If you can clean 1/6 of your bedroom in 15 minutes, what is your rate per hour?
solve pls brainliest
Answer: 0.2
happy learning
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
Please hurry
If you apply the changes below to the cubic parent function, Fx) = x2, what is
the equation of the new function?
• Reflect across the y-axis.
Vertically compress by multiplying by : 1/4
9514 1404 393
Answer:
D. J(x) = 1/4(-x)^3
Step-by-step explanation:
Reflection across the y-axis replaces x with -x. Then if Fr(x) represents the reflected function, we have ...
Fr(x) = (-x)^3.
Compression by a factor of c < 1 multiplies the function value by c. Then ...
J(x) = 1/4·Fr(x)
J(x) = (1/4)(-x)^3
Simplify the expression:
7 + -10c2 + 100
Simplify the expression:
7 + -10c² + 100
collect like terms:
7+100-10c²
107-10c²
If you meant, 7+ -10c² + 10c, then it can't be simplified further as there are no like terms.
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
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.
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)
******Please help me please help me help please help*****
Answer:
5 would be the dependent variable.
Step-by-step explanation:
5 would be the dependent variable because that is the number that is that depends on the others in the equation for it to be the final answer.
Answer:
180
Step-by-step explanation:
k = 72/2=36
y =kx
y =36(5)
y = 180
I need some help with this(ratio)(need explanation)
4x = 16.
What is the best action to use to solve
And the property that justifies that action
Answer:
[tex]\sf\longmapsto \: x = 4[/tex]
Step-by-step explanation:
[tex]\sf\longmapsto \: 4x = 16[/tex]
[tex]\sf\longmapsto \: x = \frac{16}{4} [/tex]
[tex]\sf\longmapsto \: x = 4[/tex]
OLEASE HELP ME ITS ALGEBRA THANK YOUUUU
Answer:
$8,704
Step-by-step explanation:
(9+8i)(5-5i) in standard form
Answer:
40i²-5i+45
Step-by-step explanation:
(9+8i)(5-5i)9(5-5i)+8i(5-5i)45-45i+40i-40i²45-5i-40i²40i²-5i+45Find the midpoint of the line segment joining the points P, and P2
P1 = (2, -5); P2 = (4.9)
Is your answer to problem 1a greater than, less than or equal to the answer in
the Example? Why?
Answer:
You forgot to put the picture please redo and ill edit my answer
Step-by-step explanation:
find the slope of (-1,3) and (-5,7)
Answer:
-4/4 = -1
Step-by-step explanation:
yeah-ya...... right?
This graph shows the altitude of a helicopter over time.
What is the slope of the line and what does it mean in this situation?
The slope is –2000 . This means that the helicopter descends 2000 ft each minute.
The slope is –400 . This means that the helicopter descends 400 ft each minute.
The slope is 400. This means that the helicopter ascends 400 ft each minute.
The slope is 2000. This means that the helicopter ascends 2000 ft each minute.
Answer:
B. The slope is –400
Answer: -400
Step-by-step explanation:
Your brother is 1/3 your age your sister is four years older than your brother your sister is nine years old right in equation to find your age X.
Answer:
you are 15
Step-by-step explanation:
9-4=5
5x3=15
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 :)
What is the equation of the blue line?
Answer:
y = 4x - 3
Step-by-step explanation:
When writing an equation of a line, keep in mind that you always need the following information in order to determine the linear equation in slope-intercept form, y = mx + b:
1. 2 sets of ordered pairs (x, y)
2. Slope (m)
3. Y-intercept (b)
First, we need to choose 2 points from the graph to solve for the slope:
Let (x1, y1) = (0, -3)
(x2, y2) = (1, 1)
Use the following slope formula:
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
Substitute the values of the coordinates into the formula:
[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{1 - (-3)}{1 - 0} = \frac{1 + 3}{1} = \frac{4}{1} = 4[/tex]
Therefore, the slope (m) of the line = 4.
Next, we need the y-intercept, (b). The y-intercept is the y-coordinate of the point where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0. The y-coordinate of the point (0, -3) is the y-intercept. Hence, the y-intercept (b) = -3.
Given our slope, m = 4, and the y-intercept (b) = -3, the linear equation is:
y = 4x - 3
Please mark my answers as the Brainliest if you find my explanations/solution helpful :)
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:
7.486 to 7.5 Place value
Answer:
The tenths place
4 is in the tenths place of 7.486
Step-by-step explanation:
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.)
Need helpppppppppppppppppp
Answer:
A child experiencing emotional.........
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
SORMONE PLEASE HELP ME!! ASAP ILL MARK BRAINLIEST!!!
Answer:
C
Step-by-step explanation:
To write the equation of line when slope and one point is given
[tex]y2 - y1 = m(x2 - x1)[/tex]
here m = 3/4
(x1,y1) = 3,-2
Substitute all the values in Formula
[tex]y + 2 = \frac{3}{4} (x - 3) \\ y + 2 = \frac{3}{4} x - \frac{9}{4} \\ y = \frac{3}{4} x - \frac{9}{4} - 2 \\ = \frac{3}{4} x - \frac{17}{4} \\ 4y = 3x - 17 \\ - 3x + 4y = - 17[/tex]
multiply by 4 on both sides
[tex]4y = 3x - 17 \\ - 3x + 4y = - 17[/tex]
PLZ HELP I NEED IT RIGHT NOW
Answer:
1) = 9³
2) = 4*4*4*4*4
= 4 to the fifth power
Step-by-step explanation:
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
It takes one Super Giant Pizza to feed 3 people. If you invite 36 people, how many pizzas will you need?
Answer:
12 Super Giant Pizzas
Step-by-step explanation:
36 ÷ 3 = 12
Answer:
Step-by-step explanation:
You will need to get 12 pizzas
Explanation:36÷3=12