Answers
Answer:
Step-by-step explanation:
do your work ok you go it and who still do ixl
Related Questions
Tanisha has 51 m of fencing to build a
three-sided fence around a rectangular
plot of land that sits on a riverbank. (The
fourth side of the enclosure would be the
river.) The area of the land is 304 square
meters. List each set of possible
dimensions (length and width) of the
field.
Possible dimensions #1:
meters by
meters.
Possible dimensions #2:
meters by
meters.
Answers
Answer:
Two sets of dimensions are possible:
L(m) W(m) Area(m^2) Fence (m) Perimeter
Set 1 19 16 304 51
Set 2 32 9.5 304 51
Step-by-step explanation:
Let's set L and W for the Length and Width of the perimeter. We know that:
Area = L*W
Area = 304 m^2
Perimeter = 51 m
Let's say that the side bounded by the river is the length side. No fence is required for that portion, so the fencing for the perimeter is given by:
Perimeter, P = L + 2W
P = 51 m
We can write: L+2W=51 m
Rearrange to isolate one of the two variables. Lets pick L:
L+2W=51
L=51-2W
L = (51-2W)
Now use this in the area equation:
304 m^2 = L*W
304 m^2 = (51-2W)*W
304 m^2 = (51-2W)*W
304 m^2 = 51W-2W^2
Arrange this in the standard form of a quadratice equation and solve:
-2W^2+51W-304 m^2 = 0
W = 16 and 9.5 meters
W = 16 m
Since L=51-2W
L=51-2*(16)
L = 51-32
L = 19 m
Area = L*W
L*W = 304 m^2
(19m)W = 304 m^2
W = 16 m
Check:
Does a length (L) of 19 m and a width (W) of 16 m give an area of 304 m^2 and a fencing perimeter of 51 m if one of the L sides is the river?
Area = (19 m)*(16 m) = 304 m^2 YES
Per. = 2*(16)+ 19 = 51 m YES
W = 9.5 m
Ding the same calculation for a width of 9.5 m also satisfies all the equations, as per above.
Both values of W are valid, so the twos sets of possible dimensions are:
L(m) W(m) Area(m^2) Fence (m) Perimeter
Set 1 19 16 304 51
Set 2 32 9.5 304 51
. The flashlight shown below has no batteries. Instead, it is operated by squeezing and letting go of the handle
Inside the body of the flashlight are gears.
A Kinetic → electrical → light
8 Kinetic chemical → light
C. Chemical -kinetic light
D chemical- electrical → light
Answers
The sequence of the energy conversion is; Kinetic → electrical → light Option A
What is energy conversion?From the first law of thermodynamics, we know that energy can neither be created nor destroyed but it can be converted from one form to the other. We have been told that in this case, the flashlight shown below has no batteries. Instead, it is operated by squeezing and letting go of the handle.
The letting go of the handle is kinetic energy which would lead to electrical energy that is then converted into the visible light energy.
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What is the third quartile of the given data set?
(2,5,6,7,15, 16, 17)
Answers
Answer:
16 is the third quartile
A statistics professor would like to build a model relating student scores on the first test to the scores on the second test. The test scores from a random sample of 21 students who have previously taken the course are given in the table.
Test Scores
Student First Test Grade Second Test Grade
1 50 70
2 91 58
3 55 74
4 58 65
5 79 60
6 70 60
7 97 48
8 51 73
9 51 73
10 59 66
11 69 67
12 56 70
13 56 73
14 41 76
15 49 72
16 58 68
17 58 73
18 99 53
19 87 58
20 95 50
21 97 55
Using statistical software, estimate the parameters of the model
Second Test Grade=β0+β1(First Test Grade)+εiSecond Test Grade=β0+β1(First Test Grade)+εi.
Enter a negative estimate as a negative number in the regression model. Round your answers to 4 decimal places, if necessary.
Answers
Sum of multiplied differences= -962.676 and β1 = -962.676 / ((-18.381)^2 + (22.619)^2 + (-13.381)^2 + (-10.381)^2 + (10.619)^2 + (2.619)^2 + (28.619)^2 + (-17.381)^2 + (-17.381)^2 + (-9.381)^2 + (0.619).
To estimate the parameters of the model, we can use the following steps:
Calculate the mean of the first test scores and the mean of the second test scores.
Calculate the difference between each student's first test score and the mean first test score, and the difference between each student's second test score and the mean second test score.
Multiply the differences from step 2 together for each student, and sum the results.
Divide the sum from step 3 by the sum of the squares of the differences from step 2. This will give us the value of β1.
Calculate β0 by substituting the values of β1 and the mean first and second test scores into the equation: Second Test Grade = β0 + β1(First Test Grade)
Using these steps, we can calculate the estimates of the parameters as follows:
Mean first test score = (50+91+55+58+79+70+97+51+51+59+69+56+56+41+49+58+58+99+87+95+97)/21 = 68.381
Mean second test score = (70+58+74+65+60+60+48+73+73+66+67+70+73+76+72+68+73+53+58+50+55)/21 = 64.762
Difference between student 1's first test score and mean first test score = 50 - 68.381 = -18.381
Difference between student 1's second test score and mean second test score = 70 - 64.762 = 5.238
Difference between student 2's first test score and mean first test score = 91 - 68.381 = 22.619
Difference between student 2's second test score and mean second test score = 58 - 64.762 = -6.762
Sum of multiplied differences = (-18.3815.238) + (22.619-6.762) + (-13.3818.238) + (-10.381-0.762) + (10.619*-6.238) + (2.619*-7.238) + (28.619*-16.762) + (-17.3819.238) + (-17.3819.238) + (-9.381*-0.762) + (0.619*-0.238) + (-2.3816.238) + (-2.3817.238) + (-27.38116.238) + (-18.3813.238) + (-10.381*-3.762) + (-10.3815.238) + (-10.3815.238) + (30.619*-11.762) + (18.619*-6.762) + (26.619*-14.762) + (28.619*-9.762) = -962.676
β1 = -962.676 / ((-18.381)^2 + (22.619)^2 + (-13.381)^2 + (-10.381)^2 + (10.619)^2 + (2.619)^2 + (28.619)^2 + (-17.381)^2 + (-17.381)^2 + (-9.381)^2 + (0.619)
Thus, Sum of multiplied differences= -962.676 and β1 = -962.676 / ((-18.381)^2 + (22.619)^2 + (-13.381)^2 + (-10.381)^2 + (10.619)^2 + (2.619)^2 + (28.619)^2 + (-17.381)^2 + (-17.381)^2 + (-9.381)^2 + (0.619).
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(q014) how many of the twenty-five top-grossing films of 2017 in the united states were part of a movie franchise?
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five out of of the twenty-five top-grossing films of 2017 in the united states were part of a movie franchise
If you were to attribute this film, that means you'd say that (something) caused the success of the movie Rocky. This question is basically asking what do you think made this movie a big hit? Personally, I'd say it's because of how the storyline and plot turned out. It's very intriguing and it doesn't just make the movie about boxing. The film adds some love between the protagonist and some other character, and not only that, but the movie teaches you something. Because Rocky lost to Apollo, Rocky didn't care. At least he still had Adrian. So, the movie teaches you that, even if you do lose, at least you still have something and/or someone with you.
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g what would need to be known about the pivot columns in an augmented matrix in order to know that the linear system is consistent and has a unique solutionwhat would need to be known about the pivot columns in an augmented matrix in order to know that the linear system is consistent and has a unique solution
Answers
There are no free variables for the pivot columns in an augmented matrix in order to know that the linear system is consistent and has a unique solution.
Define the term unique solution?Identical to a coefficient matrix, an augmented matrix has an additional column that contains the values from the right side of a linear system of equations. A number of equations must match the number of unknowns if a system of equations does have a single unique solution (variables).For the stated question-
It is necessary to know that a system is consistent (i.e., there is no pivot in the last column of the augmented matrix) and that there are no free variables in order to determine whether it has a unique solution (like a pivot position in every column of the coefficient matrix).
Also take note that this rules out having fewer rows than columns.
Thus, there are no free variables for the pivot columns in an augmented matrix in order to know that the linear system is consistent and has a unique solution.
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Name the x- and y - intercepts for the equation:
5x - 3y = 15
Answers
Answer:
Red=X-Int: (3,0) Y-int: (0,-5)
Step-by-step explanation:
To find the y and x intercepts you have to plug in the 0 for the variable. You'd get 5(0)-3y=15 you get this by plugging in the 0 for x and then you solve. 5 x 0 is 0 so you'd get -3y=15 divide -3 on both sides and get y=--5 meaning that is the y-intercept. You'd do the same when you look for the x-int. Just that you'd plug in a 0 for y instead of x. Which is 5x-3(0)=15. -3 x 0 is 0. So you'd have 5x=15 divide both sides by 5 and you'd get x=3 meaning that is the x intercept.
(Hopefully you were able to understand how I got the x and y intercepts for this equation)
The rectangular floor of a classroom is 28 feet in length and 38 feet in width. A scale drawing of the floor has a length of 14 inches. What is the area, in square inches, of the floor in the scale drawing?
Answers
The area of the floor of the scale drawing and the scale factor are 72 in² and 1/2 respectively.
Actual Length = 28 feets
Actual width = 38 feets
Model width = 14 inches
The scale factor = 14/28 =1/2
The length of the model can be calculated thus :
Actual Length × scale factor
Model width = 38 × 1/2= 19 inches
The Area of a rectangle can be calculated using the relation :
Area = Length × width
Area of floor = 19 inches × 14 inches = 266 inch²
Therefore, the area of the floor of the scale drawing is 266 in²
What is area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.To learn more about area refer to:
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sorry i chose the wrong image
Answers
Show calculations
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i just got some free money off of you kid
solve please
A
B
c
d
Answers
Answer:
the answer is A
Hope this helps
C
The plane x + y + z = 1 cuts the cylinder x2 + y2 = 1 in an ellipse. We want to find the points on the ellipse that lie closest to the origin. Using Lagrange Multiplier method, set up a system of equations for such points.
Answers
The points on the ellipse that lie closest to the origin are (1, 0, 0), (0, 1, 0)
Let (x, y, z) be a point on an ellipse in which plane x + y + z = 1 cuts the cylinder [tex]$x^2+y^2=1$[/tex]
Let f(x, y, z) = [tex]$x^2+y^2+z^2$[/tex]
[tex]& g_1(x, y, z)=x^2+y^2-1=0 \\[/tex]
[tex]& g_2(x, y, z)=x+y+z-1=0[/tex]
From Lagrange Multiplier Method.
There are multiple ways to define the method of Lagrange multipliers.
Suppose f and g are two functions such that they both have continuous partial derivatives.
Let (x0, y0, z0) ∈ S := {(x, y, z) : g(x, y, z) = 0} and ∇g(x0, y0, z0) ≠ 0.
The method of Lagrange’s multipliers is an important technique applied to determine the local maxima and minima of a function of the form f (x, y, z) subject to equality constraints
[tex]& \nabla f=\lambda \nabla y_1+\mu \nabla g_2 \\[/tex]
[tex]\Rightarrow & \langle 2 x, 2 y, 2 z\rangle=\lambda\langle 2 x, 2 y, 0\rangle+\mu\langle 1,1,1\rangle \\[/tex]
[tex]\Rightarrow & \langle 2 x, 2 y, 2 z\rangle=\langle 2 x \lambda+\mu, 2 y \lambda+\mu, \mu\rangle[/tex]
[tex]2 x & =2 x \lambda+\mu-(1) \\[/tex]
[tex]2 y & =2 y \lambda+\mu \ldots(2) \\[/tex]
[tex]2 z & =\mu \quad \ldots(3)[/tex]
From equation (1) [tex]$2 x(1-\lambda)=\mu=2 z$[/tex]
From equation (2) [tex]$2 y(1-\lambda)=\mu=2 z$[/tex]
Therefore if [tex]\lambda=1$[/tex], then z = 0
if [tex]\lambda \neq 1, \quad x=y=\frac{2}{1-\lambda}[/tex]
if z = 0, then after solving.
[tex]x^2+y^2=1$\\ $2 x+y=1$[/tex]
We get two points: [tex]${(1,0,0)} \geq {(0,1,0)}$[/tex]
and if x = y.
Then:
[tex]& x^2+y^2=1 \Rightarrow x^2+x^2=1 \Rightarrow 2 x^2=1 \Rightarrow x=\pm \sqrt{\frac{1}{2}} \\ & x+y+z=1[/tex]
x + y + z = 1
[tex]\Rightarrow[/tex] x + x + z = 1
[tex]\Rightarrow[/tex] 2 = 1 - 2x
= [tex]1-2\left(\pm \sqrt{\frac{1}{2}}\right)=1 \pm \sqrt{2}[/tex]
Therefore the corresponding points on the ellipse.
[tex]P_1\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 1-\sqrt{2}\right) \& P_2\left(-\frac{1}{\sqrt{2}}, \frac{-1}{\sqrt{2}}, 1+\sqrt{2}\right)[/tex]
Now we have four points
Closest to the origin:
1) (1, 0, 0)
2) (0, 1, 0)
The farthest to origin:
3) [tex]$\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 1-\sqrt{2}\right)[/tex]
4) [tex]$\left(-\frac{1}{\sqrt{2}}, \frac{-1}{\sqrt{2}}, 1+\sqrt{2}\right)[/tex]
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Daliyah is given one point on a line as (3,−1) and the slope of the line as −5.
Answers
The y-intercept of the line having point (3,−1) and slope -5 is 14.
The equation of a line in the slope-intercept form is:-
y = mx+c
where 'm' is the slope and 'c' is the y-intercept.
here, m= -5
∴ y = -5x + c .........(Partial equation)
to find b substitute (3,-1) into the partial equation
where,
x= 3 and y= -1 by substituting the values,
-1 = (-5)×3 + c => c = 15 - 1
∵ c = 14
Thus, the value of the y-intercept is 14.
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The correct question is:-
Daliyah is given one point on a line as (3,−1) and the slope of the line as −5. what is the y-intercept of the line?
Write the range for the relation.
((-1, 1), (-2, 5), (-3, 7). (5, 8))
Answers
The range of a relation is the set of all possible values of the second element of the ordered pairs in the relation. In this case, the range of the relation is the set {1, 5, 7, 8}. This can be found by looking at the second element of each ordered pair in the relation and listing all the different values that appear.
I need help I don’t know how to do this question on ixl
Answers
distance = sqrt(12^2 + 13^2) = sqrt(144 + 169) = sqrt(313) = 17.69 miles
Therefore, the distance between the library and the community pool is approximately 17.69 miles.
what is the angle of rotation that maps point P to point Q?
Answers
Answer:225 degrees
Step-by-step explanation:
A. 2.9 inches
B. 40 inches
C. 3.2 inches
D. 2.1 inches
Answers
The required measure of length of the box is 2.9 inches. Option A is correct.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
according to the question,
h = 3l - 2.5
w = 3/4l
The volume of the box,
40 = l × w × h
40 = l × 3/4l × [3l-2.5]
40 = 3/4l²[3l - 2.5]
40 = 9/4l³ - 7.5/4l²
9/4l³ - 7.5/4l² - 40 = 0
t = 2.91932
t ≈ 2.9 inches
Thus, the length of the box must be at least 2.9 inches. Option A is the right answer.
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I need the answer now
Please help me
I’ll give you the Brainiest
There is a close relationship between the air pressure inside a hurricane and its maximum sustained wind speed: Y-1.15x + 1190 where
x is the air pressure in millibars (kPa) and y is the wind speed in knots (nautical miles per hour). Using the model, what would be the wind
speed of a hurricane with an air pressure of 956 kPa? Round your answer to the nearest knot
A) 50 knots
B) 75 knots
C) 115 knots
D) 91 knots
Answers
The wind speed of a hurricane with an air pressure of 956 kPa will be 2289.4 knots.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that relationship between the air pressure inside a hurricane and its maximum sustained wind speed → y = 1.15x + 1190, where [x] is the air pressure in millibars (kPa) and [y] is the wind speed in knots (nautical miles per hour).
The air pressure inside a hurricane and its maximum sustained wind speed are related as → y = 1.15x + 1190
For x = 956 kpa of pressure, we can write -
y = 1.15 x 956 + 1190
y = 2289.4 knots
Therefore, the wind speed of a hurricane with an air pressure of 956 kPa will be 2289.4 knots.
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If BA BD, the value of x is:
4.
9.
10.
None of these choices are correct.
Answers
5x+4x=90
Simplify by combing lien terms:
9x=90
Divide both sides by 9:
x=90/9
x=10
Let’s check this answer:
5(10)+4(10)?=?90
50+40?=?90
90=90
Therefore, x=10
determine the probability of drawing either a queen or a heart? write your answer as a reduced fraction.
Answers
The probability that the card drawn is either a queen or a heart is 4/13
According to the given information
Consider the random experiment of picking one card from a deck of 52 cards that has been expertly shuffled, as well as the subsequent occurrences.
A queen is the card that was drawn.
H: the heart card was shown.
The chance that "the card drawn is a queen" is P(Q) = 4/52 = 1/13 because there are four queens.
The probability that the card selected will be a heart is P(H) = 13/52, or 1/4, because there are 13 hearts in the deck. Because the queen of hearts is one of the deck's cards, events Q and H are inclusive events. P(Q and H) = 1/52 is the likelihood that "the card picked is a queen and a heart (the queen of hearts)".
Four queens and thirteen hearts are included in the chance that "the card picked is a queen or a heart," but we do not want to count the queen of hearts twice. There are so 16 different methods to depict a queen.
The probability that the card drawn is either a queen or a heart
P(Q or H) = P(Q) + P(H) - P(Q and H)
= [tex]\frac{4}{52} + \frac{13}{52} - \frac{1}{52}[/tex]
= [tex]\frac{16}{52}[/tex]
= [tex]\frac{4}{13}[/tex]
The probability that the card drawn is either a queen or a heart is 4/13
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if f(x)=-2x+5, find x so f(x)=3
Answers
Answer:
f(x)=-2x+5
f(x)=3
then,
f(x)=-2x+5
or, 3=-2x+5
or, 2x=5-3
or,2x=2
or, x=2÷2
x=1
so, the value of x is 1
Answer:
x=1
Step-by-step explanation:
3= -2x+5
-5. -5
-2= -2x
/-2. /-2
1=x
hopes this helps
A hotel ha food proviioned for 30 day to erve 80
people. If 40 more men join the hotel, the ame proviion
would have lat for how many day?
Answers
By using the formula, days = (original number of people / new number of people) * original number of days, the same food would last for 20 days.
What is number?A number is a mathematical concept that refers to a quantity or value that can be represented by a symbol. Numbers can be used to represent quantities in various contexts, such as counting, measuring, and quantifying.
What is irrational numbers?Irrational numbers are numbers that cannot be expressed as the ratio of two integers (e.g. pi, the square root of 2).
days = (original number of people / new number of people) * original number of days
In this case, we can plug in the values as follows:
days = (80 / (80 + 40)) * 30
days = (80 / 120) * 30
days = 2/3 * 30
days = 20
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A 8-inch candle burns down in 4 hours. Assuming the candles are the same thickness and make (that is, directly proportional), how long would it take a 12-inch candle to burn down?
Answers
Answer:
To determine how long it would take a 12-inch candle to burn down, we need to first determine the relationship between the length of the candle and the time it takes to burn down. Since the candles are the same thickness and make, we can say that the time it takes for a candle to burn down is directly proportional to its length. This means that we can write an equation to represent the relationship between the length of the candle and the time it takes to burn down as follows:
t = k * l
where t is the time it takes for the candle to burn down, k is the proportionality constant, and l is the length of the candle.
We can use the information given in the problem to find the value of k. We know that an 8-inch candle burns down in 4 hours, so we can substitute these values into the equation above to find the value of k, as follows:
4 = k * 8
Solving for k, we get:
k = 0.5
Now that we know the value of k, we can use the equation above to determine how long it would take a 12-inch candle to burn down. Substituting the values for t, k, and l into the equation, we get:
t = (0.5) * (12) = 6
This means that it would take a 12-inch candle 6 hours to burn down.
6. The solid line is the parent function, f(x). Which of the following dotted line graphs shows the translation f(x) = f(x)
Answers
The function that is gotten after transformation is; f(x - 1) = -2x - 4
How to Interpret the Graph Transformation?We are told that the parent function is f(x).
Now, after transformation, the function becomes;
f(x) = f(x - 1)
Now, the solid line graph has;
y-intercept = -2
x intercept = 1
Slope = -2/1 = -2
Thus, equation is;
f(x) = -2x - 2
Thus, for f(x - 1), what it means is that we will plug in (x - 1) for x in the parent function to get;
f'(x - 1) = -2(x - 1) - 2
= -2x -2 - 2
= -2x - 4
The graph that represents the function after transformation is as attached.
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Complete question is;
The solid line is the parent function, f(x). Which of the following dotted line graphs shows the translation f(x) = f(x - 1)?
Find the 12th term of the following geometric sequence. 2, 8, 32, 128
Answers
Step-by-step explanation:
So 2 * 4 = 8
8 * 4 = 32
32 * 4 = 128
128 * 4 = 512
512*4=2048
2048*4=8192
8192*4=32768
32768*4=131072
131072*4=524288
524288*4=2097152
2097152*4=8388608
8388608*4=33554432 and that would probably be your final answer
Estimation Gabe goes to the mall. If k is the number of items he bought, the
expression 12.92k + 27 gives the amount he spent in dollars at one store. Then he
spent 20 dollars at another store. Find the expression which represents the amount
Gabe spent at the mall. Then estimate how much Gabe spent if he bought 2 items.
Answers
The total spent at the mall by Gabe is $72.84 and the expression which represents the amount is 12.92 k + 27 + 20 or 12.92 k + 47.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Given:
12.92 k + 27, where k is the number of items bought,
Calculate the expression which represents the amount Gabe spent at the mall as shown below,
Total amount = Amount spent in one store + Amount spent in the second store
Total amount = 12.92 k + 27 + 20
Calculate the estimate of Gabe spent by putting k = 2,
Total spent in mall = 12.92 × 2 + 27 + 20
Total spent in mall = 25.84 + 47
Total spent in mall = $72.84
Therefore, the total spent at the mall by Gabe is $72.84, and the expression which represents the amount is 12.92 k + 27 + 20 or 12.92 k + 47.
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find f. f ''(x) = x−2, x > 0, f(1) = 0, f(3) = 0
Answers
Answer:
Step-by-step explanation:
Here we have the second derivative of a function and we need to go back to the original function. This situation is inverse of taking derivative which is called antiderivative or integral. But because we have the second derivative, we have to integrate twice because the first integral will give me the first derivative then the second integral will give me the function itself.
1. Let's start taking the 1st integral of x-2 which is x²/2-2x+C1
2. Take the 2nd integral which is the integral of the 1st one
x³/6-2x²/2+C1x+C2
remember: the integral is the inverse of derivative, that means we have to add 1 to the power of x and divide by that power. I did that in steps 1 and 2.
3. After simplifying the second term, f(x)=x³/6-x²+C1x+C2 this is the function, but I have to find C1 and C2 the constants. We can use the two conditions given. the 1st one means that when x=1 , y=0
0=1/6-1+C1+C2 now combine like terms and move them to the left side of the equation C1+C2=5/6
the 2nd condition means that when x=3 , y=0
0=27/6-9+3C1+C2 after simplifying 3C1+C2=9/2
4. We got 2 equations with 2 variables C1 and C2, we can solve these system of equations. You can eliminate C2 and find C1 which is 11/6 then plug in C1 in any of the two equations to find C2, which is -1
5. Last step substitute C1 and C2 in the function from step 3 and you will get f(x)=x³/6-x²+11x/6-1
Which of the equations listed below would be parallel to the line divon by y= -4x + 3
Answers
Answer: A
A. y=-4x-2. Two lines are parallel if they have the same slope. In this case, the line given by y = -4x + 3 has a slope of -4, so the equation of the line that is parallel to it must also have a slope of -4. The equation y = -4x - 2 has a slope of -4, so it is the equation of a line that is parallel to the line given by y = -4x + 3.
f ''(x) = x−2, x > 0, f(1) = 0, f(8) = 0
Answers
The required function f when f"(x) = x^-2, x > 0, f(1) = 0, f(2) = 0 is f(x) = - ln x + (ln 8) x/7 + (ln 8)/7
In tthis question we have been given the second derivative of function
f"(x) = x^-2, x > 0, f(1) = 0, f(2) = 0
We need to find a function f(x).
Consider f"(x) = x^-2
Integrating above expression with respect to x we get,
f'(x) = -1/x + C
againg integrating above expression with respect to x we get,
f(x) = - ln x + Cx + D
Now we need to find C and D.
Given that f(1) = 0
- ln (1) + C + D = 0
C + D = 0 ........... (1)
And f(8) = 0
- ln 8 + 8C + D = 0
8C + D = ln 8 ..............(2)
subtracting equation (1) from equation (2),
C = (ln 8)/7
Subtituting above value of C in equation (1) we get,
D = -(ln 8)/7
So, f(x) = - ln x + (ln 8) x/7 + (ln 8)/7
Therefore, the required function : f(x) = - ln x + (ln 8) x/7 + (ln 8)/7
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Nadia typically type 32 word per minute, but her rate may vary by a much a 5 word per minute. Let x be the actual rate at which Nadia type. What i the range of rate, in word per minute, that Nadia could type?
Answers
The range of rate that Nadia can type is 27 to 37.
We will calculate the lower and upper limit stating the minimum and maximum number of words Nadia can type in a minute. It will depict the range of rate.
Minimum number of words = 32 - 5
Performing subtraction on Right Hand Side of the equation
Minimum number of words = 27
Maximum number of words = 32 + 5
Performing subtraction on Right Hand Side of the equation
Minimum number of words = 37
Hence, Nadia's range of word typing is 27 to 37 per minute.
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Let P(t) denote the population of bacteria in a
Petri disht hours after bacteria are introduced to the environment
of the Petri dish. Suppose that the initial population of bacteria
is known to be 5000, and that the bacteria population doubles
every 6 hours. Assume that the population can grow indefinitely.
Give a formula for P(t).
Answers
well, if the population is doubling from whatever they happen to be, so that means the growth rate is 100%, so if they're hmmm "g", then later they become "2g", or doubled, and the later becomes "4g" and so on, so the rate is simply 100%, because "g" plus "g" is just 2g, and "2g" plus "2g" is just 4g and so on, anyhow
[tex]\textit{Periodic/Cyclical Exponential Growth} \\\\ A=P(1 + r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &5000\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ t=hours\\ c=period\to &6 \end{cases} \\\\\\ A=5000(1 + 1)^{\frac{t}{6}}\implies A=5000(2)^{\frac{t}{6}}\implies {\Large \begin{array}{llll} P(t)=5000(2)^{\frac{t}{6}} \end{array}}[/tex]