t 3 + t 2 + 12t,
where V (t) is the number of people (in hundreds) with the virus and t is the number of weeks since the first case was observed.
(a) Sketch V (t).
(b) What is a reasonable domain of t for this problem?
(c) Find the average rate of infection from t = 0 to t = 2.
(d) Find the instantaneous rate of infection as a function of t using the limit definition of the derivative.
(e) Find V (2) and V ‘ (2). Write a sentence interpreting V (2) and V ‘ (2) in terms of the number of infected people. Make sure to include units.
(f) Sketch the tangent line to the graph you drew in a. at the point (2, V (2)). State the slope of the tangent line.
(g) Use V (2) and V ‘ (2) to estimate the value of V (2.1).
(h) Find the maximum number of people infected at the same time and when the maximum occurs. Determine the rate of infection at this time.
Functions can be used to model real life scenarios
The reasonable domain is [tex]\mathbf{[0,\infty)}[/tex].The average rate of change from t = 0 to 2 is 20 persons per weekThe instantaneous rate of change is [tex]\mathbf{V'(t) = -3t^2 + 2t + 12}[/tex].The slope of the tangent line at point (2,V(20) is 10 The rate of infection at the maximum point is 8.79 people per weekThe function is given as:
[tex]\mathbf{V(t) = -t^3 + t^2 + 12t}[/tex]
(a) Sketch V(t)
See attachment for the graph of [tex]\mathbf{V(t) = -t^3 + t^2 + 12t}[/tex]
(b) The reasonable domain
t represents the number of weeks.
This means that: t cannot be negative.
So, the reasonable domain is: [tex]\mathbf{[0,\infty)}[/tex]
(c) Average rate of change from t = 0 to 2
This is calculated as:
[tex]\mathbf{m = \frac{V(a) - V(b)}{a - b}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{V(2) - V(0)}{2 - 0}}[/tex]
[tex]\mathbf{m = \frac{V(2) - V(0)}{2}}[/tex]
Calculate V(2) and V(0)
[tex]\mathbf{V(2) = (-2)^3 + (2)^2 + 12 \times 2 = 20}[/tex]
[tex]\mathbf{V(0) = (0)^3 + (0)^2 + 12 \times 0 = 0}[/tex]
So, we have:
[tex]\mathbf{m = \frac{20 - 0}{2}}[/tex]
[tex]\mathbf{m = \frac{20}{2}}[/tex]
[tex]\mathbf{m = 10}[/tex]
Hence, the average rate of change from t = 0 to 2 is 20
(d) The instantaneous rate of change using limits
[tex]\mathbf{V(t) = -t^3 + t^2 + 12t}[/tex]
The instantaneous rate of change is calculated as:
[tex]\mathbf{V'(t) = \lim_{h \to \infty} \frac{V(t + h) - V(t)}{h}}[/tex]
So, we have:
[tex]\mathbf{V(t + h) = (-(t + h))^3 + (t + h)^2 + 12(t + h)}[/tex]
[tex]\mathbf{V(t + h) = (-t - h)^3 + (t + h)^2 + 12(t + h)}[/tex]
Expand
[tex]\mathbf{V(t + h) = (-t)^3 +3(-t)^2(-h) +3(-t)(-h)^2 + (-h)^3 + t^2 + 2th+ h^2 + 12t + 12h}[/tex][tex]\mathbf{V(t + h) = -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h}[/tex]
Subtract V(t) from both sides
[tex]\mathbf{V(t + h) - V(t)= -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h - V(t)}[/tex]
Substitute [tex]\mathbf{V(t) = -t^3 + t^2 + 12t}[/tex]
[tex]\mathbf{V(t + h) - V(t)= -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h +t^3 - t^2 - 12t}[/tex]
Cancel out common terms
[tex]\mathbf{V(t + h) - V(t)= -3t^2h -3th^2 - h^3 + 2th+ h^2 + 12h}[/tex]
[tex]\mathbf{V'(t) = \lim_{h \to \infty} \frac{V(t + h) - V(t)}{h}}[/tex] becomes
[tex]\mathbf{V'(t) = \lim_{h \to \infty} \frac{ -3t^2h -3th^2 - h^3 + 2th+ h^2 + 12h}{h}}[/tex]
[tex]\mathbf{V'(t) = \lim_{h \to \infty} -3t^2 -3th - h^2 + 2t+ h + 12}[/tex]
Limit h to 0
[tex]\mathbf{V'(t) = -3t^2 -3t\times 0 - 0^2 + 2t+ 0 + 12}[/tex]
[tex]\mathbf{V'(t) = -3t^2 + 2t + 12}[/tex]
(e) V(2) and V'(2)
Substitute 2 for t in V(t) and V'(t)
So, we have:
[tex]\mathbf{V(2) = (-2)^3 + (2)^2 + 12 \times 2 = 20}[/tex]
[tex]\mathbf{V'(2) = -3 \times 2^2 + 2 \times 2 + 12 = 4}[/tex]
Interpretation
V(2) means that, 20 people were infected after 2 weeks of the virus spread
V'(2) means that, the rate of infection of the virus after 2 weeks is 4 people per week
(f) Sketch the tangent line at (2,V(2))
See attachment for the tangent line
The slope of this line is:
[tex]\mathbf{m = \frac{V(2)}{2}}[/tex]
[tex]\mathbf{m = \frac{20}{2}}[/tex]
[tex]\mathbf{m = 10}[/tex]
The slope of the tangent line is 10
(g) Estimate V(2.1)
The value of 2.1 is
[tex]\mathbf{V(2.1) = (-2.1)^3 + (2.1)^2 + 12 \times 2.1}[/tex]
[tex]\mathbf{V(2.1) = 20.35}[/tex]
(h) The maximum number of people infected at the same time
Using the graph, the maximum point on the graph is:
[tex]\mathbf{(t,V(t) = (2.361,20.745)}[/tex]
This means that:
The maximum number of people infected at the same time is approximately 21.
The rate of infection at this point is:
[tex]\mathbf{m = \frac{V(t)}{t}}[/tex]
[tex]\mathbf{m = \frac{20.745}{2.361}}[/tex]
[tex]\mathbf{m = 8.79}[/tex]
The rate of infection is 8.79 people per week
Read more about graphs and functions at:
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HELP ME ILL GIVE BRAINLIEST!! BUT YOU HAVE TO SHOW WORK
A box measures 3 1/2 ft by 2 1/4. What is the volume of the box? Show your work.
We can't find volume through given information.
Lets find the area
L=3-1/2=7/2ftB=2-1/4=9/4ft[tex]\\ \sf\longmapsto Area=LB[/tex]
[tex]\\ \sf\longmapsto Area=\dfrac{7}{2}\times \dfrac{9}{4}[/tex]
[tex]\\ \sf\longmapsto Area=\dfrac{63}{6}[/tex]
Which of the following are possible
side lengths for a triangle?
A. 9, 4,8
B. 14, 7,6
C. 3, 8, 1
The only set of side lengths that can form a triangle is 9, 4, 8.
Option A is the correct answer.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check if each of the given sets of side lengths satisfies this condition:
A.
9, 4, 8
9 + 4 > 8 ✓
9 + 8 > 4 ✓
4 + 8 > 9 ✓
All three inequalities are true, so these side lengths can form a triangle.
B.
14, 7, 6
14 + 7 > 6 ✓
14 + 6 > 7 ✓
7 + 6 > 14 ✗
The last inequality is false, so these side lengths cannot form a triangle.
C.
3, 8, 1
3 + 8 > 1 ✓
3 + 1 > 8 ✗
8 + 1 > 3 ✓
The second inequality is false, so these side lengths cannot form a triangle.
Therefore,
The only set of side lengths that can form a triangle is A. 9, 4, 8.
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You can bike at a rate of 7 miles in 25 minutes. At this rate, how long will it take you to go 18 miles?
Answer:
64.2857
Step-by-step explanation:
take the distance traveled divided by the distance which will give you the speed traveling multiplying the distance and the speed will give you the time ot takes
2 divided by 2348=? plz help
Answer:
0.00085
Hope this helps
Answer:
0.00085
Step-by-step explanation:
2/2348= 0.00085
What is the next number in the sequence? (4, 11, 25, 53, 109, ?)
Answer:
221
Step-by-step explanation:
109×2+3=221, pattern is x2+3
--
4×2+3=11
11×2+3=25
25×2+3=53
53×2+3=109
Tyger buys a car for $3200. He renovates it and eventually sell it for $3800. Work out the percentage increase he sold the car for.
Answer:
i believe it's about 18.75% he only gained $600
A submarine dives 155 meters below sea level and then rises 117 meters. What is the new location of the submarine?
Answer:
38 meters below sea level.
Step-by-step explanation:
if the sub dives 155 BELOW sea level, this equals -155.
then it RISES 117 meters, which equals +117.
we can make this into an equation
-155+117=-38!
the location of the sub is 38 meters below sea level.
can some 1 help me please
Answer:
ygghjhghccghhfghjkvgnkvvnvcvbvf
Select the expressions that are equivalent to 6x + 9x
Answer:
4x+2x+9x
9x+7x-x
15x
x.15
I need to determine the perimeter of this rectangle 5cm x 9cm
P= cm
A=cm
Answer:
5+5+9+9 = 28 cm
Step-by-step explanation:
to determine perimeter add the length of each side (2 sides = 5cm and two sides = 9cm.)
Use a calculator to approximate cos 43° and round to
four decimal places.
Answer:
.7314
Step-by-step explanation:
I plugged this number into the calculator and got .7313537016, and then rounded it to the fourth decimal place, which gave me my answer
Please help me!
(But give in detail of how you got the answer)
Solve for s. 2/3s + 5/6s = 21
Enter the answer, as a whole number or as a fraction in simplest form, in the box.
s =
Answer:
s = 14
Step-by-step explanation:
Step 1: Combine like terms.
[tex](\frac{2}{3}s + \frac{5}{6}s) = 21[/tex] [tex](\frac{4}{6}s + \frac{5}{6}s) = 21[/tex] [tex]\frac{9}{6}s = 21[/tex] [tex]\frac{3}{2}s=21[/tex]Step 2: Multiply both sides by 2/3.
[tex]\frac{3}{2}s * \frac{2}{3} = 21 * \frac{2}{3}[/tex] [tex]s = \frac{42}{3}[/tex] [tex]s = 14[/tex]A 35-inch board is to be cut into three pieces so that the second piece is twice as long as the first piece and the third piece is 4 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces
Answer:
5 inch - first board
10 inch - second board
20 inch - third board
Step-by-step explanation:
x = first board
board two = 2x
board three =4x
x+2x+4X=35
7x=35
x=5 inch - first board
10 inch - second board
20 inch - third board
Please help me ASAP
A school counts the number of students taking AMDM and find 225 students taking AMDM. They also count the number of students taking Physics and find 248 students taking the Physics. When they compare the two lists they find 98 student taking AMDM and Physics. What is the probability of a student taking AMDM given they are taking Physics. (Answer in decimal form rounded to the thousandth)
The probability of a student taking AMDM given they are taking Physics is 39.51%.
Since a school counts the number of students taking AMDM and find 225 students taking AMDM, and they also count the number of students taking Physics and find 248 students taking the Physics, and when they compare the two lists they find 98 student taking AMDM and Physics, to determine what is the probability of a student taking AMDM given they are taking Physics, the following cross multiplication calculation must be performed:
248 = 100 98 = X 98 x 100/248 = X 9800/248 = X 39.51 = X
Therefore, the probability of a student taking AMDM given they are taking Physics is 39.51%.
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Write the slope-intercept equation of the line with slope -3/4 passing through the point (-4,5). If necessary, answer using fractions, not decimals.
Answer:
Answer:
y = -3/4x + 2
Step-by-step explanation:
y = -3/4x + b
5 = -3/4(-4) + b
5 = 3 + b
2 = b
What is 3.28 rounded to the nearest thousandth
A construction worker needs to put a rectangular window in the side of a
building. He knows from measuring that the top and bottom of the window
have a width of 8 feet and the sides have a length of 15 feet. He also
measured one diagonal to be 17 feet. What is the length of the other
diagonal?
A. 17 feet
B. 23 feet
C. 15 feet
D. 8 feet
Answer:
A. 17 feet
Step-by-step explanation:
if you practice a musical instrument each day for 2/3 of an hour how many hours of practice would you get in each week
Answer:
2/3 of an hour is 40 minutes so
40 x 7 = 280
You would practice that musical instrument 280 hours after a week
***hope this helps
Step-by-step explanation:
Answer:
14/3
Step-by-step explanation:
ILL GIVE BRAINLIEST!!!
Justin rode his bicycle 2.4 miles a day for 20 days straight. How many miles did Justin ride altogether during the 20-day stretch?
A. 48
B. 68
C. 28
D. 50.5
Justin rode his bicycle in a day = 2.4 miles
Justin ride altogether during the 20-days = ?
? = 2.4 × 20
? = 48
Therefore, Justin ride altogether during the 20-days stretch is 48 miles.
A farmer grows 142 green pepper plants and 108 red pepper plants. Each plant produces about 26 peppers. The farmer plans to sell each pepper for $3. Explain how to find a reasonable estimate for the total amount of money
There are 450 kids in 6th grade. out of these kids 40% chose French as their connection. how many kid chose French?
Answer:
180 kids chose French
Step-by-step explanation:
40/100 = x/450
4/10 = x/450
10•45= 450
4•45= 180
Find the area and perimeter.
5.6 cm
Answer:
A= 5.6 x 5.6 = 31.36
P= 5.6 × 4 = 22.4
Step-by-step explanation:
to find the area of a square, just take the length of 1 side and square it (A= length^ 2)
to find the perimeter of a square multiply length by 4 sides.
*these formulas only hold true for squares bc the length of each side is the same.
Write an equation (any form) for the quadratic graphed below:
Answer:
Quadratic equation in vertex form: y = 2(x + 3)²+ 0
Step-by-step explanation:
The vertex form of a quadratic equation is:
y = a (x - h)² + k where:
The value of a determines that the graph opens up or down. If a is positive, the graph opens up. The value of a also makes the parent function wider or narrower.
The vertex of the given parabola occurs at point (h, k) where the parabola intersects the axis of symmetry, x = h. It is also determines whether it is either the maximum or minimum point on the graph.
The quadratic equation of the graph in vertex form is: y = 2(x + 3)²+ 0
where:
a = 2
vertex (minimum point) = (-3, 0)
axis of symmetry: x = -3
Please mark my answers as the Brainliest if you find my explanations helpful :)
Select all ratios equivalent to 1:4.
I'm not too good at ratios and proportions, sorry
Yes or No. Is it a function? (-1,3), (4,6), (4,8)
Answer:
no
Step-by-step explanation:
Y'' − 2y' + y = 0 ; y(0) = 5 , y'(0) = 10
Answer:
correct
Step-by-step explanation:
Need help please explain how you got the answer
Answer:
$600
Equation:
(Base) x (percent as a decimal) x (years) = interest
(B x .16 x 7.5 = 720)
Steps:
(Base) x (percent as a decimal) = (interest) / (years)
(B x .16 = 96)
Base = (interest / years) / (percent as a decimal)
(B = 600)
How many 1/5 cm can be cut from a 30 cm piece of ribbon
Answer:
6 ang
Step-by-step explanation:
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