Differential equation is a way to represents the function and its variable by relating them.Hence the differential equation that describe the relationship between S and T is,
[tex]S \propto \dfrac{1}{log_e T}[/tex]
Given-
The quantity of S increases, the quantity of T decreases.
The rate of change of the quantity of S with respect to the quantity of T present is inversely proportional to the natural logarithm of the quantity of T.
What is differential equation?Differential equation is a way to represents the function and its variable by relating them.
As the quantity of S changes with respect to the quantity of T present is inversely proportional. Thus,
[tex]S \propto \dfrac{1}{T}[/tex]
But quantity of S changes inversely proportional to the natural logarithm of the quantity of T. The natural logarithm of a number is its logarithm to the base of e (constant).
Thus the equation can be given is,
[tex]S \propto \dfrac{1}{log_e T}[/tex]
Hence the differential equation that describe the relationship between S and T is,
[tex]S \propto \dfrac{1}{log_e T}[/tex]
Learn more about the differential equation here;
https://brainly.com/question/25731911
Pending Review Question 7
Alex borrowed $3500 from two banks. One bank charged a simple interest of 8% and another bank
charged a simple interest of 12%. If he paid a total interest of $332 for one year, find the amount that he
borrowed from each bank.
Answer:
$ 2,200 for 8%, $ 1,300 for 12%
Step-by-step explanation:
I=PRT
Let Bank 1 be x
332= x (8%) + (3,500-x) 12%
332= x (0.08) + (3,500-x) 0.12 change the percent to decimal
332= 0.08x + 420 - 0.12x
0.04x= 420-332
x= [tex]\frac{88}{0.04}[/tex]
x= 2,200 (Bank 1)
Bank 2= 3,500-Bank 1
Bank 2= 3,500- 2,200
Bank 2= 1,300
[tex](4+\sqrt{-7}) (3+\sqrt{-7})[/tex]
Which family lives the farthest from Disneyland?
Family A:
Family D
y = 95 - 55
Distance
50
Family B:
40
Family B lives 120 miles from Disneyland
and drives 60 mph.
30
Family
20
Hours
Distance
from
Disneyland
SO
10
0
1.5
0
0.2 0.4 0.6 0.8
112 Time (hours)
Family A
O Family B
O Family C
Family D
SOMEBODY ANSWER PLZ ASAP
Answer:
I think false
Step-by-step explanation:
If 13 candy bars cost $19.76, how much do 20 candy bars cost?
Answer:
$30.40
Step-by-step explanation:
to find out how much 20 candy bars would cost, first, we have to find out how much 1 candy bar costs. we do this by dividing $19.76 by 13.
$19.76 ÷ 13 = $1.52
so now we know that one candy bar costs $1.52. now, we multiply this value to 20, to know how much 20 candy bars cost. therefore, we get:
20 × $1.52 = $30.40
What is the percent of increase from 75 to 87?
Answer:
16 percent
Step-by-step explanation:
75 is the old value and 87 is the new value. In this case we have a positive change (increase) of 16 percent because the new value is greater than the old value.
Pls answer I'll give brainliest to whoever replies first
A group of campers walked 4 2/3 miles along a hiking trail. Another group of campers walked 1/4 of that distance with the first group before turning off onto another trail. How many miles did the two groups of campers walk with one another ?
Answer:
14 / 12 miles or 1 1/6 miles
Step-by-step explanation:
A group of campers walked 4 2/3 miles along a hiking trail.
Distance = 4 2/3 miles
Another group of campers walked 1/4 of that distance with the first group before turning off onto another trail.
That is; 1/4 of 4 2/3 miles
How many miles did the two groups of campers walk with one another ?
This is obtained by solving 1/4 of 4 2/3 miles
Converting 4 2/3 to an improper fraction;
4 2/3 = 14 / 3 Miles
1/4 of 14 / 3
1 / 4 * 14 / 3
= 14 / 12 miles or 1 1/6 miles
9(5r + 6s) if r = 7 and s =3
rob is saving to buy a new mp3 player. For every $15 he earns babysitting, he saves $7. On Saaturday, Rob erened $30 babysitting. How much money did he save. If he erend $30, he saved how many
Answer:
thanks for the points
Step-by-step explanation:
Find the product. 7/10 X 3/6
what is meaning of divya
Which of the following is equal to the expression below?
(5-6)2
A. -54
1
В.
D. -512
The answer is 1/5^12.
Multiply the -6 by 2 to get 5^-12. Then, to make the exponent positive, move it to the denominator to get your answer, 1 over 5^12.
Mira's six test scores are given. What is the
positive difference between the mean of the
scores and the median of the scores?
86, 72, 92, 62, 99, 93
Answer:
Step-by-step explanation:
What is the total volume of Diet
Coke in this six pack? Each can
is 5 inches tall and has a diameter
of 3 inches.
a. 47.1 in 3
b. 141.3 ins
c. 35.3 in
d. 211.95 in3
Answer:
so what was it because i need help NEVER MIND ITS 211.95
Step-by-step explanation:
Answer: 211.95 in3
Step-by-step explanation:
Subtracting fractions
Answer:
Step-by-step explanation:
Make sure the denominators are the same.
Subtract the numerators. Put the answer over the same denominator.
Simplify the fraction (if needed).
can anyone help me please?
Answer: I think it might be A bit Im not sure
Step-by-step explanation:
Answer:
i think its A not suree
Step-by-step explanation:
If 8 x/2 = 2 3/8 x 4 ¾ find x
Answer:
x = 361/32
Step-by-step explanation:
I'm assuming that "8 x/2" is a mixed number.
Trina is cooking her favorite dish. She started with 51/2fluid ounces of vegetable oil. While she cooks, she uses a teaspoon
of vegetable oil, which is 1/6 of a fluid Ounce, x times. After she made the dish, Trina had at least 3 1/3 fluid Ounces of
vegetable oil left. Which statement best describes the number of times she used a teaspoon of vegetable oil?
Answer:
trina used a teaspoon of vegetable oil at most 13 times
Step-by-step explanation:
hope this helps :D
In parts (a)−(d) below, either use the information given to determine the distribution of the random variable, or show that the information given is not sufficient by describing at least two different random variables that satisfy the given condition. (a) X is a random variable such that MX(t) = e 6t 2 when |t| < 2. (b) Y is a random variable such that MY (t) = 2 2−t for t < 0.5. (c) Z is a random variable such that MZ(t) = [infinity] for t ≥ 5. (d) W is a random variable such that MW (2)
Answer:
a.) X ≈ N (0, 12)
b.) Y ≈ exp(2)
c.) The given distribution is not defined.
d.) Not a standard form of any distribution .
Step-by-step explanation:
Given - In parts (a)−(d) below, either use the information given to determine
the distribution of the random variable, or show that the information
given is not sufficient by describing at least two different random
variables that satisfy the given condition.
To find - (a) X is a random variable such that Mₓ(t) = [tex]e^{6t^{2} }[/tex] when |t| < 2.
(b) Y is a random variable such that [tex]M_{Y}[/tex](t) = [tex]\frac{2}{2 - t}[/tex] for t < 0.5.
(c) Z is a random variable such that [tex]M_{Z}[/tex](t) = ∞ for t ≥ 5.
(d) W is a random variable such that [tex]M_{W}[/tex](2) = 2
Proof -
a.)
As we know that the moment generating function of normal distribution is given by
Mₓ(t) = [tex]e^{ut + \frac{1}{2}t^{2} \sigma^{2}}[/tex]
Now,
Mₓ(t) = [tex]e^{6t^{2} }[/tex]
= [tex]e^{0(t) + \frac{12}{2} t^{2} }[/tex]
⇒μ = 0, σ = 12
Nd it is represented by
X ≈ N (0, 12)
b.)
Moment generating function of exponential function is given by
[tex]M_{Y}[/tex](t) = [tex]( 1 - \frac{t}{\theta})^{-1}[/tex]
Now,
[tex]M_{Y}[/tex](t) = [tex]\frac{2}{2 - t}[/tex] for t < 0.5.
= [tex]\frac{1}{\frac{2 - t}{2} }[/tex]
= [tex]\frac{1}{1 - \frac{t}{2} }[/tex]
= [tex]( 1 - \frac{t}{2} )^{-1}[/tex]
And it is represented by
Y ≈ exp(2)
c.)
Z is a random variable such that [tex]M_{Z}[/tex](t) = ∞ for t ≥ 5.
The given distribution is undefined.
d.)
[tex]M_{W}[/tex](2) = E([tex]e^{2w}[/tex] )
= [tex]\int\limits^{-\infty}_{\infty} {e^{2w} f(w) } \, dw[/tex]
= 2
It is not the standard form of any distribution.
Which inequality describes the graph?
Answer:
I think it is B. -3x < - 30, but I might be wrong.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
since you see that the line goes from 10 and does not include it it would be x<10
or because we have to flip sign when multiplying negative -3x>-30
so A
WHICH NUMBER IS BIGGER? -10 OR -1 EXPLAIN *
Answer:
-1, because the number is a negative think like your in debt. which would you like to be in one dollar in debt or ten dollars in b\debt
Step-by-step explanation:
Matching Equivalent Expressions
Quick
Check
Match each addition expression on the left with an equivalent expression on the right.
15 + 9
2(3 + 2)
8 + 10
2(5+6)
6 + 4
3(5 + 3)
10 + 12
2(4+5)
Answer:
15+9 is 3(5+3)
8+10 is 2(4+5)
6+4 is 2(3+2)
10+12 is 2(5+6)
If you were to reflect point B across the y axis, which quadrant would it be located
Answer:
the answer is (6,2)
Step-by-step explanation:
Hope this helps
{ x is an odd whole number less than 9}
This may be more complicated than it looks but here are the odd numbers before nine:
1, 3, 5, 7
Hope this helps!
Mel paid $15.75 for 6 greeting
cards. Some of the cards cost
$2.50 each, and some cost $3.25
each. Let x represent the number
of cards that cost $2.50 each,
and y represent the number of
cards that cost $3.25 each. This
situation can be represented by
the system x + y = 6 and
2.5x + 3.25y = 15.75. How many
of each type of card did Mei
purchase?
Answer:
Step-by-step explanation:
x + y = 6 -------------(I)
y = 6 -x
2.5x + 3.25y = 15.75 -------------(II)
substitute y = 6 - x in equation (II)
2.5x + 3.25*(6 - x) = 15.75 {Distributive property: a(b +c) =a*b + b*c}
2.5x + 3.25*6 - x * 3.25 = 15.75
2.5x + 19.5 - 3.25x = 15.75
2.5x - 3.25x + 19.5 = 15.75 {Combine like terms}
-0.75x + 19.5 = 15.75
-0.75x=15.75 - 19.5
-0.75x = -3.75
x = -3.75/-0.75
x = 5
Plugin x = 5 in (I)
5 + y = 6
y = 6 - 5
y = 1
hi can you please help me with my work
Which of the following represents a function
Answer:
The last one
Step-by-step explanation:
The Memorial baseball team purchased three times as many gloves as bats this year. If each glove cost $50 and each bat cost $30 and a TOTAL of $720 was spent on gloves and bats, Find the cost of one glove and one bat.
Answer:
$80
Step-by-step explanation:
PLZ HELY ILL MARK BRANILEST
Answer:
518
Step-by-step explanation:
14 x 74 = 1036 1036 / 2 = 518
( really need brainliest , hope it helps )
( first )
