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2 years ago

Q1 a) Kamahi invests some money which earns compound interest every year. His investment

2 answers:

7 0

Without any more information, it sounds like interest is compounded continuously, in which case the value of the investment A is given by

$A=Pe^{rt}$

where P is the principal investment, r is the interest rate, and t is the number of years.

At the end of the second year (t = 2), the value is A = 60,500, and after the fourth year (t = 4), the value is A = 73,205. So solve the system

$\begin{cases}60,500=Pe^{2r}\\73,205=Pe^{4r}\end{cases}$

for r. You can eliminate P by dividing

$\dfrac{Pe^{4r}}{Pe^{2r}}=\dfrac{73,205}{60,500}\implies e^{2r}=\dfrac{121}{100}$

Take the logarithm (log here means natural log) of both sides to get

2r = log(121/100)

r = 1/2 log(121/100)

r ≈ 0.0953

So the interest rate is about 9.53%.

gulaghasi [49]2 years ago

3 0

Answer: 2=2

Step-by-step explanation:

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An open-top rectangular box with square base is to be made from 100 square feet of material, as shown.

-Dominant- [34]

The largest possible volume of the given box is; 96.28 ft³

<h3>How to maximize volume of a box?</h3>

Let b be the length and the width of the base (length and width are the same since the base is square).

Let h be the height of the box.

The surface area of the box is;

S = b² + 4bh

We are given S = 100 ft². Thus;

b² + 4bh = 100

h = (100 - b²)/4b

Volume of the box in terms of b will be;

V(b) = b²h = b² * (100 - b²)/4b

V(b) = 25b - b³/4

The volume is maximum when dV/db = 0. Thus;

dV/db = 25 - 3b²/4

25 - 3b²/4 = 0

√(100/3) = b

b = 5.77 ft

Thus;

h = (100 - (√(100/3)²)/4(5.77)

h = 2.8885 ft

Thus;

Largest volume = [√(100/3)]² * 2.8885

Largest Volume = 96.28 ft³

Read more about Maximizing Volume at; brainly.com/question/1869299

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4 0

1 year ago

Marcus wants to use a model to determine the difference

grigory [225]

Electron transfer theory describes the parameters which control the rate at which an electron is transferred from one atom or molecule to another.

<h3>What was the basic principle of Marcus theory?</h3>

In theoretical chemistry, Marcus theory is a theory originally developed by Rudolph A. Marcus, starting in 1956, to explain the rates of electron transfer reactions – the rate at which an electron can move or jump from one chemical species.
Marcus' method (also referred to as Marcus's method and Method of Marcus) is a structural analysis method which was designed to design concrete slabs with rectangular, orthogonal shapes. It represents an adaptation of the strip method.
Marcus Hush theory (M-H theory) was developed in 1956 by Rudolph A. Marcus which explains the fundamentals of the redox/ electron transfer reactions in terms of the rate of jumping/moving an electron from oxidant species (electron donor) to the reductant (electron acceptor).
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We want to see how we can model the difference: -8 - 3 + 3

The correct option is D:

"add 3 positive counters and 3 negative counters"

We know that Marcus starts with 8 negative counters, corresponding to the first term in our difference.

Now, let's study the math of our expression.

-8 - 3 + 3

Remember that we can perform the operation in any order we want, so we can write this as:

-8 + (-3 + 3)

Notice that the thing inside the parentheses is equal to zero, so we have:

- 8 + (-3 + 3) = -8

So to not change the value, we add 3 and we subtract 3.

Now if we have 8 negative counters, and we want to add 3 positive counters and not change the value, then we also need to add 3 negative counters to "cancel" the 3 positive counters we added.

Then the correct option is D.

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brainly.com/question/23140234

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8 0

1 year ago

A radio station had 120 tickets to a concert. They gave away 2 times as many tickets to listeners as to employees. How many tick

enyata [817]

Step-by-step explanation:

If the tickets given to employees = 40

Then tickets given to listeners = 2 x no of employees tickets

= 2 x40 = 80