Consider the differential equation dy/dx = 1/3x(y-2)^2.
(a) A slope field for the given differential equation is shown below. Sketch the solution curve that passes through the point (0, 2), and sketch the solution curve that passes through the point (1, 0).
(b) Let y = f(x) be the particular solution to the given differential equation with initial condition f(1) = 0. Write an equation for the line tangent to the graph of y = f(x) at x = 1. Use your equation to approximate f(0.7).
(c) Find the particular solution y = f(x) to the given differential equation with initial condition f(1) = 0.
(This
was on the no-calculator section of the recently-released AP Calculus
AB 2018 exam so I appreciate it if you tried to limit calculator usage)
Answers
Since we can surmise that [tex]y=2[/tex] is an equilibrium for this ODE (that is, the derivative along this line is 0 everywhere), and the slope at (1, 0) is positive, we know that as [tex]x\to+\infty[/tex], the function [tex]y(x)[/tex] will converge to 2. In other words, as [tex]x[/tex] gets larger, the slope field suggests that the solution curve through (1, 0) will start to plateau and steadily approach [tex]y=2[/tex]. On the other hand, as [tex]x\to-\infty[/tex], the slope field tells us that the curve would rapidly diverge off to [tex]-\infty[/tex]. (When you actually draw the solution, you would end up with something resembling the plot of [tex]-e^{-x}[/tex].)
b) The tangent line to [tex]y=f(x)[/tex] at [tex]x=1[/tex], given that [tex]f(1)=0[/tex], takes the form
[tex]\ell(x)=f(1)+f'(1)(x-1)[/tex]
[tex]\ell(x)=f'(1)(x-1)[/tex]
When [tex]x=1[/tex], we have [tex]y=0[/tex], so
[tex]f'(1)=\dfrac13\cdot1\cdot(0-2)^2=\dfrac43[/tex]
and so the tangent line to [tex]f(x)[/tex] at [tex]x=1[/tex] is
[tex]\ell(x)=\dfrac43(x-1)[/tex]
Using the tangent line as an approximation, we would find
[tex]f(0.7)\approx\ell(0.7)=\dfrac43\left(\dfrac7{10}-1\right)=-\dfrac4{10}=-0.4[/tex]
c) The ODE is separable, so we can write
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac13x(y-2)^2\iff\dfrac{\mathrm dy}{(y-2)^2}=\dfrac x3\,\mathrm dx[/tex]
Integrating both sides gives us
[tex]-\dfrac1{y-2}=\dfrac{x^2}6+C[/tex]
Given that [tex]y(1)=0[/tex], we get
[tex]-\dfrac1{0-2}=\dfrac{1^2}6+C\implies C=\dfrac13[/tex]
so the particular solution is
[tex]-\dfrac1{y-2}=\dfrac{x^2}6+\dfrac13[/tex]
You're asked to find the solution in the form [tex]y=f(x)[/tex], so you should solve for [tex]y[/tex]. You would end up with
[tex]y=-\dfrac6{x^2+2}+2=\dfrac{2(x^2-1)}{x^2+2}[/tex]
To sketch the solution curves passing through (0, 2) and (1, 0), we can use the slope field provided. The tangent line to y = f(x) at x = 1 can be found by taking the derivative of f(x) and substituting x = 1. We can find the particular solution to the differential equation by integrating it with the given initial condition f(1) = 0.
Explanation:(a) Solution curves through (0, 2) and (1, 0)To sketch the solution curves, we can use the slope field provided. For the point (0, 2), the slope is 1/3(0)(2-2)^2 = 0. Thus, at (0, 2) the solution curve is horizontal. For the point (1, 0), the slope is 1/3(1)(0-2)^2 = 8/3. Thus, at (1, 0) the solution curve is directed upwards with a slope of 8/3.
(b) Tangent line at (1, 0) and f(0.7)Since f(1) = 0, we already know that the point (1, 0) lies on the graph of y = f(x). The equation of the tangent line to y = f(x) at x = 1 can be found by finding the derivative of f(x) and substituting x = 1. In this case, the derivative is dy/dx = 1/3x(y-2)^2, so at x = 1, we have dy/dx = 1/3(1)(0-2)^2 = -8/3. Therefore, the equation of the tangent line is y - 0 = (-8/3)(x - 1), which simplifies to y = -8/3(x-1). To approximate f(0.7), we can substitute x = 0.7 into the equation of the tangent line to get y = -8/3(0.7 - 1) = -8/3(0.3) = -8/10 = -0.8.
(c) Find the particular solution with f(1) = 0To find the particular solution, we can integrate the differential equation with the given initial condition. Starting with dy/dx = 1/3x(y-2)^2, we can rewrite it as (y-2)^(-2)dy = 1/3xdx. Integrating both sides will give us the equation of the particular solution.
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Related Questions
Tanya is 42 years old. she would like to open aretirement account so she will have half a million dollars in the account when she retires at the age 65. how much did she deposit each month into an account with an apr of 2.75% to reach her goal?
Answers
using the annuity formula:
A=P[((1+r)^n-1)/r]
A=future value
r=rate
n=number of years
from the information given:
A=$500000
r=2.75%
n=65-42=23 years
p=$x
thus plugging our values in the formula we get:
500000=x[((1+0.0275)^(23)-1)/(0.0275)]
500000=31.50x
x=15,872.04883
She deposited 15,873.04883 per year
The monthly deposit will therefore be:
15873.04883/12=$1322.67
Seven of the 10 children at Art can't make an average of 8 paintings. The remaining children make an average of 12 paintings. What is the average number of paintings made by children that are Camp. Enter your answer in the Box
Answers
Total number of paintings made by the remaining = 3*12 = 36
Total number of paintings = 56+36= 92 paintings
Average number of paintings by all the children = 92/10 = 9.2 ≈ 9 paintings
Which of the following events has an expected value that is in the sample space? A. tossing a number cube once B. flipping a coin C. randomly picking a number between one and nine, inclusive D. randomly picking a number between one and ten, inclusive
Answers
A) The event is "tossing a number cube once"
The sample space of this event is {1,2,3,4,5,6}.
The expected value of this event is
[tex]1\times \frac{1}{6}+2\times \frac{1}{6}+3\times \frac{1}{6}+4\times \frac{1}{6}+5\times \frac{1}{6}+6\times \frac{1}{6}\\ \\ =\frac{1}{6}+\frac{1}{3}+\frac{1}{2}+\frac{2}{3}+\frac{5}{6}+1\\ \\ =\frac{7}{2} = 3.5[/tex]
Since 3.5 is not in the sample space of the event. Therefore, option (A) is not correct.
(B) The event is "Flipping a coin"
Sample space of this event is {HH,TT,HT,TH}
Since sample space of this event is not numbers, therefore, this cannot be the correct option either.
(C) The event is, "Randomly picking a number between 1 and 9, inclusive."
The sample space of this event is {1,2,3,4,5,6,7,8,9}.
Expected value of this event is [tex]\frac{1}{9}(1+2+3+4+5+6+7+8+9) = \frac{1}{9}(45) = 5[/tex]
Since 5 is the expected value and it is present in the sample space for this event. Therefore, option (C) is a correct choice.
(D) The sample is "Randomly picking a number between one and ten, inclusive".
The sample space of this event is {1,2,3,4,5,6,7,8,9,10}.
Therefore, expected value of the event is [tex]\frac{1}{10}(1+2+3+4+5+6+7+8+9+10) = \frac{1}{10}(55)=5.5[/tex]
Since 5.5 is not present in the sample space of this event. Therefore, option (D) is not correct either.
Hence, the correct choice is option (C).
please help
i got one of them right
Answers
The trick is to know whether you should be reading your totals going down or across. We will be discussing this possibility carefully for the first question in the group.
In the meantime, letter the questions from A to H
A
A is the first member of a group of 5 where you read going down. You know this because you are give the gender first and then you want the total of the people (boys and girls) who participate in this activity.
So for A you have 8 boys who will choose swimming out of 17 (the rest of course are girls).
P(boy if swimming is the activity) = 8/ 17 = 0.47
B
P(girl if the activity is sports) = 7/27 = 0.26 Did you catch on that you were reading down?
C
P(Girl if the activity is reading) = 4/6 = 0.67
D
P(Boy if the activity is sports) = 20/27 = 0.74
E
This is the first question of the second group. Here you will get your totals by reading across. The reason is that you are given the activity, now you must supply the gender from the total number of people in the group of either boys or girls.
P(Swimming given that it is a girl) = 9/20 = 0.45 In other words you know you area working with girls. What you need to declare is the probability of what these girls will choose.
F
P(probability of reading if it is a boy) = 2/30 = 0.07 Think very carefully how these answers are derived. It's all a matter of reading which total to take and why. In this case you are taking the total number of boys and how many of them are doing the activity.
G
P(Swimming if a Boy) = 8/30 = 0.27
H
P(reading if a girl) = 4/20 = 0.2
Very interesting question. You'll learn a lot if you consider which comes first and what that means.
Heather made a total of $451.78 last month at her part-time job. If she worked 14 hours, how much did she make per hour?
Answers
451.78/14=32.27.
She earned $32.27 per hour.
Heather made $32.27 per hour at her part-time job.
Explanation:To find out how much Heather made per hour at her part-time job, we need to divide her total earnings by the number of hours she worked. Heather made a total of $451.78 and worked 14 hours, so we can calculate her hourly rate by dividing $451.78 by 14.
$451.78 / 14 = $32.27 per hour
Therefore, Heather made $32.27 per hour at her part-time job.
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Assume that all six outcomes of a six-sided number cube have the same probability. What is the theoretical probability of each roll?
• 1:
• 2:
• 3:
• 4:
• 5:
• 6:
Using the uniform probability model you developed, what is the probability of rolling an even number?
1/6 Roll a number cube 25 times. Record your results here.
1st toss
2nd toss
3rd toss
4th toss
5th toss
6th toss
7th toss
8th toss
9th toss
10th toss
11th toss
12th toss
13th toss
14th toss
15th toss
16th toss
17th toss
18th toss
19th toss
20th toss
21st toss
22nd toss
23rd toss
24th toss
25 toss
How many results of 1 did you have? ______________
How many results of 2 did you have? ______________
How many results of 3 did you have? ______________
How many results of 4 did you have? ______________
How many results of 5 did you have? ______________
How many results of 6 did you have? ______________
Based on your data, what is the experimental probability of each roll? •
1 _______ • 2 _______ • 3 _______ • 4 _______ • 5 _______ • 6 _______ Using the probability model based on observed frequencies, what is the probability of rolling an even number? Was your experimental probability different than your theoretical probability? Why or why not?
Answers
Assume that all six outcomes of a six-sided number cube have the same probability. What is the theoretical probability of each roll?
• 1: 1/6
• 2: 2/6
• 3: 3/6
• 4: 4/6
• 5: 5/6
• 6: 6/6
Using the uniform probability model you developed, what is the probability of rolling an even number?
1/6 Roll a number cube 25 times. Record your results here.
1st toss=6 2nd toss=4 3rd toss=6 4th toss=6 5th toss=3 6th toss=3 7th toss=4 8th toss=2 9th toss=6 10th toss=5 11th toss=1 12th toss=4 13th toss = 5 14th toss =1 15th toss=4 16th toss=2 17th toss=2 18th toss=2 19th toss=6 20th toss=5 21st toss=3 22nd toss=4 23rd toss=3 24th toss=3 25 toss=5
How many results of 1 did you have? __2____________ How many results of 2 did you have? ____4__________ How many results of 3 did you have? ____5__________ How many results of 4 did you have? ______5________ How many results of 5 did you have? ______4________ How many results of 6 did you have? ______5________
Based on your data, what is the experimental probability of each roll? 1. 2/25 or 0.08
2. 4/25 or 0.16
3. 5/25 or 0.24
4. 5/25 or 0.2
5.4/25 or 0.16
6. 5/25 or 0.2Using the probability model based on observed frequencies, what is the probability of rolling an even number? 3/6 = ½ or 0.5
Was your experimental probability different than your theoretical probability? Why or why not? It somewhat is! The denominator is 25 for the experimental probability, and 6 for the theoretical probability.
Have a lovely day! Cheerio. :)
The theoretical probability of rolling each number ([tex]1[/tex] through [tex]6[/tex]) on a six-sided number cube is [tex]\(\frac{1}{6}\)[/tex]. The probability of rolling an even number ([tex]2, 4,[/tex] or [tex]6[/tex]) is [tex]\(\frac{3}{6}\)[/tex] or [tex]\(\frac{1}{2}\).[/tex]
Since there are six possible outcomes when rolling a six-sided number cube and each outcome is equally likely, the probability of rolling any specific number is calculated by dividing the number of favorable outcomes (which is 1 for each specific number) by the total number of possible outcomes (which is [tex]6[/tex]). Therefore, the theoretical probability [tex]\(P\)[/tex] for each roll is:
[tex]\[ P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{6} \][/tex]
To find the probability of rolling an even number, we consider the number of even outcomes ([tex]2, 4[/tex], and [tex]6[/tex]) and divide by the total number of possible outcomes:
[tex]\[ P(\text{even}) = P(2) + P(4) + P(6) = \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2} \][/tex]
The experimental probability is calculated based on the results of the [tex]25[/tex]rolls. For each number, the experimental probability is the number of times that number was rolled divided by the total number of rolls ([tex]25[/tex]). For example, if the number [tex]1[/tex] was rolled [tex]4[/tex] times, the experimental probability of rolling a [tex]1[/tex] would be [tex]\(\frac{4}{25}\).[/tex]
The probability of rolling an even number based on observed frequencies would be the sum of the experimental probabilities of rolling a [tex]2, 4[/tex], or [tex]6[/tex]. If the number of rolls for each even number was [tex]\(x\), \(y\),[/tex] and [tex]\(z\)[/tex]respectively, then the experimental probability of rolling an even number would be [tex]\(\frac{x + y + z}{25}\).[/tex]
The experimental probability may differ from the theoretical probability due to random variation and the finite number of trials. In a small number of trials, the observed frequencies may not match the theoretical probabilities exactly. However, as the number of trials increases, the experimental probabilities should converge to the theoretical probabilities. This is due to the law of large numbers, which states that the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.
Jill collected a total of 19 gallons of honey. If she distributed all of the honey equally between 9 jars how much will be in each ja
Answers
an office building in downtown Tampa is 975 feet tall. suppose a scale model of the building was made and its height was 6 1/2 inches tall what is the scale of the model?
Answers
scale factor=measure in the model/measure in the actual
measure in the model=6 1/2 in----> (6*2+1)/2---> 13/2 in
measure in the actual=975 ft
scale factor=(13/2)/975----> 13/(975*2)---> 13/1950
scale factor= 13/1950---> divide by 13----> 1 in/ 150 ft
the answer is
1 in/ 150 ft
Find the local extreme values of the function f(x, y) = xy - x2 - y2 - 3x - 3y + 12
Answers
First compute the first-order partial derivatives and find the critical points.
[tex]f_x=y-2x-3[/tex]
[tex]f_y=x-2y-3[/tex]
Both first order derivatives vanish at [tex](x,y)=(-3,-3)[/tex].
Computing the Hessian, we get
[tex]\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}-2&1\\1&-2\end{bmatrix}[/tex]
We have [tex]\det\mathbf H(x,y)=3>0[/tex], which means [tex](-3,-3)[/tex] is an extremum of [tex]f(x,y)[/tex]. Since [tex]f_{xx}(-3,-3)=-2<0[/tex], this extremum is a local maximum of [tex]f(x,y)[/tex] with a value of 21.
The perimeter of the base of a regular quadrilateral prism is 32 cm. The height of the prism is 2 times greater than the length of the base edge. Find the sum of all edges of the prism.
Answers
A regular quadrilateral prism has 12 edges. It is given perimeter of the base 32 cm. Length of each edge of base will be 32÷4=8 cm. The 4 edges at the top will also have the same number of edges that is 4 with measure 8cm each.
Given: The height of the prism is 2 times greater than the length of the base edge.Height of prism = 2(8)= 16cm. Number of edges with measure 16 cm is 4.
Sum of all the 12 edges= 8+8+8+8+16+16+16+16+8+8+8+8=128 cm.
What is the slope of the line that passes through (2, 5) and (-1, 5) ?
A. -3
B. 0
C. undefined
D. 3
Answers
The answer is to this is B. 0
The diagram below shows the radius of the circular opening of a drinking cup. which of the following is the closest to the circumference of the opening in cm
Answers
Answer:
Its a 12
Step-by-step explanation:
IMPORTANT HELP HURRY
Andrew is two years older than Beatrice, and Chris is three years younger than Beatrice. The product of Andrew's age and Chris' age is 66. How old is Beatrice? (1 point) Extra Content
HINT: Look at the Answers
A. A b2 − b − 72 = 0; 8 years old
B. B b2 − b − 72 = 0; 9 years old
C. C b2 − b − 72 = 0; 10 years’ old
D. D b2 − b − 72 = 0; 11 years’ old
Answers
Therefore Andrew = x + 2
Chris = x - 3
Andrew * Chris = 66
(x + 2)(x - 3) = 66 Remove the brackets.
x^2 + 2x - 3x - 6 = 66
x^2 - x - 6 = 66 Subtract 66 from both sides.
x^2 - x - 72 = 0
(x - 9)(x + 8) = 0
Find the possible values of Bea's age
x - 9 = 0
x = 9 That value works. She can be plus 9 years old.
x + 8 = 0
x = - 8. There's no way she can be - 8 years old
So Bea is 9.
9 <<<<<< Answer
FInd the volume of the cylinder in terms of Pi.
Answers
The formula for the area of a cylinder is [tex]\pi[/tex][tex]r^{2}[/tex]×h
First, we do not have to worry about pi because we are leaving our answer in terms of it so we can move on to the radius squared.
The radius is halfway across a circle so our radius would be 4 and we have to square that and we will get a product of 16.
Lastly, we have to multiply 16 by 8 because 8 is the height of the cylinder
16 × 8 = 128
Therefore, the volume of the cylinder would be 128[tex]\pi[/tex] in.³
A random sample of 150 people was taken from a very large population. ninety of the people in the sample were female. the standard error of the proportion is
Answers
Answer: 0.04
Step-by-step explanation:
The standard error of the proportion is basically gives the spread of the sample proportions about the population mean.Given : Sample size : n= 150
No. of females in the sample : x= 90
Proportion of females = [tex]\hat{p}=\dfrac{x}{n}=\dfrac{90}{150}=0.6[/tex]
Standard error of proportions :
[tex]SE=\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex] , where [tex]\hat{p}[/tex] = sample proportion and n= sample size .
Substitute the corresponding values , we get
[tex]SE=\sqrt{\dfrac{0.6(1-0.6)}{150}}[/tex]
[tex]SE=\sqrt{\dfrac{0.6 (0.4)}{150}}[/tex]
[tex]SE=\sqrt{0.0016}=0.04[/tex]
Hence, the standard error of the proportion is 0.04 .
The standard error of the proportion is 0.04
Since the random sample is 150 people and the number of female in the sample is 90 people
First step is to determine the sample proportion (p)
[tex]Sample proportion (p) =90/150[/tex]
[tex]Sample proportion (p) =0.6[/tex]
Now let determine the standard error of the proportion using this formula
[tex]Standard error= \sqrt{p(-p)/n}[/tex]
Where:
[tex]p=Sample proportion (p)=0.6[/tex]
[tex]p=(1-0.6)= 0.4[/tex]
[tex]n=150[/tex]
Let plug in the formula
Standard error=\sqrt{(0.6) (0.4)/150}[tex]Standard error=\sqrt{(0.6) (0.4)/150}[/tex]
[tex]Standard error= \sqrt{0.24/150}[/tex]
[tex]Standard error= \sqrt{0.0016}[/tex]
[tex]Standard error= 0.04[/tex]
Inconclusion The standard error of the proportion is 0.04
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hey can you please help me posted picture of question
Answers
1. You have the following expression:
(3+3i)-(13+15i)
2. If you want to substract both terms, you need to substract the real numbers and the complex numbers. Then, you obtain:
3+3i-13-15i
(3-13)+(3i-15i)
3. Then, you obtain the following result:
-10-12i
4. Therefore, as you can see, the correct answer is the last option (option D), which is:
D. -10-12i
1.
Find the annual percentage rate, using the annual percentage rate table.
Amount Financed: $2,650
Finance Charge: $484.69
Number of Payments: 36
Answers
Finance Charge: $484.69
Number of Payments: 36
(Finance Charge)/(Amount Financed)*100$=($484.69)/($2,650)*100$
(Finance Charge)/(Amount Financed)*100$=(0.1829)*100$
(Finance Charge)/(Amount Financed)*100$=$18.29
In the row of number of Payments 36, we look for:
(Finance Charge)/(Amount Financed)*100$=$18.29, and we see to which annual porcentage rate it corresponds in the first row
Answer: 11.25%
Ben purchased a 2 liter bottle of soda.
Which of these is equal to 2 liters?
A) 1,000 dl
B) 1,000 ml
C) 2,000 dl
D) 2,000 ml
Answers
The answer to the above question can be explained as under -
Here, we need to convert large units into smaller units of same class i.e. to convert liters into milliliters.
We know that,
1 liter = 1000 milliliters
So, 2 liter of soda will have -
2 X 1 liter = 2 X 1000 milliliters
2 liters of Soda = 2,000 milliliters
Thus, the correct option will be = D) 2,000 ml
what is 66% of 740kilometers
Answers
Convert 66% into a decimal by moving the imaginary decimal point in the front two places to the left.
66% ⇒ 0.66
Now multiply 0.66 × 740.
0.66 × 740 = 488.4
66% of 740 km is 488.4 kilometers.
So, 66% of 740 kilometers is 488.4 kilometers.
I hope this helps!
what is the value of log 0.5^16?
A. -4.00
B. -0.25
C.1.51
D. 2.41
Answers
The above answer will be calculated as -
Which correlation coefficient below is most likely to represented on the graph
Answers
(D) 0.95
Answer:
The correct option is D.
Step-by-step explanation:
The correlation coefficient represent the relationship between two variables. It is denoted by r and the value of r lies from -1 to 1.
If r=-1 and close to -1, then it represents strong negative correlation.
If -1<r<0 and close to -0.5, then it represents weak negative correlation.
If r=0 and close to 0, then it represents no correlation.
If 0<r<1 and close to 0.5, then it represents weak positive correlation.
If r=1 and close to 1, then it represents strong positive correlation.
From the given graph it is clear than the data represents the strong positive correlation because the data set lie close to the positive strait line. So, the value of r is near to 1.
Option 1, 2 represent the negative correlation and option 3 represents weak positive correlation.
Since 0.95 close to 1, therefore it represents strong positive correlation.
Hence option D is correct.
what ratio is less than 15:24.these are the answer choices > 1:2, 7:8, 19:24, 6:8
Answers
Short answer: 1:2
Why?
To find this out, we must simplify 15:24. 15:24 can be simplified to 5/8. So, which is 5/8 larger than? (5/8 < 19/24) ~~ (5/8 < 7/8) ~~ (5/8 < 6/8) ~~ (5/8 > 1/2)
5/8 > 1/2
Hope this helped you! ♥
Answer:
Step-by-step explanation:
tour answer would me a or 1:2
The graph of the equation xy=4 is symmetric with respect to which of the following?
a.
the y-axis
c.
the line y = x
b.
the line y=-x+4
d.
the x-axis
Answers
Therefore, the answer is the second option shown above, which is:
the line y = x
Below is a graph where you can see the symmetry of xy = 4 with respect to the oblique axis x = y. This axis cuts the curves just at its apex
Answer:
a
Step-by-step explanation:
its a
your total savings varies inversely with the amount spent on Bill's. if your savings is $300 when your cost of Bill's are $65. What would your savings be when your cost of Bills is $145.
Answers
S α 1/B
S = k/B Where k = Constant.
When S = $300, B = 65
Then,
300 = k/65
k = 300*65 = 19500
Therefore,
For B = $145,
S= 19500/145 = $134.48
A certain kind of animal weighs about 75 pounds at birth and gains about 2 pounds per day for the first few weeks. Determine those days for which the animal's weight is more than 125 pounds.
The animal's weight is more than 125 pounds when the animal is more than
........... days old.
Answers
25
Step-by-step explanation:Let w represent the weight of the animal in pounds, and d the age in days. The problem statement tells us ...
... w = 75 +2d
We want to find d when w > 125.
... 75 +2d > 125 . . . . . substitute the above expression for w
... 2d > 50 . . . . . . . . . subtract 75
... d > 25 . . . . . . . . . . . divide by 2
The animal will weigh more than 125 pounds when it is more than 25 days old.
The cost of producing transistors decreases by 20% every year. If it currently costs $440 to produce a billion transistors, how much will it cost to produce a billion transistors in 7 years? If necessary, round your answer to the nearest cent.
Answers
C(n) = 440(1-0.2)^n, where C(n) = cost of production of billion transistors in year n.
In short,
C(n) = 440(0.8)^n
In seven years, n = 7 and therefore cost of production of billion transistors is,
C(n) = 440(0.8)^7 = $92.27
y=ab^x
where:
y= cost after time x
a=initial cost
b=growth factor
thus plugging in the values in the expression we get:
y=440(0.80)^x
hence
when x=7, then:
y=440(0.8)^7
y=$92.275
y~$92.30
What is the y-value if the vertex of 4x^2 + 8x - 8
Answers
The x-value is -b/(2a) = -8/(2·4) = -1.
The corresponding y-value is ...
... 4(-1)² +8(-1) -8 = 4 -8 -8 = -12
The y-value of the vertex is -12.
Answer:
The y-value of the vertex is [tex]-12[/tex]
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
[tex]f(x)=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
In this problem we have
[tex]f(x)=4x^{2}+8x-8[/tex] -----> this a vertical parabola open upward
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)+8=4x^{2}+8x[/tex]
Factor the leading coefficient
[tex]f(x)+8=4(x^{2}+2x)[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]f(x)+8+4=4(x^{2}+2x+1)[/tex]
[tex]f(x)+12=4(x^{2}+2x+1)[/tex]
Rewrite as perfect squares
[tex]f(x)+12=4(x+1)^{2}[/tex]
[tex]f(x)=4(x+1)^{2}-12[/tex]
The vertex is the point [tex](-1,-12)[/tex]
The y-value of the vertex is [tex]-12[/tex]
the library is 4 miles from the post office how many yards is the library from the post office
Answers
Divide 406 by −14. A) −29 B) −34 C) 34 D) 44
Answers
A. -29
Hope this helps !
11.34<11.340 true or false