5

Sociol] sts navenmounoenalcame rates am Inmmerceoempefaiure150 @OC Dedde Inp cnme [BIe nas Deen approrime6512Lunetenumoecnmesmorinano[ne avefaqe Tcninit Omcarammdez...

Question

Sociol] sts navenmounoenalcame rates am Inmmerceoempefaiure150 @OC Dedde Inp cnme [BIe nas Deen approrime6512Lunetenumoecnmesmorinano[ne avefaqe Tcninit Omcarammdezrees Fahrenheit Ino dyurdnu (un uraluicMay wes 77" ardbyAemalon4tIcmpttaluu a; meoMaat7ot-1 chinu ralu [eq atu urd 6nldtAl Ine Hay iha crime rata Simolily vounanswar "rsing cnimeFer Morih

Sociol] sts navenmounoenalcame rates am Inmmerceo empefaiure 150 @OC Dedde Inp cnme [BIe nas Deen approrime 6512 Lunete numoe cnmes morinano [ne avefaqe Tcninit Omcaramm dezrees Fahrenheit Ino dyurdnu (un uraluic May wes 77" ardby Aemalon4t Icmpttaluu a; meo Maat 7ot-1 chinu ralu [eq atu urd 6nldt Al Ine Hay iha crime rata Simolily vounanswar " rsing cnime Fer Morih



Answers

Sociologists have found that crime rates are influenced by temperature. In a mid western town of 100,000 people, the crime rate has been approximated as

$$C=\frac{1}{10}(T-60)^{2}+100$$

where $C$ is the number of crimes per month and $T$ is the average monthly temperature in degrees Fahrenheit. The average temperature for May was $76^{\circ},$ and by the end of May the temperature was rising at the rate of $8^{\circ}$ per month. How fast is the crime rate rising at the end of May?

So this is another slightly worried you're related rates. Problem. Um, so let's identify relations in question were told that the crime, right, see, which is the object of consideration in this question equals 1 10 off the temperature of minus 60 squared plus 100. And this is in a town of 100,000 people. But that doesn't matter. What does matter is that the temperature we are interested in is 76 degrees fire. It hides and up. The temperature is increasing with eight Greece per day. And the question is, of course, at what grade is the crime rate increasing? So, um, we have everything we need for a related rates problem. So we can start by differentiating differentiating this relation. You find that the rate of change and crime rates equals, um, one 10 times chain rule. So too, T minus 60 multiplies by Petey G plus nothing because 100. It's constant tire. So, um, well, we can simplify this a little bit. We can oh, catch these constants or collapses Constance into 11 50. Um, but that's our differentiation stuff. Then you substitution step. In this case, the CVT equals 1/5 76 minus 60 multiplied by eight and then sold. So in this case, the equation solves the real just compute in this case, so interested in D C B T. And it's isolated on one side of the equation. So 76 minus 60 is 16 so we have 16 times eight. Fight it by five, um, which isn't actually an insecure selection still stuck into a calculator. You bet 16 times a divided by five equals 25 0.6, so the crime rate is going up by 25.6 incidents per day.

To solve this question, have to convert both off these temperatures from degrees foreign heart into degrees Celsius. For that, we can use this equation. So for the first temperature, we have two. Following this temperature in degrees Celsius is equals to five, divided by nine times the temperature in degrees Fahrenheit, which is 136 minus 32. Then these results in a temperature off five, divided by nine times 104 on. This results in approximately 57.8, so the temperature is 57.8 degrees Celsius for the first item. For the next temperature, we have the following. The temperature in degrees sells yes, is given by five divided by nine times miners 129 minus 32. And this results in the following five divided by nine times. Here we have a negative number minus 161 and these results in approximately minus 89.4. So the second temperature is minus 89.4 degrees Celsius. And these is the answer to this question.

So you can get the data. A couple of things come here. So four thing is that the maximum point occurs in the seventh month and the highest temperature is 105.1 and the minimum temperature occurs in January, which is the first month of the year, and that minimum temperature is 65.5 degrees Fahrenheit. So forth thing we can calculate is the amplitude, which is maximum temperature minus the minimum temperature divided by two. So that would be 100 and 5.1 minus 65 point 5/2. So we get a value for a which is equal to 1928 now. The next thing we notice, since it's a year, so the period is going to be 12. So be which is to pine divided by a period would be to pie divided by 12 which is higher work six. So we got a Reebok be now. The next thing that we can calculate is D, which is the vertical shift so D is equal to maximum, plus the minima divided by two. So we have 105.1 plus 65.5 and divide that by two. That gives you 85.3. Now. The next thing we need to do is where we first get this mean temperature. So this D would actually be the mean temperature, so the mean temperature first occurs. I didn't pay pro aan act Mies. That's when T is equal to four. So now we are ready to fight our equation. Which would be why is equal to a, which is 19.8 sign times pi over six. This is B Times T minus four and then plus D, which is 85.3 So expanding that Why is he going to 19 point it sign high over six times T minus two pi over three plus 85.3

So looking at the daytime the table What we find is that the maximum temperature occurs in February, which is the second month, and that maximum temperature is 81.3 and the minimum temperature offers in July, which is the seventh month and that minimum temperature is 68.73 spire night. So from here we can calculate the values Bianca Cute, eh, which is maximum minus the minimum, divided by two. So that would be 81.3 minus 68.7, divided by two. So that equals 6.3. The period since the temperatures given over a year would B 12 and B is equal to two pi divided by the period. So that would be to pie divided by 12. And that's equal to pi work. Six. Next, we'll calculate the mean temperature, which would be put to D so D is equal to maximum, plus the minimum divided like to so the maximum we have is 81.3, and the minimum we have a 60 year 600.7 so at them, and then divide a sum by two that gives the value for T is equal to 80.0. Now these mean temperature first uppers in March so mean temperature first occurs in March, and we know that march is the third month off the year and also during March. So the tempter in February is higher and the temperature in April is lower. So the model would be why is equal to negative A, which is a 6.3 sign off pi over six times T minus three and then plus 80.0. Or why is equal to negative 6.3 sign off high over 16 minus piped over to plus 80.0.


Similar Solved Questions

5 answers
John decides to start saving money for a new car: He knows he can invest money into an account which will earn 6.5% APR, compounded weekly, and would like to have saved $10,000 after 5 years_How much money will he need to invest into the account now so that he has S10,000 after 5 years? 7226.76 Previewb_ Determine the APY (Annual Percent Yield) for the account:27.73%PreviewDetermine the 5-year percent change for the account_ 27.73 % Preview
John decides to start saving money for a new car: He knows he can invest money into an account which will earn 6.5% APR, compounded weekly, and would like to have saved $10,000 after 5 years_ How much money will he need to invest into the account now so that he has S10,000 after 5 years? 7226.76 Pre...
5 answers
Previous ProblemProblem ListNext Problempoint)Find the area of the shaded region below:x=y _2y=1X=ey=-Area
Previous Problem Problem List Next Problem point) Find the area of the shaded region below: x=y _2 y=1 X=e y=- Area...
5 answers
JO>~Jdry In neta LO Would ge genetic drift events like population bottlenecks increase or decrease genetic diversity in a population?
JO> ~Jdry In neta LO Would ge genetic drift events like population bottlenecks increase or decrease genetic diversity in a population?...
5 answers
Briefly compare and contrast competitive Versus non-competitive inhibition Discuss the role of these rcspcctivc inhibitors on Knand Var Provide relevant biochemical cxample of cach inhibitor and why It 15 uportant
Briefly compare and contrast competitive Versus non-competitive inhibition Discuss the role of these rcspcctivc inhibitors on Knand Var Provide relevant biochemical cxample of cach inhibitor and why It 15 uportant...
5 answers
The relative order of reactivity of $mathrm{F}^{-}, mathrm{Cl}^{-} mathrm{Br}$ and $mathrm{I}^{-}$is/ are(a) $mathrm{F}^{-}<mathrm{Cl}^{-}<mathrm{Br}^{-}<mathrm{I}^{-}$in polar solvent(b) $mathrm{F}^{-}>mathrm{Cl}^{-}>mathrm{Br}>mathrm{I}^{-}$in non polar solvent(c) $mathrm{F}^{-}<mathrm{Cl}^{-}<mathrm{Br}^{-}<mathrm{I}^{-}$in non polar solvent(d) $mathrm{F}^{-}>mathrm{Cl}^{-}>mathrm{Br}^{-}>mathrm{I}^{-}$in polar solvent
The relative order of reactivity of $mathrm{F}^{-}, mathrm{Cl}^{-} mathrm{Br}$ and $mathrm{I}^{-}$is/ are (a) $mathrm{F}^{-}<mathrm{Cl}^{-}<mathrm{Br}^{-}<mathrm{I}^{-}$in polar solvent (b) $mathrm{F}^{-}>mathrm{Cl}^{-}>mathrm{Br}>mathrm{I}^{-}$in non polar solvent (c) $mathrm{F}^{...
5 answers
Question 3 Sketch the region of integration and reverse the order of integration of the integral 6' $ sin(z + y6.7) dydr (5 points)
Question 3 Sketch the region of integration and reverse the order of integration of the integral 6' $ sin(z + y6.7) dydr (5 points)...
5 answers
A7,50 %g walermolon dropped Irom rost Irom tha root of & 18.5 t-tall building and Idels m approclable air resistance.K= ValueUnitsSubmltroquctlanswctPart !Just Beforo it slrikes the Founa mhal Le watemt an speed? Exprcs your onswer with tho appropriate unlts.ValueUnitsSubmitRrauertaneot
A7,50 %g walermolon dropped Irom rost Irom tha root of & 18.5 t-tall building and Idels m approclable air resistance. K= Value Units Submlt roquctlanswct Part ! Just Beforo it slrikes the Founa mhal Le watemt an speed? Exprcs your onswer with tho appropriate unlts. Value Units Submit Rrauertaneo...
5 answers
T F Changes to a function parameter always affect the original argument as well.
T F Changes to a function parameter always affect the original argument as well....
5 answers
Evaluale the definite integral J (212 40none of the aboveQuestion 1010 ptsEvaluate the definite integral f" x' dr:
Evaluale the definite integral J (2 1 2 40 none of the above Question 10 10 pts Evaluate the definite integral f" x' dr:...
1 answers
Evaluate the integrals. $$\int_{-1}^{1} \int_{0}^{1} \int_{0}^{2}(x+y+z) d y d x d z$$
Evaluate the integrals. $$\int_{-1}^{1} \int_{0}^{1} \int_{0}^{2}(x+y+z) d y d x d z$$...
1 answers
You are now 25 years old and would like to retire at age 55 with a retirement fund of $\$ 1,000,000 .$ How much should you deposit at the end of each month for the next 30 years in an IRA paying $10 \%$ annual interest compounded monthly to achieve your goal? Round to the nearest dollar.
You are now 25 years old and would like to retire at age 55 with a retirement fund of $\$ 1,000,000 .$ How much should you deposit at the end of each month for the next 30 years in an IRA paying $10 \%$ annual interest compounded monthly to achieve your goal? Round to the nearest dollar....
5 answers
Consider the permutation 2 3 4 5 6 0 = 6 3 1 2 Write 0 as product of disjoint cycles. Write 0 as product of transpositions. 8 Compute 02 and write 02 as product of disjoint cycles. Compute 0~ 1 and write ~1 as a product of disjoint cycles.
Consider the permutation 2 3 4 5 6 0 = 6 3 1 2 Write 0 as product of disjoint cycles. Write 0 as product of transpositions. 8 Compute 02 and write 02 as product of disjoint cycles. Compute 0~ 1 and write ~1 as a product of disjoint cycles....
5 answers
If the equilibrium constant; Keq; for the reaction A+ B => C+ D is 1.2X 102 M, select the standard Iree-energy change &G: following reaction at 37 "€ (or 310 K) with R 8.314 Jlmol K 1.07107 Jimol1A Alntoll1472 JolDC6 Tma
If the equilibrium constant; Keq; for the reaction A+ B => C+ D is 1.2X 102 M, select the standard Iree-energy change &G: following reaction at 37 "€ (or 310 K) with R 8.314 Jlmol K 1.07 107 Jimol 1A Alntoll 1472 Jol DC6 Tma...
5 answers
~/1 points SercP11 22.3.PO11.Mi;My NotesAsk Your Teacherluser buam incident Jn ungle "88 to the verticu anto solutiom COm svrup watln (a) If the beam refracted to 19.409 the vertical what the index cf refraction the syrup solution?(b) Suppose the Iightwith wave length 632.8 nmvacuun; FindTave lengththe solution_(c) Find Its frequencysolution,(d) FindSpeedtne solution; MsNeed Help?Read ItMagter It
~/1 points SercP11 22.3.PO11.Mi; My Notes Ask Your Teacher luser buam incident Jn ungle "88 to the verticu anto solutiom COm svrup watln (a) If the beam refracted to 19.409 the vertical what the index cf refraction the syrup solution? (b) Suppose the Iight with wave length 632.8 nm vacuun; Find...
5 answers
Determine whether the series is absolutely convergent or conditionally convergent or divergent: (-1)' a) Vnz n=2(-1)"(2nt +7) b) 6n9 _ Zn n=1
Determine whether the series is absolutely convergent or conditionally convergent or divergent: (-1)' a) Vnz n=2 (-1)"(2nt +7) b) 6n9 _ Zn n=1...
5 answers
Question 6The line integralds where € is the line segment joining the points (0, 0) and (1, 1) , can be evaluated by
Question 6 The line integral ds where € is the line segment joining the points (0, 0) and (1, 1) , can be evaluated by...

-- 0.020380--