**A building has a 9’ deep basement (foundation) wall that
is 160’ long. The wall has no windows. On average, 8’ of the wall
is below grade (underground). Assume an outside air temperature of
10°F, an inside temperature of 70°F, and an average ground
temperature of 45°F.**

**a. Determined the rate of heat loss through the wall
below grade if it is uninsulated.**

**b. Determine the rate of heat loss through the wall
below grade if it is insulated with an R-value of about 12
hr*°F*ft2/Btu.**

**A commercial building is built on a slab on grade
foundation that is a 120’ by 48’ rectangular shape.
Assume the outside design temperature is -5°F. Determine the rate
of heat loss through the exterior
edge of a concrete slab.**

**a. For an uninsulated slab edge perimeter.**

**b. For a slab edge perimeter insulated with 1” of
perimeter insulation (an R-value of about 2.5).**

**c. For a slab edge perimeter insulated with 2” of
perimeter insulation (an R-value of about 5).**

In: Advanced Math

What are the conditions on the parameters for linear multistep methods so that the methods are regular? Would appreciate a detailed explanation.

In: Advanced Math

A mass weighing 19lb stretches a spring 8in. The mass is attached to a viscous damper with damping constant 4lb⋅s/ft. The mass is pushed upward, contracting the spring a distance of 2in, and then set into motion with a downward velocity of 7in/s. Determine the position u of the mass at any time t. Use 32ft/s2 as the acceleration due to gravity. Pay close attention to the units. Answer must be in inches

In: Advanced Math

Suppose that f(t) is the unique solution to the IVP y' = t + y^2 , y(0) = 5 and g(t) is the unique solution to the IVP y' = 1/(y + t^2) , y(5) = 0.

a. Determine an IVP that the function y = f(g(t)) solves. [Hint: You differential equation part will contain the functions t, g(t), and y in its expression.

b. (2 points) Show that the function y = t also solves this IVP.

c. (2 points) Use the uniqueness part of the Existence & Uniqueness Theorem to conclude that f and g are inverses.

In: Advanced Math

1. Methylergonovine maleate is available in 0.2 mg tablets. The prescription is for 0.4 mg every 8 hours after delivery for 48 hours. How many tablets are needed for one day (24 hours)? Round your final answer to one decimal place. Type your final answer and label in the answer. Thank you!

2. An infant was born at 30 weeks weighing 2 pounds 9 oz. (1.162 kg). The baby is being fed Special Care Formula (24 calories per ounce). Based on a premature infant's cardiac needs of 130 calories/kg/day.

a. How many calories per day does this baby require?

b. How many ml of formula is required every 24 hours to provide the needed calories determined in the previous question?

c. Using the conversion factor of 1 ounce=30 ml, how many ml should be given at each feeding in order to provide the needed calories, if the infant is feed every three hours? Round your final answer to the nearest whole calorie. Type you final answer and label. Thank you!

3. The client is experiencing a postpartum hemorrhage. The physician prescribes 30 IU Oxytocin added to a 500 ml bag of Lactated Ringers to run at 150 ml/hr. Oxytocin is available 10 IU per ml.

a. How many ml of Oxytocin will be added to the bag of Lactated Ringers? Round your final answer to one decimal place with label.

b. After one hour at the prescribed rate of 150 ml/hr, how many units of Oxytocin has the client received?

c. The mother is still hemorrhaging. The primary care provider prescribes Carboprost tromethamine 350 mcg intramuscularly. The drug is available in 250 mcg per 1 ml. how much volume in ml will the nurse administer? Please round answer to one decimal place. Thank you!

4. The nurse is preparing to administer 1 mg Phytonadione Intramuscularly to a newborn. The medication on hand is 2 mg/1 ml. What is the correct volume of the injection in ml? Round your final answer to two decimal places.

5. The nurse is to give a new mother Ibuprofen 800 mg by mouth for severe uterine cramping after delivery. The pharmacy stocks Ibuprofen as 200 mg tablets. How many tablets will the nurse give? Round your final answer to one decimal place. Thank you!

In: Advanced Math

Compute the Fourier series for the triangle and sawtoothwaves,
i.e. the following functions, periodically extended to R:

f(x) = |x|, −1 < x ≤ 1; g(x) = x−π ,−π ≤ x < π . Plot each
function and its Fourier polynomials of degrees up to 4.

In: Advanced Math

`Hello math expert... `

`plz answer clearly. `

`Is Virus Covid-19 (exponential function), or is it only (doubled )for infections?`

`plz explain mathematically? `

`i think it is duobled not exponential but i can not explain... `

`i need help in detail plz?? `

In: Advanced Math

G
is a group and H is a normal subgroup of G. List the elements of
*G/H* and then write the table of *G/H*.

1. G=Z10, H= {0,5}. (Explain why G/H is congruent to Z5)

2. G=S4 and H= {e, (12)(34), (13)(24), (14)(23)

In: Advanced Math

Give an example of a ring homomorphism f:R -> S where M is a
maximal ideal of R but M^e is not a maximal ideal of S

note that I^e - is the extension notation f(I)S generated by
f(I) as the entension of R, a commutative ring

In: Advanced Math

For
3 digits password.

a). Find all possible outcomes of 3 digits of 0-9 numbers with
no repetition allowed

b). Find all possible outcomes of 3 digits of 0-9 numbers with
repeition allowed but no more than two repetition

c). Find all possible outcomes of 3 digits of 0-9 for
repetition numbers only.

d) Find all possible outcomes of 3 digits of 0-9 for repeition
numbers only but no more than 2 repetition.

e). Find all possible outcomes of 3 digits of 0-9 for
non-repetition numbers only but no more than 2 repetition
allowed.

please complete all. this is not difficult. complicated math
is not needed

In: Advanced Math

(answer all three parts} Normal (i.e. average)
internal temperature for humans is approximately 98 degrees,
If a given population has a standard deviation of 1.2 degrees, what
is the maximum temperature for the lowest 35% of the
population? What is the minimum temperature for the highest
25% of the population.

2. If you take a 50 question true-false final exam
(two-points each question) and you never paid attention in the
class (or knew anything about the topic on your own), what is
probability you will receive a grade of 56 or less, in which case
you will fail the class? What is the probability you will get
at least 30 questions right, which will give you a passing
grade in the class?

In: Advanced Math

A forest has three components and nine vertices. How many edges does it have? Explain. It is not enough to give an example; you must show that all examples of such a forest have the asserted number of edges.

In: Advanced Math

The *Bessel equation* of order *p* is
t^{2}y" + ty' + (t^{2} - p^{2})y = 0. In
this problem, assume that p = 1/2:

a.) Show that y_{1} = sin(t / sqrt(t)) and y_{2}
= cos(t / sqrt(t)) are linearly independent solutions for 0 < t
< infinity.

b.) Use the result from part (a), and the preamble in Exercise
3, to find the general solution of t^{2}y" + ty' +
(t^{2} - (1/4))y = t^{3/2}cos(t). (answer should
be: 1/2 sin(t) sqrt(t))

**Preamble of Exercise 3: The formula for a particular solution
given in (3.42) applies to the more general problem of solving y" +
p(t)y' + q(t)y = f(t). In this case, y_{1} and
y_{2} are independent solutions of the associated
homogeneous equation y" + p(t)y' + q(t)y = 0.

Please show work!

In: Advanced Math

Solve the given initial-value problem. y′′′ + 18y′′ + 81y′ = 0, y(0) = 0, y′(0) = 1, y′′(0) = −10.

In: Advanced Math