Step-by-step explanation:
scale = 1/100000 .
hope this helps you.
PLEASE HELP ME ITS ALGEBRA THANK YOUUUU
Answer:
All you have to do is divide 896 ÷ 32 which is 28 and multiply is by 3 since its 3 more nights and the answer is 84 centimeters.
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:
https://brainly.com/question/18806107
Which expressions are equivalent to?
Answer:
-6(b+2) +8
= -6b -12 +8
= -6b -4
Step-by-step explanation:
Please answer the following question:
Answer:
l
Step-by-step explanation:
The sum of two consecutive odd numbers Is 364. Find the larger number.
Answer:
183
Step-by-step explanation:
If they are two consecutive odd numbers, than these two numbers will be close to half of the sum (364).
364/2=182
Now Find the two odd numbers in between 182, which are 181 and 183.
I had this type of question a few times recently, and this method worked every time :).
Bonus information:
For two consecutive odd/even numbers, find the half of the sum.
For three consecutive odd/even numbers, start off by finding the third of the sum. And so on...
Hope this helped! :D
Walmart sells a 40-ounce jar of peanut butter for $5.58
What is the Unit Price?
A gardener will use up to 220 square feet for planting flowers and vegetables. She wants the area used for vegetables to be at least twice the area used for flowers. Let x denote the area (in square feet) used for flowers. Let y denote the area (in square feet) used for vegetables. Shade the region corresponding to all values of x and y that satisfy these requirements.
a student sketched some art on an 8 inch x 10 inch piece if paper he wants to resize it to fit an 4 inch x 6 inch frame. What percent of the original sketch was still able to be included?
Thomas Clemens lives in a town that charges a 0.5% city income tax rate. How much city income tax did he owe last year if he had federal taxable income of $45,883?
Answer:
$2294.15
Step-by-step explanation:
45883 x .05 = 2294.15
Which graph best represents the solution to the system of equations shown below? y = -4x + 19 y = 2x + 1 A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair 7, 3. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair 3, 7. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 3, negative 7. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 7, negative 3.
Answer:
Option 3 is the correct answer.
A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 3, negative 7.
Step-by-step explanation:
y = -4x - 19 y = 2x − 1
-4x - 19 = 2x - 1
6x = -18
x = -3
y = 2(-3) - 1 = -7
Find the missing length indicated
Step-by-step explanation:
10)
again, drawing the height into a right triangle creates 3 right triangles : the original one, and the 2 on both sides of the height.
all these 3 triangles are similar to each other (the angles must be the same).
therefore the ratio of 2 sides in one triangle must be the same as the ratio of the corresponding 2 sides in the other triangles.
so,
x/36 = 64/x
x² = 64×36
x = sqrt(64×36) = 8×6 = 48
11)
same principle.
x/36 = 100/x
x² = 100×36
x = sqrt(100×36) = 10×6 = 60
12)
same as 11)
x/9 = (16+9)/x = 25/x
x² = 25×9
x = sqrt(25×9) = 5×3 = 15
Complete the multiplication problem to find the answer
Answer:
B
Step-by-step explanation:
Answer: B
Step-by-step explanation:
Solve: 1 × -23 = Question 9 options: -1 1 23 -23
Answer:
-23
Step-by-step explanation:
1 × -231. When multiply a positive number by a negative number, the answer will always be negative.
2. When we multiply any number by 1, that number will stay the same.
[tex]1 * -23[/tex] [tex]-23[/tex]Therefore, the answer is -23!
SOMEONE HELP PLZ 20 POINTS
JUST NEED HELP IN THE LAST 4
Answer:
the last one is
four cubed plus 8 to the 4th power
4^3 + 8^4
4160
Step-by-step explanation:
Help me please!!!!!✨✨✨✨✨✨✨✨✨✨
Find all exact solutions on the interval [0,2π) csc^2(x)-9= -5
Answer:
d
Step-by-step explanation:
due at 5:30 help asap!! look at the photo
Are the linear expressions equivalent? Drag the choices to the boxes to correctly complete the table
Answer:
First one is equivalent second one is not equivalent
Step-by-step explanation:
If 2.5 kg of potatoes cost $8.25 how much will u pay for 7 kg
Answer:
$23.10
Step-by-step explanation:
To get how much money you will have to pay for 7kg, you need to find out how much you have to pay for 1 kg. You will divided y divided by x = y.
8.25 (y) divided by 2.5 (x) = $3.30
You will pay $3.30 for 1 kg
So $3.30 x 7 = 23.10
You will pay $23.10 for 7 kg of potatoes.
** I hope this helps
Is seven radical 2 rational?
If seven radical 2 means [tex]7\sqrt{2}[/tex], then the number is irrational.
It means that it goes on and on after the decimal place.
√2 is a surd, so it's irrational.
The water level in a lake was monitored and was noted to have changed −1 1/5 inches in one year. The next year it was noted to have changed −1 3/10 inches.
What was the total change in the water level over the two years?
Enter your answer as a simplified mixed number by filling in the boxes.
$$
in.
Answer:
-2 1/2
Step-by-step explanation:
Yadmine scored 104 points for attempting all 40m questions. If she was awarded 5 points for every correct answer and had 3 points deducted for every incorrect answer, how many questions did Yasmin answer incorrectly?
Using a system of linear equation to represent the problem given, there are 12 incorrect answers given
Points per correct score = 5 Points deducted per incorrect score = 3 Number kd questions answered = 40Let :
Number of correct answers = cWe could create an equation thus:
5(c) - 3(40 - c) = 104
Expand
5c - 120 + 3c = 104
8c = 104 + 120
8c = 224
c = (224 ÷ 8)
c = 28
Number of incorrect answers = 40 - 28 = 12
Therefore, there are 12 incorrect answers
Learn more : https://brainly.com/question/18112348
Graph the ordered pair solutions of y = |x+2| when x = -5, -3, 0, 3, and 5
Mark deposit $ 200 into an account that pays an interest rate 3.5% compounded annually. He doesn't add or remove from his account for 4 years how much money will markbhave in 4 years
Answer:
30,012.5
Step-by-step explanation:
We power the number by itself for the past years so in this it will be 3.5 powered by itself four times equaling 150.0625 multiplied by the first deposit which is 200 so 200*150.0625= 30,012.5
Hope this helps
Determine the midpoint of segment CD
Answer:
9
Step-by-step expation:
Which table can be represented by a line?
A)
А
B)
B
C С
D
D
Step-by-step explanation:
if you really want to get answer you should follow me
PLEASE HELP ME AND HURRY TOO NO LIBKS PLEASE I WILL GIVE BRAINLIEST
A batting machine uses an automatic baseball feeder. During baseball
practice the feeder is a full. An attendant fills it with 15 baseballs so
that the feeder is now full. How many baseballs does the feeder
hold when full?
A. Write an equation to represent the problem.
The feeders in battling machine are represented in proportions and fractions.
The equation that represents the problem is: [tex]\mathbf{\frac 16x + 15 = \frac 23x}[/tex]The feeder can hold 30 baseballs, when fullThe given parameters are:
[tex]\mathbf{Initial = \frac 16x}[/tex] ------ 1/6 full
[tex]\mathbf{Additional = 15}[/tex] --- baseballs added
[tex]\mathbf{Final = \frac 23x}[/tex] ---- 2/3 full
So, the equation that represents the problem is:
[tex]\mathbf{Initial + Additional = Final}[/tex]
So, we have:
[tex]\mathbf{\frac 16x + 15 = \frac 23x}[/tex]
The number of baseballs it can hold is calculated as follows:
[tex]\mathbf{\frac 16x + 15 = \frac 23x}[/tex]
Multiply through by 6
[tex]\mathbf{x + 90 = 4x}[/tex]
Collect like terms
[tex]\mathbf{4x - x = 90 }[/tex]
[tex]\mathbf{3x = 90 }[/tex]
Divide through by 3
[tex]\mathbf{x = 30 }[/tex]
Hence, the feeder can hold 30 baseballs, when full
Read more about proportions and fractions at:
https://brainly.com/question/20337104
Express the number in terms of i
Answer:
[tex]\sqrt[]{9} i[/tex]
Step-by-step explanation:
[tex]\sqrt[]{ab}=\sqrt[]{a} *\sqrt[]{b} \\Therefore, \sqrt[]{-9} =\sqrt[]{9}*\sqrt[]{-1} \\\\\sqrt[]{-1}=i\\\\So, \sqrt[]{-9}= \sqrt[]{9}i[/tex]
Doug entered a canoe race. He rowed 3 1/2 miles in 1/2 hour what is his average speed in miles per hour
Answer: 7 miles per hour
Step-by-step explanation:
3 1/2 miles = 7/2 miles
1/2 hours= 30 minutes
So,
In 30 mins, travelled 7/2 miles
In 1 min, travelled 7/2 ÷ 30= 7/2× 1/30 = (7×1)/(2×30) = 7/60 miles
In 60 mins, travelled (7×60)/60 miles = 420/60 miles = 7 miles.
Hence, the speed is 7 miles per hour.
If p<0,q>0 and q=r what statement about is r true
Answer:
hell no
Step-by-step explanation:
bbbb