The price of a cup of coffee was $2.65 yesterday. today, the price fell to $2.50 . find the percentage decrease. round your answ
1 answer:
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Answer:
From the calculation for both the accounts, it is clear that both the account double in the same time period of 14 years 26 days .
Step-by-step explanation:
Given as :
The principal for the first account = p = $100
The rate of interest = r = 5% compounded annually
The account gets double , so, Amount = A = $200
Let the time after which account gets double = t years
So<u>, From Compound Interest method</u>
Amount = Principal ×
As amount is double its principal
So, A = 2 × $100 = $200
Or, A = p ×
Or, $200 = $100 ×
Or, =
Or, 2 =
Taking Log both side
=
Or, 0.3010 = t
Or, 0.3010 = t × 0.0211
∴ t =
I.e t = 14.26
So, The time period to get account double is 14 years 26 days
<u>Again </u>
Amount = Principal ×
Or, A = p ×
As amount is double its principal
So, A = 2 × $1000 = $2000
Or, $2000 = $1000 ×
Or, =
Or, 2 =
Taking Log both side
=
Or, 0.3010 = t
Or, 0.3010 = t × 0.0211
∴ t =
I.e t = 14.26
So, The time period to get account double is 14 years 26 days
Hence From the calculation for both the accounts, it is clear that both the account double in the same time period of 14 years 26 days . Answer
The polynomial equation <u>x³ - 4x² - 7x + 28 = 0</u>, has solutions <u>-√7, √7,</u> and <u>4</u>, among which <u>√7</u> and <u>4</u> are positive real solutions. Hence we have two positive real solutions. Hence, <u>option D</u> is the right choice.
In the question, we are asked for the number of positive real solutions for the polynomial equation, x³ - 4x² - 7x + 28 = 0.
To find the solutions, we do as follows:
x³ - 4x² - 7x + 28 = 0,
or, (x³ - 7x) - (4x² + 28) = 0 {Grouping},
or, x(x² - 7) - 4(x² - 7) = 0 {Taking common},
or, (x - 4)(x² - 7) = 0 {Grouping},
or, (x - 4)(x + √7)(x - √7) = 0 {Using the formula: }.
By the zero-product rule, the solutions are:
x - 4 = 0, or, x = 4,
x + √7 = 0, or, x = -√7,
x - √7 = 0, or, x = √7.
Thus, the positive real solutions are 4, and √7. Hence, there are two positive real solutions.
Thus, the polynomial equation <u>x³ - 4x² - 7x + 28 = 0</u>, has solutions <u>-√7, √7,</u> and <u>4</u>, among which <u>√7</u> and <u>4</u> are positive real solutions. Hence we have two positive real solutions. Hence, <u>option D</u> is the right choice.
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The complete question is:
"Which of the following expresses the possible number of positive real solutions for the polynomial equation shown below?
x³-4x²-7x+28=0
a. two or zero
b. three or one
c. one
d. two"
Answer:
Julie jogged five times further than Jan.
Step-by-step explanation:
We can find this solution just by dividing Julie's distance by Jan's:
So Julie jogged five times further.