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Air flows into a compressor in a jet engine at 0.03 m3/s and 247 kPa.  During the process the temperature of the air increases from -35 °C to 444 °C.  Determine the power input required in kW to 2 decimal places.  Take the gas constant R=0.287 (kPam3)/(kgK) and the specific heat at constant pressure of the air to be 1.018 kJ/(kgK).of air to be 1.009 kJ/(kgK).

A car travels at 108 kph from A to B for t seconds, applies the brakes for 4 seconds between B and C to give the car a constant deceleration and a speed of 72 kph at C, and finally travels at this speed from C to D, also for t seconds. If the total horizontal distance from A to D is 3100 m, determine the distance between A and B.

iL(6s-4)/((s-2)^(2) +16)

At t=0 the current to a dc electric motor is reversed, resulting in an angular displacement of the motor shaft given by 𝜃(𝑡) = (250 𝑟𝑎𝑑/𝑠 )𝑡 − (20.0 𝑟𝑎𝑑/𝑠 2 )𝑡 2 − (1.50 𝑟𝑎𝑑/𝑠 3 ) 𝑡 3 . (a) At what time is the angular velocity of the motor shaft zero? (b) Calculate the angular acceleration at the instant that the motor shaft has zero angular velocity. (c) How many revolutions does the motor shaft turn through between the time when the current is reversed and the instant when the angular velocity is zero? (d) How fast was the motor shaft rotating at t=0 when the current was reversed? (e) Calculate the average angular velocity for the time period from t=0 to the time calculated in part (a). A

implicit differentiation1.if y^2=×

2.if ×^2+3×y+2y^2=3,find dy/dx at point (-1,2)

The table shows the number of students in a school's beginning and advanced orchestra classes. The student pay a fee for instruction books: $5 for brass, $5 for woodwinds, and $8 for strings. Find the amount each class will spend on books.

$\begin{array}{|ccc|}\hline & Advanced& Beginning\\ Brass& 12& 28\\ Strings& 22& 25\\ Woodwinds& 18& 30\\ \hline\end{array}$

The following advanced exercise use a generalized ratio test to determine convergence of some series that arise in particular applications, including the ratio and root test, are not powerful enough to determine their convergence. The test states that if $ $\underset{n\to \mathrm{\infty }}{lim}\frac{a_{2n}}{a_n}<1/2$ then ${\displaystyle \sum a_n}$ converges, while if $\underset{n\to \mathrm{\infty }}{lim}\frac{a_{2n+1}}{a_n}>1/2$ then ${\displaystyle \sum a_n}$  diverges. Let ${\displaystyle a_n=\frac{n^{\ln n}}{{\left(\ln n\right)}^n}}$. Show that $\frac{a_{2n}}{a_n}\to 0$ as ${\displaystyle n\to \mathrm{\infty }}$

Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken eight blood tests for uric acid. The mean concentration was $\overline{x}=5.35\mathrm{mg}$ . $\mathrm{dl}.$ The distribution of uric acid in healthy adult males can be assumed to be normal, with $\sigma =1.85\mathrm{mg}$. $\mathrm{dl}$ .Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error?

Painful bone metastases are common in advanced prostate cancer. Physicians often order treatment with strontium-89 (89Sr), a radionuclide with a strong affinity for bone tissue. A patient is given a sample containing 4 mCi of ${\displaystyle {89}^{Sr}}$.
If 20% of the ${\displaystyle {89}^{Sr}}$ remains in the body after 90 days, write a function of the form ${\displaystyle Q\left(t\right)=Q0e^{-kt}}$ to model the amount Q(t) of radioactivity in the body t days after the initial dose.
b. what is the biological half-life of ${89}^{Sr}$ under this treatment? Round to the nearest tenth of a day.

Advances in medical science and healthier lifestyles have resulted in longer life expectancies. The life expectancy of a male whose current age is x years old is $f(x)=0.0069502x^2-1.6357x+93.76(60\le x\le 75)$ years. What is the life expectancy of a male whose current age is 65? A male whose current age is 75?

As of October, 2016 the world`s largest pumpkin weighed 1190 kilograms. In order to grow a record-setting pumpkin, the fruits mass must increase by an average of $1.27f{t}^3/day$. If we assume that the dinsity of raw pumpkin is approximately $0.50g/c{m}^3$ we can convert this to an increase in volume of $1.27f{t}^3/day$. Question: If the volume of a spherical pumpkinn is increasing at $\frac{1}{27}f{t}^3/day$, then how fast is the surface area of the pumpkin changing when the diameter of the pumpkin is b ft?
Give your answer with two decimal places, and ensure that you include unots.
Note: Equations for the volume and surface area of a sphere are on D2L in several places.

Although tea is the world’s most widely consumed beverage after water, little is known about its nutritional value. Folacin is the only B vitamin present in any significant amount in tea, and recent advances in assay methods have made accurate determination of folacin content feasible. Consider the accompanying data on folacin content for randomly selected specimens of the four leading brands of green tea.

$\underline{\begin{array}{}\text{Brand}& \text{Observations}& & & & & & \\ 1& 7.9& 6.2& 6.6& 8.6& 8.9& 10.1& 9.6\\ 2& 5.7& 7.5& 9.8& 6.1& 8.4& & \\ 3& 6.8& 7.5& 5.0& 7.4& 5.3& 6.1& \\ 4& 6.4& 7.1& 7.9& 4.5& 5.0& 4.0& \end{array}}$
(Data is based on “Folacin Content of Tea,” J. Amer. Dietetic Assoc., 1983: 627–632.) Does this data suggest that true average folacin content is the same for all brands? a. Carry out a test using α=.05α=.05 via the P-value method. b. Assess the plausibility of any assumptions required for your analysis in part (a). c. Perform a multiple comparisons analysis to identify significant differences among brands.

Maurice and Lester are twins who have just graduated from college. They have both been offered jobs where their take-home pay would be $2500 per month. Their parents have given Maurice and Lester two options for a graduation gift. Option 1: If they choose to pursue a graduate degree, their parents will give each of them a gift of $35,000. However, they must pay for their tuition and living expenses out of the gift. Option 2: If they choose to go directly into the workforce, their parents will give each of them a gift of $5000. Maurice decides to go to graduate school for 2 years. He locks in a tuition rate by paying $11,500 for the 2 years in advance, and he figures that his monthly expenses will be $1000. Lester decides to go straight into the workforce. Lester finds that after paying his rent, utilities, and other living expenses, he will be able to save $200 per month. Their parents deposit the appropriate amount of money in a money market account for each twin. The money market accounts are currently paying a nominal interest rate of 3 percent, compounded monthly. At the end of 2 years, Lester receives a raise and decides to save $250 each month. Maurice receives a $5000 graduation gift from his parents and deposits this amount into his money market account. Maurice goes to work and saves $500 each month. Complete the equations below for the money market account balance for each twin. Let the initial balance u0 be the account balance at the end of 2 years. Write an expression for this month's account balance un in terms of un−1. Recall that the interest rate for the account is 3 percent, compounded monthly. Maurice: $u_0=\mathrm{\$}5248.47,u_n=\text{\_\_\_\_\_.}$Lester: $u_0=\text{\_\_\_\_\_},u_n=\text{\_\_\_\_\_}$.