Answer:
dA/dt = 12 - 2A/(100 + t)
Step-by-step explanation:
The differential equation of this problem is;
dA/dt = R_in - R_out
Where;
R_in is the rate at which salt enters
R_out is the rate at which salt exits
R_in = (concentration of salt in inflow) × (input rate of brine)
We are given;
Concentration of salt in inflow = 4 lb/gal
Input rate of brine = 3 gal/min
Thus;
R_in = 4 × 3 = 12 lb/min
Due to the fact that solution is pumped out at a slower rate, thus it is accumulating at the rate of (3 - 2)gal/min = 1 gal/min
So, after t minutes, there will be (100 + t) gallons in the tank
Therefore;
R_out = (concentration of salt in outflow) × (output rate of brine)
R_out = [A(t)/(100 + t)]lb/gal × 2 gal/min
R_out = 2A(t)/(100 + t) lb/min
So, we substitute the values of R_in and R_out into the Differential equation to get;
dA/dt = 12 - 2A(t)/(100 + t)
Since we are to use A foe A(t), thus the Differential equation is now;
dA/dt = 12 - 2A/(100 + t)
Un prestigioso empresario decide repartir su herencia de S/ 176 000 entre sus tres hermanos Roberto, Luis y Armando, de manera DP al número de sus hijos e IP al monto de sus deudas. ¿Cuánto le corresponde a cada hermano?
Roberto :N° hijos 4,Monto de deudas (S/) : 2 000
Luis: N° hijos 3, Monto de deudas (S/): 6 000
Armando:N° hijos 5, Monto de deudas (S/): 8 000
Answer:
Amount received per brother based on number of children plus debt is given as
Roberto, S/ 55,333.33
Luis, S/ 46,000
Armando, S/ 74,666.67
Step-by-step explanation:
English Translation
A prestigious businessman decides to distribute his inheritance of S / 176,000 among his three brothers Roberto, Luis and Armando, DP to the number of his children and IP to the amount of his debts. How much corresponds to each brother?
Roberto: No of children 4, Amount of debts (S /): 2 000
Luis: No. of children 3, Amount of debts (S /): 6,000
Armando: No of children 5, Amount of debts (S /): 8,000
Solution
The man shares the inheritance according to the number of children per person and according to each brother's debts.
Assuming the debts are first settled,
The total debts = 2000 + 6000 + 8000 = S/ 16,000
We assume that each brother receives the respective debt amounts first, then the remaining cash is divided amongst the 3 brothers according to the number of their children.
Total amount available = S/ 176,000
total debt = S/ 16,000
Amount available less debts = 176,000 - 16,000 = S/ 160,000
There are 4, 3 and 5 children respectively for the 3 brothers.
Total number of children = 4+3+5 = 12.
Amount corresponding based on a per child basis =( S/ 160,000/12) = S/ 13,333.33
Meaning that each brother receives the following amount based on their children's sake
Roberto, 4 × S/ 13,333 = S/ 53,333.33
Luis, 3 × S/ 13,333.33 = S/ 40,000
Armando, 5 × S/ 13,333 = S/ 66,666.67
Total amount each brother then receives when the amount received due to debts are added
Roberto, 53,333.33 + 2,000 = S/ 55,333.33
Luis, 40,000 + 6,000 = S/ 46,000
Armando, 66,666.67 + 8,000 = S/ 74,666.67
To check, 55,333.33 + 46,000 + 74,666.67 = 176,000 (total inheritance!)
Hope this Helps!!!
Queremos ver como se reparte una dada suma entre 3 hermanos, siendo que tenemos unas dadas restricciones, donde debemos trabajar con relaciones directamente proporcionales e inversamente proporcionales.
Veremos que:
Roberto recibe: $112,640
Luis recibe: $28,160
Armando recibe: $35,200
Sabemos que lo que se reparte es directamente proporcional al número de hijos de cada hermano, e inversamente proporcional a las deudas de cada hijo.
Entonces, definamos las variables:
R = lo que recibe Roberto.
L = Lo que recibe Luis
A = lo que recibe Armando.
Tendremos que:
R + L + A = $176,000
directamente proporcional significa: y = k*xInversamente proporcional significa: y = k/zEntonces como lo que recibe cada hermano es directamente proporcional al número de hijos (x) e inversamente proporcional a la deuda (z) lo que cada hermano recibe será:
R = k*4/2,000L = k*3/6,000A = k*5/8,000Entonces podemos escribir:
R + L + A = $176,000
k*4/2,000 + k*3/6,000 + k*5/8,000 = $176,000
k*(4/2,000 + 3/6,000 + 5/8,000) = $176,000
k*(0.003125) = $176,000
k = $176,000/(0.003125) = $56,320,000
Ahora que conocemos el valor de k, podemos calcular lo que cada hermano recibe:
R = $56,320,000*(4/2,000) = $112,640
L = $56,320,000*(3/6,000) = $28,160
A = $56,320,000*(5/8,000) = $35,200
Si quieres aprender más, puedes leer:
https://brainly.com/question/18365407
Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x – 3)? (0,6) (0,–6) (6,0) (–6,0)
Answer: (-6, 0)
Step-by-step explanation:
X-intercepts of equations are any points on the equation that lie on the x-axis, or the horizontal line "y = 0".
In order to find the x-intercept of an equation, find the points that will satisfy the equation "y = 0":
y = (x + 6)(x - 3)
y = 0
(x + 6)(x - 3) = 0
With this equation, you can find which points lie on the x-axis.
When x = -6, the equation is: 0 * -9 = 0, which is correct.
When x = 3, the equation is 9 * 0 = 0, which is correct.
Make sure you're picking the correct coordinate out of the answer choices.
The x-coordinates are -6 and 3, and the y-coordinates are 0, because the points lie on the x-axis.
The correct answer is (-6, 0).
(3, 0) is also correct, but the question does not require it.
Answer:
D
Step-by-step explanation:
The Sunshine Droogs are unhappy as they have not yet been paid for their concert. It was agreed they would be paid eleven thousand, four hundred and fifty three pounds for the concert. What is this amount in numbers?
Answer:
11453
Step-by-step explanation:
What are the zeroes of the polynomial x(x²+4x-12)
Answer:
x= 0, 2, -6
Hope this helps!
an amount was invested at r% per quarter. what value of r will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested
Answer:
[tex]r=25.7\%[/tex] will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested
Step-by-step explanation:
Given: An amount was invested at r% per quarter.
To find: value of r such that accumulated amount at the end of one year is 1.5 times more than amount invested
Solution:
Let P denotes amount invested and n denotes time
As an amount (A) was invested at r% per quarter,
[tex]A=P\left ( 1+\frac{r}{400} \right )^{4n}[/tex]
According to question, accumulated amount at the end of one year is 1.5 times more than amount invested.
So,
[tex]A=1.5P+P=2.5P\\A=2.5P\\P\left ( 1+\frac{r}{400} \right )^{4n}=2.5P[/tex]
Put n = 1
[tex]P\left ( 1+\frac{r}{400} \right )^{4}=2.5P\\\left ( 1+\frac{r}{400} \right )^{4}=2.5\\1+\frac{r}{400} =(2.5)^{\frac{1}{4}}\\\frac{r}{100}=(2.5)^{\frac{1}{4}}-1\\r=100\left [ (2.5)^{\frac{1}{4}}-1 \right ]\\=25.7\%[/tex]
What’s the correct answer for this question?
Answer:
B
Step-by-step explanation:
The triangular prism must have a larger base than the cylinder
Help me solve the equivalent expression (4x+2)-3x+5
Answer:
X+7
Step-by-step explanation:
Remove the parentheses:
4x+2-3x+5
Collect like terms:
4x-3x=x
2+5=7
Solution:
X+7
Hey there!
(4x + 2) - 3x + 5
= 4x + 2 - 3x + 5
COMBINE the LIKE TERMS
= (4x - 3x) + (2 + 5)
= 4x - 3x + 2 + 5
= 1x + 7
= x + 7
Therefore, your answer is: x + 7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
What is the equation of the line that is parallel to the given
line and passes through the point (-4,-6 )?
x= -6
x=-4
y=-6
y=-4
Answer:
The line on the graph is y = 4, where no matter what the value of x is, the value of y will always be 4. Therefore, any line parallel to this one will be y = ?. If it passes through (-4, -6), that means that the equation is y = -6.
Answer:
С)))) Y= -6
Step-by-step explanation:
just did on edg. :D
Help help , Please help! Brainliest if correct! What was the equation of the graph below before it was shifted to the left 1.5 units? A. G(x)=(x3)^3-(x-3) B. G(x)=(x-1.5)^3 C. G(x)=(x)^3 D.G(x)=x^3-x
Answer:
A. G(x) = (x -3)^3 -(x -3)
Step-by-step explanation:
The graph before it was shifted left will be a right-shift of the equation shown. That is accomplished by replacing x with (x-1.5). Then the right-shifted equation is ...
G(x) = ((x-1.5) -1.5)^3 -((x -1.5) -1.5)
G(x) = (x -3)^3 -(x -3) . . . . matches choice A
Suppose f(x) is continuous on [3,6] and −3≤f′(x)≤5 for all x in (3,6). Use the Mean Value Theorem to estimate f(6)−f(3).
Answer: -9 ≤ f(6) - f(3) ≤ 15
Step-by-step explanation:
In order to use the Mean Value Theorem, it must be continuous and differentiable. Both of these conditions are satisfied so we can continue.
Find f(6) - f(3) using the following formula:
[tex]f'(c)=\dfrac{f(b)-f(a)}{b-a}[/tex]
Consider: a = 3, b = 6
[tex]\text{Then}\ f'(c)=\dfrac{f(6)-f(3)}{6-3}\\\\\\\rightarrow \quad 3f'(c)=f(6) - f(3)[/tex]
Given: -3 ≤ f'(x) ≤ 5
-9 ≤ 3f'(c) ≤ 15 Multiplied each side by 3
→ -9 ≤ f(6) - f(3) ≤ 15 Substituted 3f'(c) with f(6) - f(3)
Which of the following is a radical equation?
X3 - 13
X+ 15 - 13
√x+3-13
x+3 - 13
Answer:
√x+3-13
Step-by-step explanation:
This answer is a radical equation because a square root is used in the equation. This makes the equation radical. The other choices have no square roots so they can't be the answers.
What is the value of k?
k=
8
m
o
4
k
N
M
Answer: It’s 2
Step-by-step explanation:
look at picture
what’s the sum of x+x^2+2 and x^2-2-x ?
Answer: The correct answer is: " 2x² " .
________________________________
Step-by-step explanation:
________________________________
We are asked: "What is the sum of: "x + x² + 2" and "x² − 2 − x" ?
Since we are to find the "sum" ;
→ We are to "add" these 2 (two) expressions together:
→ (x + x² + 2) + (x² − 2 − x) ;
Note: Let us rewrite the above, by adding the number "1" as a coefficient to: the values "x" ; and "x² " ; since there is an "implied coefficient of "1" ;
→ {since: "any value" ; multiplied by "1"; results in that exact same value.}.
→ (1x + 1x² + 2) + (1x² − 2 − 1x) ;
Rewrite as:
→ 1x + 1x² + 2) + (1x² − 2 − 1x) ;
Now, let us add the "coefficient" , "1" ; just before the expression:
"(1x² − 2 − 1x)" ;
{since "any value", multiplied by "1" , equals that same value.}.
And rewrite the expression; as follows:
→ (1x + 1x² + 2) + 1(1x² − 2 − 1x) ;
Now, let us consider the following part of the expression:
→ " +1(1x² − 2 − 1x) " ;
________________________________
Note the distributive property of multiplication:
→ " a(b+c) = ab + ac " ;
and likewise:
→ " a(b+c+d) = ab + ac + ad " .
________________________________
So; we have:
→ " +1(1x² − 2 − 1x) " ;
= (+1 * 1x²) + (+1 *-2) + (+1*-1x) ;
= + 1x² + (-2) + (-1x) ;
= +1x² − 2 − 1x ;
↔ ( + 1x² − 1x − 2)
Now, bring down the "left-hand side of the expression:
1x + 1x² + 2 ;
and add the rest of the expression:
→ 1x + 1x² + 2 + 1x² − 1x − 2 ;
________________________________
Now, simplify by combining the "like terms" ; as follows:
+1x² + 1x² = 2x² ;
+1x − 1x = 0 ;
+ 2 − 2 = 0 ;
________________________________
The answer is: " 2x² " .
________________________________
Hope this is helpful to you!
Best wishes!
________________________________
Answer:
The correct answer is: " 2x² " .
________________________________
Step-by-step explanation:
________________________________
We are asked: "What is the sum of: "x + x² + 2" and "x² − 2 − x" ?
Since we are to find the "sum" ;
→ We are to "add" these 2 (two) expressions together:
→ (x + x² + 2) + (x² − 2 − x) ;
Note: Let us rewrite the above, by adding the number "1" as a coefficient to: the values "x" ; and "x² " ; since there is an "implied coefficient of "1" ;
→ {since: "any value" ; multiplied by "1"; results in that exact same value.}.
→ (1x + 1x² + 2) + (1x² − 2 − 1x) ;
Rewrite as:
→ 1x + 1x² + 2) + (1x² − 2 − 1x) ;
Now, let us add the "coefficient" , "1" ; just before the expression:
"(1x² − 2 − 1x)" ;
{since "any value", multiplied by "1" , equals that same value.}.
And rewrite the expression; as follows:
→ (1x + 1x² + 2) + 1(1x² − 2 − 1x) ;
Now, let us consider the following part of the expression:
→ " +1(1x² − 2 − 1x) " ;
________________________________
Note the distributive property of multiplication:
→ " a(b+c) = ab + ac " ;
and likewise:
→ " a(b+c+d) = ab + ac + ad " .
________________________________
So; we have:
→ " +1(1x² − 2 − 1x) " ;
= (+1 * 1x²) + (+1 *-2) + (+1*-1x) ;
= + 1x² + (-2) + (-1x) ;
= +1x² − 2 − 1x ;
↔ ( + 1x² − 1x − 2)
Now, bring down the "left-hand side of the expression:
1x + 1x² + 2 ;
and add the rest of the expression:
→ 1x + 1x² + 2 + 1x² − 1x − 2 ;
________________________________
Now, simplify by combining the "like terms" ; as follows:
+1x² + 1x² = 2x² ;
+1x − 1x = 0 ;
+ 2 − 2 = 0 ;
________________________________
The answer is: " 2x² " .
Step-by-step explanation:
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. Suppose that the mean income is found to be $18.5 for a random sample of 2253 people. Assume the population standard deviation is known to be $6.1. Construct the 98% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
Answer:
= ( $18.2, $18.8)
Therefore, the 98% confidence interval (a,b) = ( $18.2, $18.8)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $18.50
Standard deviation r = $6.10
Number of samples n = 2253
Confidence interval = 98%
z(at 98% confidence) = 2.33
Substituting the values we have;
$18.5+/-2.33($6.1/√2253 )
$18.5+/-2.33($0.128513644290)
$18.5+/-$0.299436791196
$18.5+/-$0.3
= ( $18.2, $18.8)
Therefore at 98% confidence interval (a,b) = ( $18.2, $18.8)
Solve the following absolute value equation:
|2x-5|=7
x= -6 or x = 1
x = 6 or x = 1
x= -6 or x= -1
x = 6 or x= -1
Answer:
x = 6 x = -1
Step-by-step explanation:
When we have absolute value equations, we get two solutions, one positive and one negative
2x - 5 =7 2x -5= -7
Add 5 to each side
2x-5+5 = 7+5 2x -5+5 = -7+5
2x =12 2x = -2
Divide each side by 2
2x/2 =12/2 2x/2 = -2/2
x = 6 x = -1
solve sqrt 3-5x= sqrt x+2 what is the value of x
Answer:
[tex]x=\frac{1}{6}[/tex]
Step-by-step explanation:
[tex]\sqrt{3-5x}=\sqrt{x+2}\\Square\:both\:sides\\\left(\sqrt{3-5x}\right)^2=\left(\sqrt{x+2}\right)^2\\\mathrm{Expand\:}\left(\sqrt{3-5x}\right)^2:\quad 3-5x\\\mathrm{Expand\:}\left(\sqrt{x+2}\right)^2:\quad x+2\\3-5x=x+2\\\mathrm{Solve\:}\:3-5x=x+2:\quad x=\frac{1}{6}\\x=\frac{1}{6}\\\mathrm{Verify\:Solutions}:\quad x=\frac{1}{6}\space\mathrm{True}\\\mathrm{The\:solution\:is}\\x=\frac{1}{6}[/tex]
Answer:
A- 1/6
Step-by-step explanation:
GOT IT RIGHT ON EDGE
Let f(x)=−9x+1. Match the function with the description.
The graph of g is a reflection in the y-axis of the graph of f.
The graph of g is a reflection in the x-axis of the graph of f.
The graph of g is a horizontal translation 16 units right of the graph of f.
The graph of g is a vertical translation 16 units down of the graph of f.
Answer:
I guess that we want to find the function g(x) for the 4 cases.
first, f(x) = -9*x + 1.
a) The graph of g is a reflection in the y-axis of the graph of f.
First remember: if we have the point (x,y) and we reflect it over the y-axis, we get (-x,y)
then g(x) = f(-x) = -9*-x + 1 = 9*x + 1.
b) The graph of g is a reflection in the x-axis of the graph of f.
if we have a point (x, y) and we reflect it over the x-axis, the point transforms into (x, -y)
then we have: g(x) = -f(x) = 9*x - 1
c) The graph of g is a horizontal translation 16 units right of the graph of f.
When we want to have a translation in the x-axis, we must change x by x - A.
If A is positive, this transformation moves the graph by A units to the right, in this case, A = 16.
g(x) = f(x - 16) = -9*(x - 16) + 1
d) The graph of g is a vertical translation 16 units down of the graph of f.
For vertical translations, if we want to move the graph by A units down (A positive) we should do y = f(x) - A
In this case, A = 16.
then: g(x) = f(x) - 16 = -9*x + 1 - 16 = -9*x - 15.
x/x-2+x-1/x+1=-1
I'm having trouble figuring this out, an explanation on how to solve would suffice.
Answer:
x = sqrt(5)/2 - 1/2 or x = -1/2 - sqrt(5)/2
Step-by-step explanation:
Solve for x over the real numbers:
x - 2 + x/x + 1 - 1/x = -1
x - 2 + x/x + 1 - 1/x = x - 1/x:
x - 1/x = -1
Bring x - 1/x together using the common denominator x:
(x^2 - 1)/x = -1
Multiply both sides by x:
x^2 - 1 = -x
Add x to both sides:
x^2 + x - 1 = 0
Add 1 to both sides:
x^2 + x = 1
Add 1/4 to both sides:
x^2 + x + 1/4 = 5/4
Write the left hand side as a square:
(x + 1/2)^2 = 5/4
Take the square root of both sides:
x + 1/2 = sqrt(5)/2 or x + 1/2 = -sqrt(5)/2
Subtract 1/2 from both sides:
x = sqrt(5)/2 - 1/2 or x + 1/2 = -sqrt(5)/2
Subtract 1/2 from both sides:
Answer: x = sqrt(5)/2 - 1/2 or x = -1/2 - sqrt(5)/2
Let D= {(x,y) | x^2+y^2 ≤ 4x} Using polar coordinates, What is the integral: ∬y^2/ (x^2+y^2)dxdy?
In polar coordinates, the inequality changes to
[tex]x^2+y^2\le4x\implies r^2\le4r\cos\theta\implies r\le4\cos\theta[/tex]
which is a circle of radius 2 and centered at (2, 0). The set D is then
[tex]D=\left\{(r,\theta)\mid0\le r\le4\cos\theta\land0\le\theta\le\pi\right\}[/tex]
The integral is then
[tex]\displaystyle\iint_D\frac{y^2}{x^2+y^2}\,\mathrm dx\,\mathrm dy=\int_0^\pi\int_0^{4\cos\theta}\frac{r^2\sin^2\theta}{r^2}r\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\int_0^\pi\int_0^{4\cos\theta}r\sin^2\theta\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac12\int_0^\pi((4\cos\theta)^2-0^2)\sin^2\theta\,\mathrm d\theta[/tex]
[tex]=\displaystyle8\int_0^\pi\cos^2\theta\sin^2\theta\,\mathrm d\theta[/tex]
There are several ways to compute the remaining integral; one would be to invoke the double-angle formula,
[tex]\sin(2\theta)=2\sin\theta\cos\theta[/tex]
so that the integral is
[tex]=\displaystyle8\int_0^\pi\frac{\sin^2(2\theta)}4\,\mathrm d\theta[/tex]
[tex]=\displaystyle2\int_0^\pi\sin^2(2\theta)\,\mathrm d\theta[/tex]
Then invoke another double-angle formula,
[tex]\sin^2\theta=\dfrac{1-\cos(2\theta)}2[/tex]
to change the integral to
[tex]=\displaystyle\int_0^\pi1-\cos(4\theta)\,\mathrm d\theta[/tex]
[tex]=(\pi-\cos(4\pi))-(0-\cos0)=\boxed{\pi}[/tex]
If the figures below are similar, find the scale factor of Figure B to Figure A.
48
27
60
А
16
B
20
9
Answer:
The scale factor is 3.
Step-by-step explanation
Figure B has side measures 16, 20, and 9. Figure A has side measures 48, 27, and 60. The ratio of each of the corresponding sides is 1:3 (16:48, etc). Therefore, the scale factor of Figure B to Figure A is 3.
Find the function y1 of t which is the solution of 121y′′+110y′−24y=0 with initial conditions y1(0)=1,y′1(0)=0. y1= Note: y1 is a linear combination of the two independent solutions of this differential equation that you found first. You are not being asked for just one of these. You will need to determine the values of the two constant parameters c1 and c2. Similarly for finding y2 below. Find the function y2 of t which is the solution of 121y′′+110y′−24y=0 with initial conditions y2(0)=0,y′2(0)=1. y2= Find the Wronskian W(t)=W(y1,y2). W(t)= Remark: You can find W by direct computation and use Abel's theorem as a check. You should find that W is not zero and so y1 and y2 form a fundamental set of solutions of 121y′′+110y′−24y=0.
Answer:
Step-by-step explanation:
The original equation is [tex]121y''+110y'-24y=0[/tex]. We propose that the solution of this equations is of the form [tex] y = Ae^{rt}[/tex]. Then, by replacing the derivatives we get the following
[tex]121r^2Ae^{rt}+110rAe^{rt}-24Ae^{rt}=0= Ae^{rt}(121r^2+110r-24)[/tex]
Since we want a non trival solution, it must happen that A is different from zero. Also, the exponential function is always positive, then it must happen that
[tex]121r^2+110r-24=0[/tex]
Recall that the roots of a polynomial of the form [tex]ax^2+bx+c[/tex] are given by the formula
[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]
In our case a = 121, b = 110 and c = -24. Using the formula we get the solutions
[tex]r_1 = -\frac{12}{11}[/tex]
[tex]r_2 = \frac{2}{11}[/tex]
So, in this case, the general solution is [tex]y = c_1 e^{\frac{-12t}{11}} + c_2 e^{\frac{2t}{11}}[/tex]
a) In the first case, we are given that y(0) = 1 and y'(0) = 0. By differentiating the general solution and replacing t by 0 we get the equations
[tex]c_1 + c_2 = 1[/tex]
[tex]c_1\frac{-12}{11} + c_2\frac{2}{11} = 0[/tex](or equivalently [tex]c_2 = 6c_1[/tex]
By replacing the second equation in the first one, we get [tex]7c_1 = 1 [/tex] which implies that [tex] c_1 = \frac{1}{7}, c_2 = \frac{6}{7}[/tex].
So [tex]y_1 = \frac{1}{7}e^{\frac{-12t}{11}} + \frac{6}{7}e^{\frac{2t}{11}}[/tex]
b) By using y(0) =0 and y'(0)=1 we get the equations
[tex] c_1+c_2 =0[/tex]
[tex]c_1\frac{-12}{11} + c_2\frac{2}{11} = 1[/tex](or equivalently [tex]-12c_1+2c_2 = 11[/tex]
By solving this system, the solution is [tex]c_1 = \frac{-11}{14}, c_2 = \frac{11}{14}[/tex]
Then [tex]y_2 = \frac{-11}{14}e^{\frac{-12t}{11}} + \frac{11}{14} e^{\frac{2t}{11}}[/tex]
c)
The Wronskian of the solutions is calculated as the determinant of the following matrix
[tex]\left| \begin{matrix}y_1 & y_2 \\ y_1' & y_2'\end{matrix}\right|= W(t) = y_1\cdot y_2'-y_1'y_2[/tex]
By plugging the values of [tex]y_1[/tex] and
We can check this by using Abel's theorem. Given a second degree differential equation of the form y''+p(x)y'+q(x)y the wronskian is given by
[tex]e^{\int -p(x) dx}[/tex]
In this case, by dividing the equation by 121 we get that p(x) = 10/11. So the wronskian is
[tex]e^{\int -\frac{10}{11} dx} = e^{\frac{-10x}{11}}[/tex]
Note that this function is always positive, and thus, never zero. So [tex]y_1, y_2[/tex] is a fundamental set of solutions.
A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq. Ft. How much were the dimensions increased?
Answer:
4 ft
Step-by-step explanation:
288=16 * 18
12+4=16
14+4=18
The dimensions increased by 4 feet.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Given;
Dimensions of rectangle = 12 + x and 14 + x
The area of the rectangle= (12 + x) (14 + x) = 288
x² + 26x + 168 = 288
x² + 26x - 120 = 0
(x + 30) (x - 4) = 0
x=-30, x =4
Hence, The dimensions increased by 4 feet.
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It is believed that approximately 12% of the population of the United States is lefthanded. Suppose researchers suspect that the proportion of left-handed people is higher in certain states than the national average. The researchers conduct a sample of 200 randomly selected people in the state of Maine and find that 29 people in the sample are left-handed.
a. Write the null hypothesis and alternative hypothesis and define your parameter.
b. Show that the necessary conditions (Randomization Condition, 10% Condition, Sample Size Condition) are satisfied to perform a hypothesis test. Briefly explain how each condition is satisfied.
c. Perform the hypothesis test and find the P-value. (To show your work: Write down what values you are entering into the hypothesis testing calculator.)
d. Is there strong evidence that the left-handed rate in the state of Maine is higher than the national average? Briefly explain how you know.
Answer:
Step-by-step explanation:
a. Null hypothesis: P = p
Alternatives hypothesis: P =/ p
Where P is the hypothesized population proportion and p is the sample proportion
b. Performing a test of proportions
Randomization: the sample was randomly selected in the study
The population size is at least 20 times as big as the sample size.
The sample includes both successes and failures with 29 success and 171 failures.
c. To perform the hypothesis test: we have to find the standard deviation first
Sd = sqrt[ P * ( 1 - P ) / n ]
where P is the hypothesized value of population proportion, n is the sample size.
Sd = √[0.12*(1-0.12)/200]
Sd = √[0.12*(0.88/200]
Sd = √[0.12*(0.0044)]
Sd = √0.000528
Sd = 0.023
Then we can find the z score
z = (p - P) / σ where p = 29/200 = 0.145
z = (0.145-0.12)/ 0.023
z = 0.025/0.023
z = 1.09
Calculation the p value using 0.05 level of significance and a two waited test (p value calculator),
A p-value of 0.2757 which is greater than 0.05, thus we will fail to reject the null stating that there is not enough strong evidence that the left-handed rate in the state of Maine is higher than the national average.
Sean tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation h = -16t2 + 72t + 100. what is the height of the bridge
Answer:
100
Step-by-step explanation:
When t=0 (no time has passed), the coin is at height 100. This means the bridge must be 100 units high for this to be possible.
Answer:
100
Step-by-step explanation:
:3
This table gives a few (x,y) pairs of a line in the coordinate plane. What is the y-intercept of the line? (full problem attached)
Answer:
(0,34)
Step-by-step explanation:
For each rise of 14 in the x direction, this graph rises by -8 in the y direction. This means that, when x is 0, and the graph intersects the y axis, the y value will be 50-8-8=34. Therefore, the y intercept of this line is (0,34). Hope this helps!
Answer:
The answer is (0,34)
Which is greater between |5| amd |2|
Answer:
|5| = 5 and |2| = 2 and because 5 > 2, our answer is |5| > |2|.
Answer:
|5|
Step-by-step explanation:
5 is greater than 2
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions. CHECK ALL THAT APPLY
Answer:
A. it would be shifted up
Step-by-step explanation:
Y=MX+B
B is the Y-intercept.
Answer:
a. it would be shifted up
Step-by-step explanation:
the difference between the original and the new function is that the b value is changed from -6 to +8, meaning the y-intercept value has increased. this would shift the graph up by 14.
Find the area of a circle with radius, r = 9cm.
Give your answer in terms of π .
Answer:
[tex]81\pi[/tex]
Step-by-step explanation:
[tex]Area = \pi * r^{2} \\\pi *9^{2} =81\pi[/tex]
Answer:
81 π
Step-by-step explanation:
formula is radius squared times pi or π so the answer would be 9x9=81 and you said to leave in terms of π so the answer is 81 π.
The total mass of the Sun is about 2×10^30 kg, of which about 76 % was hydrogen when the Sun formed. However, only about 12 % of this hydrogen ever becomes available for fusion in the core. The rest remains in layers of the Sun where the temperature is too low for fusion.
Part A
Use the given data to calculate the total mass of hydrogen available for fusion over the lifetime of the Sun.
Express your answer using two significant figures.
Part B
The Sun fuses about 600 billion kilograms of hydrogen each second. Based on your result from part A, calculate how long the Sun’s initial supply of hydrogen can last. Give your answer in both seconds and years.
Express your answer using two significant figures.
Part D
Given that our solar system is now about 4.6 billion years old, when will we need to worry about the Sun running out of hydrogen for fusion?
Express your answer using two significant figures.
Answer:
A. 1.8 ×[tex]10^{30}[/tex] Kg
B i. 3.0 × [tex]10^{17}[/tex] seconds
ii. 9.6 × [tex]10^{9}[/tex] years
C. After 9.2 × [tex]10^{9}[/tex] (9.2 billion) years
Step-by-step explanation:
Given that the mass of the Sun = 2× [tex]10^{30}[/tex] Kg.
Mass of hydrogen when Sun was formed = 76% of 2× [tex]10^{30}[/tex] Kg
= [tex]\frac{76}{100}[/tex] ×2× [tex]10^{30}[/tex] Kg
= 1.52 × [tex]10^{30}[/tex] Kg
Mass of hydrogen available for fusion = 12% of 1.52 × [tex]10^{30}[/tex] Kg
= [tex]\frac{12}{100}[/tex] × 1.52 × [tex]10^{30}[/tex] Kg
= 1.824 ×[tex]10^{30}[/tex] Kg
A. Total mass of hydrogen available for fusion over the lifetime of the sun is 1.8 ×[tex]10^{30}[/tex] Kg.
B. Given that the Sun fuses 6 × [tex]10^{11}[/tex] Kg of hydrogen each second.
i. The Sun's initial hydrogen would last;
[tex]\frac{1.8*10^{30} }{6*10^{11} }[/tex]
= 3.04 × [tex]10^{17}[/tex] seconds
The Sun's hydrogen would last 3.0 × [tex]10^{17}[/tex] seconds
ii. Since there are 31536000 seconds in a year, then;
The Sun's initial hydrogen would last;
[tex]\frac{3.04*10^{17} }{31536000}[/tex]
= 9.640 × [tex]10^{9}[/tex] years
The Sun's hydrogen would last 9.6 × [tex]10^{9}[/tex] years.
C. Given that our solar system is now about 4.6 × [tex]10^{9}[/tex] years, then;
[tex]\frac{9.6*10^{9} }{4.6*10^{9} }[/tex]
= 2.09
So that; 2 × 4.6 × [tex]10^{9}[/tex] = 9.2 × [tex]10^{9}[/tex] years
Therefore, we need to worry about the Sun running out of hydrogen for fusion after 9.2 × [tex]10^{9}[/tex] years.
Part(A): The total mass of hydrogen available 9.6 billion years.
Part(B): The total time is 5.10 billion years.
Part(D): The hydrogen will last [tex]5.04\times 10^9 \ years[/tex]
Mass of the sun:Our sun is the largest object in our solar system. The mass of the sun is approximately [tex]1.988\times 1030[/tex] kilograms
Part(A):
Given that,
The total mass of the Sun =[tex]2\times10^{30} kg[/tex]
Mass of hydrogen in Sun = [tex]2\times10^{30} \times0.76\ kg[/tex]
The mass of hydrogen ever available for fusion is,
[tex]2\times10^{30} \times 0.76 \times 0.12 kg = 1.824\times 10^{29}[/tex]
Mass of hydrogen fuses each second = 600 billion kg/second.
Time hydrogen will last in seconds=[tex]1.824\times 10^{29}seconds.[/tex]
[tex]= 0.00304\times 10^{29 }= 3.04\times 10^{17}.[/tex]
Time hydrogen will last in seconds =[tex]1 year = 31,536,000 seconds.[/tex]
[tex]31,536,000 x = 3.04\times 10^{17} = 9.6 \ billion \ years.[/tex]
(B) Present age of sun = [tex]9.6-4.5 \ billion \ years[/tex]
The time when we need to worry about Sun running out of hydrogen for fusion = 5.10 billion years.
(D) The solar system is 4.6 billion years old that is [tex]4.6\times 10^9\ years[/tex]
And in part (B) we have calculated that hydrogen will last [tex]9.64\times 10^9[/tex] then,
[tex]9.64\times 10^9-4.6\times 10^9=5.04\times 10^9[/tex]
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5+7.(9-4)
5+7=11
11×5=55
Answer: itz 605
Step-by-step explanation: