In: Math

Let *f*(*t*) be the weight (in grams) of a solid
sitting in a beaker of water after *t* minutes have elapsed.
Suppose that the solid dissolves in such a way that the rate of
change (in grams/minute) of the weight of the solid at any time
*t* can be determined from the weight using the
forumula:

*f*′(*t*)=−4*f*(*t*)(6+*f*(*t*))

If there is 1 grams of solid at time *t*=2 estimate the
amount of solid 1 second later.

Let f (t) be the amount of yeast (in grams) in a culture of
yeast at time t (in minutes), and let g (t) represent the rate at
which the culture of yeast is growing (in grams/min) at time t (in
minutes).
(a) Write an expression in terms of f (t) for the amount the
culture grew (in grams) from 25 to 30 minutes.
(b) Write an expression in terms of g (t) for the amount the
culture grew (in...

A beaker is sitting on a scale. Block A in the figure hangs by a cord from spring balance D and is submerged in a liquid C contained in beaker B. The mass of the beaker is 1.35kg; the mass of the liquid is 1.70kg. Balance D reads 3.55kg and balance E reads 7.50kg. The volume of block A is 3.90×10-3 m^3.What is the density of the liquid?p=? kg/m^3What will the balance D read if block A is pulled up...

Let f(t)=5t2−t.
a) Find f(t+h):
b) Find f(t+h)−f(t):
c) Find f(t+h)−f(t)/h: side note: (f(t+h)=f(t) is on top of
fraction and h is on bottom)
d) Find f′(t):
pls circle the 4 answers

Let f(t) =t^2−1 and g(t) =e^t.
(a) Graph f(g(t)) and g(f(t)).
(b) Which is larger,f(g(5)) or g(f(5))? Justify your answer.
(c) Which is larger, (f(g(5)))′or g(f(5))′? Justify your
answer.

A
beaker with 195 mL of acetic acid buffer with a pH of 5.000 is
sitting in a lab. The total molarity of acid and conjugate base in
the buffer is 0.100 M. If 8.50 mL of 0.330 M HCl solution is added
to the beaker, how much would the pH change? the pKa of the acetic
acid is 4.740.

Let
f (t) =
{
7
0 ≤ t ≤ 2π
cos(5t)
2π < t ≤ 4π
e3(t−4π)
t > 4π
(a)
f (t) can be written in the form
g1(t) +
g2(t)U(t −
2π) +
g3(t)U(t −
4π)
where U(t) is the Heaviside function. Enter the
functions g1(t),
g2(t), and
g3(t), into the answer box below (in
that order), separated with commas.
(b)
Compute the Laplace transform of
f (t).

1. Let T : Mn×n(F) → Mn×n(F) be the transposition map, T(A) =
At. Compute the characteristic polynomial of T. You may wish to use
the basis of Mn×n(F) consisting of the matrices eij + eji, eij −eji
and eii.
2. Let A = (a b c d) (2 by 2 matrix) and let T :
M2×2(F) → M2×2(F) be deﬁned asT (B) = AB. Represent T as a 4×4
matrix using the ordered basis {e11,e21,e12,e22}, and use this
matrix to...

Submerged Sphere in a Beaker
A cylindrical beaker of height 0.100m
and negligible weight is filled to the brim with a fluid of
density
? = 890kg/m3 . When the beaker is placed on
a scale, its weight is measured to be 1.00N
.(Figure 1)
A ball of density ?b =
5000kg/m3 and volume V =
60.0cm3 is then submerged in the fluid,
so that some of the fluid spills over the side of the beaker. The
ball is held...

Compound A is a water-soluble solid at room temperature with a
molecular weight of 138.12 amu. Describe one (or more)
experiment(s) that you would perform in lab to determine if
Compound A is a strong acid, weak acid, strong base, weak base, or
none of these in water. State what you would do, what you would
measure, and how you would decide the nature of Compound A in
water?

Let T : P3(R) → P4(R) be defined by T(f(x)) = 5f′(x)-∫ f(t)dt
(integral from 0 to x)
1. Show that T is a linear transformation.
2.Find dim (P3(R)) and dim (P4(R)).
3.Find rank(T). Find nullity(T)
4. Is T one-to-one? Is T onto? Justify your answers.

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