Answer:
[tex]\dfrac{dV}{dt} =-4 \pi k (\dfrac{3}{4 \pi})^\dfrac{2}{3} }}V^{\dfrac{2}{3}}[/tex]
k = 3.022
Step-by-step explanation:
Given that:
A spherical raindrop evaporates at a rate proportional to its surface area.
The surface area SA of a spherical object is given by the relation:
SA = 4πr²
Write down a differ- ential equation for its volume as a function as a function of time.
So; to differentiate Volume (V) in respect to time (t) ;then:
[tex]\dfrac{dV}{dt} =-k( 4 \pi r^2)[/tex]
Likewise; we know known that the volume of a sphere V = [tex]\dfrac{4}{3} \pi r^3[/tex]
Thus, from above;
[tex]3V = 4 \pi r^3[/tex]
[tex]\dfrac{3V}{4 \pi} = r^3[/tex]
[tex]r^3 = (\dfrac{3}{4 \pi })^{\dfrac{2}{3}}V^{\dfrac{2}{3}}[/tex]
[tex]r^2 = 4 \pi( \dfrac{3}{4 \pi})\dfrac{2}{3}V\dfrac{2}{3}[/tex]
Thus; solving the differential:
[tex]\dfrac{dV}{dt} =-k( 4 \pi * 4 \pi( \dfrac{3}{4 \pi})\dfrac{2}{3}V\dfrac{2}{3})[/tex]
[tex]\dfrac{dV}{dt} =-4 \pi k (\dfrac{3}{4 \pi})^\dfrac{2}{3} }}V^{\dfrac{2}{3}}[/tex]
So;
we are to find the constant proportionality K
If Volume V = 1 cm³ and the time = 10 sec
[tex]\dfrac{1}{10} =-4 \pi k (\dfrac{3}{4 \pi})^\dfrac{2}{3} }}(1)^{\dfrac{2}{3}}[/tex]
0.1 = - 4π k (0.3848 × 1)
0.1 = - 4π k × 0.3848
4π k = 0.3848/0.1
4π k = 3.848
k = 3.848/4π
k = 3.022
How are ΔABC and ΔADE related?
Answer:
They are congruent
Step-by-step explanation:
Answer this as quick as possible please! (NO EXPLANATION REQUIRED!) <3
Answer: 9 Apples
Step-by-step explanation:
Given the following :
Total number of bags = 12
Mean of the distribution(m) = 8
Number of apples (x):
6 - - - - 7 - - - - 8 - - - - 9 - - - - 10
Frequency (f) :
1 - - - - 4 - - - - 2 - - - - 3 - - - - 1
Therefore :
Let number of apples in the 12th bag = y
Frequency of 12th bag : (12 - 11) = 1
Mean of distribution(m) :
Sum of ( f * x) / sum of f
Sum of (f * x) = (6*1)+(7*4)+(8*2)+(9*3)+(10*1)+(y*1)
Sum of (f * x) = (6+28+16+27+10+y) = 87 + y
Sum of f = 12
From :
m = Sum of ( f * x) / sum of f
8 = (87 + y) / 12
87 + y = 12 * 8
87 + y = 96
y = 96 - 87
y = 9
Number of apples in 12th bag is 9 apples
1)Find the third side of a triangle when two sides of the triangle is 4 and the included angle measuring 89 degrees
2)you were asked by your teacher to add up the numbers 1 to 100. Please show all work
3)determine if the foci for the following ellipse are correct and explain your reasoning 7x2 + 8y2 = 30; foci: (sqrt11, 0), (-sqrt11, 0)
Answer:
1) The length of the third side is 5.607 units
2) The sum of the numbers from 1 to 100 is 5050
3) For the x-axis, foci: ((√15/28), 0) and (-(√15/28), 0)
For the y-axis, foci: (0, (√15/28)) and (0, -(√15/28))
Step-by-step explanation:
1) When two sides of the triangle are equal to 4 then the triangle is an isosceles triangle
Given that the included angle (the angle between the two sides) is 89°, we have;
The other two base angles are equal to {180 - 89)/2 = 91/2 = 45.5°
Therefore, we have from cosine rule;
a² = b² + c² - 2·b·c·cos(A)
We note that the angle opposite the third side is the included angle 89°, therefore, when we put a as the third side in the above equation, we have;
a² = 4² + 4² - 2×4×4×cos(89°)
a² = 31.44
a = 5.607
The length of the third side is 5.607 units
2) The numbers 1 to 100 form an arithmetic series with the first term, a = 1 and the common difference, d = 1 with the number of terms n = 100
The sum of an arithmetic progression, Sₙ, is given as follows;
[tex]S_n = \dfrac{n}{2}\cdot (2 \cdot a + (n - 1) d)[/tex]
Therefore, by plugging in the values, we have;
Sₙ = 100/2*(2*1 + (100 - 1)*1) = 100/2*(101) = 5050
The sum of the numbers from 1 to 100 is 5050
3) The foci of an ellipse 7·x² + 8·y² = 30 is found as follows;
Dividing both sides of the equation by 30 gives;
7/30·x² + 8/30·y² = 30/30
7/30·x² + 8/30·y² = 30/30
7/30·x² + 4/15·y² = 1
Which is of the form;
x²/a² + y²/b² = 1
For the x-axis we have
c² = a² - b²
c² = 30/7 - 15/4 = 15/28
h = 0, k = 0
Foci: ((√15/28), 0) and (-(√15/28), 0)
For the y-axis, we have;
x²/b² + y²/a² = 1
The foci are then (0, (√15/28)) and (0, -(√15/28)).
Factor 2x^2+25x+50. Rewrite the trinomial with the x-term expanded, using the two factors
Answer:
[tex]\boxed{(x+10)(2x+5)}[/tex]
Step-by-step explanation:
=> [tex]2x^2+25x+50[/tex]
Using mid-term break formula
=> [tex]2x^2+20x+5x+50[/tex]
=> 2x(x+10)+5(x+10)
Taking (x+10) common
=> (x+10)(2x+5)
Let ƒ(x) = x^2 + 2x and g(x) = 2x. Evaluate the composition (ƒ ∘ g)(2).
Answer:
The answer is option D.
Step-by-step explanation:
f(x) = x² + 2x
g(x) = 2x
To find (ƒ ∘ g)(2) first find (ƒ ∘ g)
To find (ƒ ∘ g) wherever you see x in f(x) replace it with g(x)
That's
(ƒ ∘ g) = (2x)² + 2(2x)
= 4x² + 4x
Substitute 2 into the expression
That's
(ƒ ∘ g)(2) = 4(2)² + 4(2)
= 4(4) + 8
= 16 + 8
= 24
Hope this helps you.
a closet of towels contains exactly 10 white towels. the probability of choosing a white towel from the closet is 2/5. how many of the towels in the closet are not white?
Hey there! :)
Answer:
15 towels.
Step-by-step explanation:
We are given:
10 white towels
P( choosing a white towel) = 2/5.
Find the total number of towels in the closet:
2/5x = 10
Divide both sides by 2/5:
2/5x · (5/2) = 10 · (5/2)
x = 25.
Subtract the number of white towels from the total to find the number non-white towels:
25 - 10 = 15 towels.
the number 792 and 990, written as the product of their prime factors are 792 = 23 x 32 x 11 and 990 = 2 x 9 x 5 x 1. Hence, find the greatest whole number that can divide both 792 and 990 exactly.
Answer:
198
Step-by-step explanation:
Create two equations, one that will model a linear relation and one that will not (e.g., y = -3x +2, y = 4x2 -7). Describe the ways by which you could determine whether it is a linear relation. Include calculations, graphs, tables of values and anything else you feel will support your argument.
Answer:
linear: y = x + 1
non-linear: y = x² + 1
Step-by-step explanation:
In a linear relationship, from one pair (x1,y1) to other one (x2,y2) that satisfies the equation, there is a constant k, so that k = (y2 - y1)/(x2 - x1).
Equation: y = x + 1
Computing some points as an example:
x | y
0 | 1
1 | 2
2 | 3
3 | 4
(2-1)/(1-0) = (3-2)/(2-1) = (4-3)/(3-2) = 1. Therefore, the equation is linear.
Equation: y = x² + 1
Computing some points as an example:
x | y
0 | 1
1 | 2
2 | 5
3 | 10
(2-1)/(1-0) ≠ (5-2)/(2-1) ≠ (10-5)/(3-2). Therefore, the equation is not linear.
Which equation has the solutions x = 1 plus-or-minus StartRoot 5 EndRoot? x2 + 2x + 4 = 0 x2 – 2x + 4 = 0 x2 + 2x – 4 = 0 x2 – 2x – 4 = 0
Answer:
x^2 - 2x - 4 = 0.
Step-by-step explanation:
Written in factor form we have:
(x - ( 1 + √5)( x - (1 - √5)) = 0
(x - 1 -√5)( x - 1 +√5)) = 0 Expanding:
x^2 - x +√5x - x + 1 - √5 - √5x + √5 - 5 = 0
x^2 - 2x - 4 = 0.
Answer: D!!!!!!!
Step-by-step explanation:
plz help !! write two real world situations that you can model using the exponential function f(x)=2 to the power of x
Answer:
Two real world situations are shown below.
Step-by-step explanation:
Initial population of a certain bacteria is 1 thousand and the population doubles in each hour. So, population of bacteria (in thousands) after x hours is
[tex]f(x)=1(2)^x[/tex]
[tex]f(x)=(2)^x[/tex]
A person invests 1 lakh rupees in shares and the amount is twice at the end of each year. So, total amount (in lakhs) after x years is
[tex]f(x)=1(2)^x[/tex]
[tex]f(x)=(2)^x[/tex]
Hello does anybody know what the answer to this question is : 32² x 4 Will give brainliest :)
Answer:
4096
Step-by-step explanation:
used a calculator but u always do indicies first due to bidmas
Answer:
4096
Step-by-step explanation:
The little two on top of the 32 means squared or that we need to multiply 32 by itself.
So 32*32 equals 1024
Then we multiply it by 4 to give us 4096.
what is 20 times 13 times 50?
Answer:
=13000
Step-by-step explanation:
20×13×50
=1000×13
=13000
Answer:
13 000
Step-by-step explanation:
we use associativity20 × 13 × 50 =
= (20×50) × 13
= 1 000 × 13
= 13 000
Maya is signing her daughter up for summer activities. Some of the activities cost $10, and some of them cost $20. Maya pays a total of $130 for 9 activities. How many of each activity did she sign her daughter up for?
Answer:
(5,4)
Step-by-step explanation:
10x + 20y = 130
x + y = 9
you can solve by substitution
x = 9 - y
10 (9 - y) + 20y = 130
90 - 10y + 20y = 130
90 + 10y = 130 (subtract 90 from both sides)
10y = 40
y = 4
Plug the answer back in the original equations to solve for x
x + 4 = 9 (subtract 4 from both sides)
x = 5
The number of activities that cost $10 is 4.
The number of activities that cost $20 is 5.
What are the linear equations that represent the question?
10a + 20b = 130 equation 1
a + b = 9 equation 2
Where:
a = number of activities that cost $10b = number of activities that cost $20What is the number of activities cost $20?Multiply equation 2 by 10
10a + 10b = 90 equation 3
Subtract equation 3 from equation 2
$10b = $40
b = $40 / $10
b = 4
What is the number of activities cost $10?Subtract 4 from 9: 9 - 4 = 5
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
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VERY MAD NOONE WILL ANSWER ME
Answer: Only C
Step-by-step explanation:
Equation C simplified to 0 = 0, meaning x has no effect on the equation and cancels out. Thus, it can be any value.
** BRAINLIEST IF ANSWERED**
The area of the regular hexagon is 50 in sq. What is the measure of the apothem? *
10 in
2 in
25 in
5 in
Answer:
Area of apothem is 8.33 inches
Step-by-step explanation:
Mathematically,
Area of hexagon = 1/2 * apothem * number of sides * length of side
Area = 50 in square
apothem = ?
number of sides = 6
Length of side = 2 inches
Substituting the values, we have;
50 = 1/2 * A * 6 * 2
50 = 6A
A = 50/6
A = 8.33 inches
A school has 300 eighth-grade students and 200 ninth-grade students. The secretary randomly selects 12 eighth-grade students and 8 ninth-grade students to obtain a sample of size 20. What kind of sampling is this?
Simple random sampling
Stratified random sampling
Systematic sampling
Convenience sampling
Answer:
stratified random sampling
Step-by-step explanation:
Dara drove from home to the airport to pick up her
friend and then came back home on the same route.
Her average speed on the way to the airport was
55 miles
per
hour (mph), and her average speed on
the way back home was 45 mph. If the total driving
time was 1 hour and 20 minutes, how far, in miles, is
the airport from Dara's home?
Answer:
33 miles
Step-by-step explanation:
Trip to airport:
distance = d1
speed = s1 = 55 mph
time = t1
Trip home:
distance = d2
speed = s2 = 45 mph
time = t2
We are told the same route was used for both trips, so
d1 = d2
The total time was 1 hr 20 min = 1 hr + 20/60 hr = 4/3 hr.
t1 + t2 = 4/3
t2 = 4/3 - t1
speed = distance/time
distance = speed * time
d1 = s1 * t1
d2 = s2 * t2
d1 = d2, so
s1 * t1 = s2 * t2
t2 = 4/3 - t1; s1 = 55; s2 = 45
55 * t1 = 45(4/3 - t1)
55t1 = 60 - 45t1
100t1 = 60
t1 = 0.6
The time to get the the airport was 0.6 hr. Now we find the distance.
d1 = s1 * t1
d1 = 55 * 0.6
d1 = 33
The distance is 33 miles.
The airport is at a distance of 33 miles from Dara's home.
What is the relation between speed, distance, and time?Speed is directly proportional to distance and inversely proportional to time. Its equation is given as:
Speed = Distance/Time.
The other equations, formed using this equation are:
Distance = Speed*Time
Time = Distance/Speed.
How to solve the question?In the question, we are informed that Dara drove from home to the airport to pick up her friend and then came back home on the same route. Her average speed on the way to the airport was 55 miles per hour (mph), and her average speed on the way back home was 45 mph.
We are asked to find the distance between Dara's home and the airport, if the total driving time was 1 hour 20 minutes.
We assume the distance between Dara's home and the airport to be x miles.
As she went to the airport and came back from the airport via the same route, her distance in both the cases will be x miles.
Time taken by Dara to go from home to the airport,
t1 = Distance/Speed = x/55 (Since, her average speed on the way to the airport was 55 mph).
Time taken by Dara on the way back home,
t2= Distance/Speed = x/45 (Since, her average speed on the way back home was 45 mph).
Now, total driving time can be written as,
t1 + t2,
= x/55 + x/45,
= (9x + 11x)/495,
= 20x/495,
= 4x/99.
Now, we know that this time is given as 1 hour and 20 minutes = 1 1/3 hours = 4/3 hours.
Therefore, we an write the equation:
4x/99 = 4/3,
or, x = (4*99)/(4*3) = 33.
Therefore, the airport is at a distance of 33 miles from Dara's home.
Learn more about speed, distance, and time at
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How many grams of fat in 96g of margarine
Answer:
11g's of fat are in 96g's of margarine
Step-by-step explanation:
The polynomial equation x cubed + x squared = negative 9 x minus 9 has complex roots plus-or-minus 3 i. What is the other root? Use a graphing calculator and a system of equations.
Answer:
-1,3i,-3i
Step-by-step explanation:
X^3+x^2=-9x-9
x^3+x^2+9x+9=0
x^2(x+1)+9(x+1)=0 factorize by taking x+1 common factor
(x+1)(x^2+9)=0
x+1=0 then x=-1
(x^2+9)=0 then x=+ 0r - 3i
Answer: -1 is the correct answer
Step-by-step explanation:
What’s an constant in numbers
Answer:
Always the same variable.
Step-by-step explanation:
When the question says "x is always constant", it means that the x variable does not change, and it is always the same number.
Answer:
Step-by-step explanation:
In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants.
BRAINLIEST! HELP ASAP MATH PLSSS
Answer: The answer would be the second one.
Step-by-step explanation:
It is hard to explain but, I made and equation that would go with the problem which would be 2 points for every goal plus the free goals for every goal. (2g+f) and in then end it should all equal 15 so the equation so far would be 2g+f =15. This then leave you with three answers left. then I had plugged in a random number to solve it. g and f exacly should be the same number because for every goal you get a free point so if you get one goal then one extra point, if three goals then three extra points. so if you plug in 5 then 2 times 5 plus 5 is 15. The similarities between g and f is if you subtract them it is always going to be zero. Which makes the second answer correct for this problem.
The sum of three consecutive integers is 36. Find the largest integer.
Answer:
13
Step-by-step explanation:
(n-2) +(n-1) +n =3n-3=36
n=(36+3)/3=13
Consecutive integers are 11,12 and 13
Answer: 13
Step-by-step explanation:
The easy way to do this is simply to divide 36 by three. 36/3 = 12. Thus, 12 is the middle integer and the integers are 11,12,13, the largest of which is 13.
Personnel selection. Suppose that 6 female and 6 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at random from the 12 finalists, what is the probability of selecting (A) 3 females and 2 males? (B) 4 females and 1 male? (C) 5 females? (D) At least 4 females?
Answer:
The answer is below
Step-by-step explanation:
The possible ways of choosing r items from a total of n item is given as C(n,r) = [tex]\frac{n!}{(n-r)!r!}[/tex]
Suppose that 6 female and 6 male applicants have been successfully screened for 5 positions.
Since they are 12 finalists and only 5 positions, the total number of possible outcomes is:
[tex]Total\ number\ of \ outcome (n(s))=C(12,5)=\frac{12!}{(12-5)!5!} =792[/tex]
A) 3 females and 2 males
The possible ways of choosing 3 females and 2 males is given as:
[tex]n(e)=C(6,3)*C(6,2) = \frac{6!}{(6-3)!3!}* \frac{6!}{(6-2)!2!}=20*15=300[/tex]
probability of selecting 3 females and 2 males P(E) = [tex]\frac{n(e)}{n(s)}=\frac{300}{792}=0.379[/tex]
B) 4 females and 1 males
The possible ways of choosing 4 females and 1 males is given as:
[tex]n(e)=C(6,4)*C(6,1) = \frac{6!}{(6-4)!4!}* \frac{6!}{(6-1)!1!}=15*6=90[/tex]
probability of selecting 4 females and 1 males P(E) = [tex]\frac{n(e)}{n(s)}=\frac{90}{792}=0.1136[/tex]
C) 5 females
The possible ways of choosing 5 females is given as:
[tex]n(f)=C(6,5) = \frac{6!}{(6-5)!5!}=6[/tex]
probability of selecting 5 females = [tex]\frac{n(f)}{n(s)}=\frac{6}{792}[/tex]
(D) At least 4 females
This can be done by choosing 4 females out of 6 females i.e. C(6,4) , 5 females out of 6 females i.e C(6,5) and 1 male out of six male i.e (6,1)
The possible ways of choosing atleast 4 females is given as:
[tex]n(h)=C(6,5)*C(6,4)*C(6,1)= \frac{6!}{(6-5)!5!}* \frac{6!}{(6-4)!4!}* \frac{6!}{(6-1)!1!}=6*15*6=540[/tex]
probability of selecting atleast 4 females = [tex]\frac{n(h)}{n(s)}=\frac{540}{792}[/tex]
If an apple has a mass of 25 kg and a momentum of 50 kg-m/s
south, what is its velocity?
O 5 m/s south
O 125 m/s north
0 0.2 m/s south
2 m/s south
Answer:
2m/s south
Step-by-step explanation:
p = mv
Where p is the momentum, m is the mass, while v is the velocity.
Given that
m = 25kg
v = ?
p = 50kgm/s
Substituting the values into the formula.
50kgm/s = 25×v
50kgm/s = 25v
Divide both sides by 25
v = 50/25
v = 2m/s
From the option list, the answer is
2m/s south
PLEASE HELP ASAP The equation cos x=sqrt3/2 is an identity. True or false
Answer:
Step-by-step explanation:truest
Answer:
Its False
Step-by-step explanation:
to be an identity the equation has to be true for all values in the domain, sqrt3/2 is a specific value
Please help ASAP. Plz answer top question thanks so much. Your help is much appreciated.
Answer:
It 7 hours and 5 minutes to complete the race because it would be 8 times 50 which equals 400 and 400 plus 250 which equals 650 and 650 divided by 60 is 7.5 which is 7 hours and 5 minutes I believe so 7.5 is the answer
Hope it helps :D
an iscoclees triangle may be right or acute but never obtuse
Answer:
An isosceles triangle is a triangle in which the two sides of the polygon are equal as well as the angles opposite to these sides are also corresponding
What is the perimeter of quadrilateral DOBC?
Answer:
Hey there if you meant the picture below, I wrote the answers for you
Step-by-step explanation:
Hope my you understand my handwriting
8+8+6+6
And that how to get your answer
By xBrainly
what is the perimeter of P:(2,2) Q:(6,2) R:(6,5) S:(2,5)
Answer: 14
Step-by-step explanation:
P(6)- Q(2) = 4
Q(5) - R(2) = 3
R(6) - S(2) = 4
S(5) - P(2) = 3
4 + 3 + 4 + 3 = 14
Brainliest is appericiated!
Answer:
Perimeter = 14
Step-by-step explanation:
to find the perimeter first find the distance between the two points :
d=√((x2-x1)²+(y2-y1)²)
PQ:(2,2)(6,2)
d=√(6-2)^2+(2-2)^2
= √16=4
PQ=4
RS: (6,5),(2,5)
d=√(6-2)^2+(5-5)^2
d=4
RS=4
QR:(6,2),(6,5)
QR=3
SP(2,5),(2,2)
SP=3
perimeter=2length+2width
P=2l+2w
p=2(4)+2(3)
p=8+6=14
"The assumption that is necessary for a linear programming model to be appropriate and that ensures that the value of the objective function and the total resources used can be found by summing the objective function contribution and the resources used for all decision variables is known as"
Answer:
Is known as "Additivity"
Step-by-step explanation:
Additivity is an assumption in linear programing that hold that the sum of individual resources used by each product separately determines the total amount of resources used which implies that there exist no interaction between the decision variables.