Answer:
The doomsday is 146 days
Step-by-step explanation:
Given
[tex]\frac{dy}{dt} = ky^{1 +c}[/tex]
First, we calculate the solution that satisfies the initial solution
Multiply both sides by
[tex]\frac{dt}{y^{1+c}}[/tex]
[tex]\frac{dt}{y^{1+c}} * \frac{dy}{dt} = ky^{1 +c} * \frac{dt}{y^{1+c}}[/tex]
[tex]\frac{dy}{y^{1+c}} = k\ dt[/tex]
Take integral of both sides
[tex]\int \frac{dy}{y^{1+c}} = \int k\ dt[/tex]
[tex]\int y^{-1-c}\ dy = \int k\ dt[/tex]
[tex]\int y^{-1-c}\ dy = k\int\ dt[/tex]
Integrate
[tex]\frac{y^{-1-c+1}}{-1-c+1} = kt+C[/tex]
[tex]-\frac{y^{-c}}{c} = kt+C[/tex]
To find c; let t= 0
[tex]-\frac{y_0^{-c}}{c} = k*0+C[/tex]
[tex]-\frac{y_0^{-c}}{c} = C[/tex]
[tex]C =-\frac{y_0^{-c}}{c}[/tex]
Substitute [tex]C =-\frac{y_0^{-c}}{c}[/tex] in [tex]-\frac{y^{-c}}{c} = kt+C[/tex]
[tex]-\frac{y^{-c}}{c} = kt-\frac{y_0^{-c}}{c}[/tex]
Multiply through by -c
[tex]y^{-c} = -ckt+y_0^{-c}[/tex]
Take exponents of [tex]-c^{-1[/tex]
[tex]y^{-c*-c^{-1}} = [-ckt+y_0^{-c}]^{-c^{-1}[/tex]
[tex]y = [-ckt+y_0^{-c}]^{-c^{-1}[/tex]
[tex]y = [-ckt+y_0^{-c}]^{-\frac{1}{c}}[/tex]
i.e.
[tex]y(t) = [-ckt+y_0^{-c}]^{-\frac{1}{c}}[/tex]
Next:
[tex]t= 3[/tex] i.e. 3 months
[tex]y_0 = 2[/tex] --- initial number of breeds
So, we have:
[tex]y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}[/tex]
-----------------------------------------------------------------------------
We have the growth term to be: [tex]ky^{1.01}[/tex]
This implies that:
[tex]ky^{1.01} = ky^{1+c}[/tex]
By comparison:
[tex]1.01 = 1 + c[/tex]
[tex]c = 1.01 - 1 = 0.01[/tex]
[tex]y(3) = 16[/tex] --- 16 rabbits after 3 months:
-----------------------------------------------------------------------------
[tex]y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}[/tex]
[tex]16 = [-0.01 * 3 * k + 2^{-0.01}]^{\frac{-1}{0.01}}[/tex]
[tex]16 = [-0.03 * k + 2^{-0.01}]^{-100}[/tex]
[tex]16 = [-0.03 k + 0.9931]^{-100}[/tex]
Take -1/100th root of both sides
[tex]16^{-1/100} = -0.03k + 0.9931[/tex]
[tex]0.9727 = -0.03k + 0.9931[/tex]
[tex]0.03k= - 0.9727 + 0.9931[/tex]
[tex]0.03k= 0.0204[/tex]
[tex]k= \frac{0.0204}{0.03}[/tex]
[tex]k= 0.68[/tex]
Recall that:
[tex]-\frac{y^{-c}}{c} = kt+C[/tex]
This implies that:
[tex]\frac{y_0^{-c}}{c} = kT[/tex]
Make T the subject
[tex]T = \frac{y_0^{-c}}{kc}[/tex]
Substitute: [tex]k= 0.68[/tex], [tex]c = 0.01[/tex] and [tex]y_0 = 2[/tex]
[tex]T = \frac{2^{-0.01}}{0.68 * 0.01}[/tex]
[tex]T = \frac{2^{-0.01}}{0.0068}[/tex]
[tex]T = \frac{0.9931}{0.0068}[/tex]
[tex]T = 146.04[/tex]
The doomsday is 146 days
How do you graph x+6y=0
Answer:
We need to put this equation into either form of a line, pererably, slope intercept form!
Step-by-step explanation:
To do this, out goal is to get y alone.
1. We subtract x on both sides.
2 We divide 6 on both sides.
3. Our answer is y= -x/6 ( negative x divided by 6)
4. The y-intecept value is when x is equal to zero, so plug in 0 for x and solve for y.
5. The y intercept is (0,0)
6. From (0,0) point, you go down -1 and move 1 to the right each time!
The graph will be a line with a slope of -1/6 that passes through the points (0,0), (6,-1), and (-6,1).
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
To graph this equation, start by rearranging it to solve for y.
y = -x/6
Next, plot a few points to fill in the graph.
when x is 0,
y is 0.
When x is 6,
y is -1, and
when x is -6, y is 1.
Finally, connect the plotted points with a straight line.
The final graph will be a line with a slope of -1/6 that passes through the points (0,0), (6,-1), and (-6,1).
Hence, graph will be a line with a slope of -1/6 that passes through the points (0,0), (6,-1), and (-6,1).
To learn more on Graph click:
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HELP PLS!!! BRAINLIEST WILL BE GIVEN
The Math Club makes 35 bars of soap a week and sells these at $20 each. Before the soap can be sold, 6 bars were eaten by a polar bear. If they sell the remaining bars of soap, how much will they make this week?
Answer:I don't really know
Step-by-step explanation: I kind of just come on here to stump my parents.
Please help me!!!!!!!
it is 15 if you add and then divid
7. Below are the steps taken to simplify the expression. Which justification matches Step c of the simplified expression? *
7x+8y+5x+3(y+1)
a. 7x + 8y + 5x + 3y + 3
b. 7x + 5x + 8y + 3y + 3
c. (7x + 5x) + (8y + 3y) + 3
d. 12x + 11y+ 3
A. Associative Property of Addition
B. Commutative Property of Addition
C. Combine Like Terms
D. Distributive Property
Answer:
A. Associative property of addition
Step-by-step explanation:
The associative property is about the grouping of terms/numbers in parentheses in an equation.
what are the steps on finding common denominators. PLEASE HELP
Step-by-step explanation:
to find a common denominator, you have to find a number that "works" with every other number.
for example, say you have
2/4 and 8/12
First you need to find the common factor between 4 and 12, so list all your fours
4, 8, 12, 16, 20
Now list all your twelves
12, 24, 36, 48, 60
to find the common factor you look at both your list of numbers and find one that's the same, sometimes it takes a long list of numbers to find the common factor, but you will run into one.
So by looking at our list we see that 4 and 12 share the common factor of 12. but since 8/12 already has a denominator of 12, we are going to leave it alone.
now think about what you would multiply 4 by, to get to 12. The answer is
4 x 3 = 12
to make the numerator correct, you multiply it by the same number you did 4, so since your faction is 2/4 you should do 2 x 3 = 6
now you have your answer,
2/4 and 8/12 turns into
6/12 and 8/12
and that's how you find it, let me know if you have questions :)
Need help I will offer brainalist + 10 points for correct answer (:
i will give a crown if you are the first one to answer and if you get it right and if you just get it right then i will i give you a full star rating and a thanks
Answer:
10x+8
Step-by-step explanation:
Answer:
10x + 8 is the answer
Step-by-step explanation:
To simplify the equation we must use the Distributive Property meaning that
we must distribute 2 to each term
5x(2) + 4(2)
10x + 8
There You Go, Have a Wonderful Day, And Hope This Helps
What is the name given to a five-sided polygon that has congruent sides? A. hexagon B. regular hexagon C. pentagon D. regular pentagon
Answer:
C
Step-by-step explanation:
Pentagon
Hope this helps (:
Answer
C). pentagon is the correct answer.
Step-by-step explanation:
A pentagon has 5 congruent sides and 5 angles.
Can somebody please give me the answer I will mark u brilliant
Answer:
x = 6.7
Step-by-step explanation:
We know that 3.5 + x = 10.2, so if we do inverse operations we can find out the value of x.
10.2 - 3.5 = 6.7
we can check our work by substituing it back in the equation for x
6.7 + 3.5 = 10.2
so now we know that x = 6.7. I hope this helps :)
Answer: x=6.7
Step-by-step explanation:
x+3.5=10.2
-3.5 -3.5
x= 6.7
What is the simplified form of the following expression? 4x2|y3z| 4x4y8
Answer:
16x⁶y⁸|y³z|.........
Answer:
B
Step-by-step explanation:
EDGE
Express each decimal to fraction 77.0075
Answer:
77[tex]\frac{3}{400}[/tex]
Step-by-step explanation:
Answer:
30803/400
Step-by-step explanation:
77.0075 = 770075/10000
= 154015/2000
= 30803/400
????????????????????????
Answer:
[tex]P(Sum = 9) = \frac{1}{9}[/tex]
Step-by-step explanation:
Given
Outcomes of rolling two dice
Required
P(Sum = 9)
From the given outcomes, we have:
[tex]n(S) = 36[/tex] -- the sample size
[tex]Sum = 9:=\{(3,6),(4,5),(5,4),(6,3)\}[/tex]
So.
[tex]n(Sum = 9) = 4[/tex]
The probability is:
[tex]P(Sum = 9) = \frac{n(Sum = 9)}{n(S)}[/tex]
[tex]P(Sum = 9) = \frac{4}{36}[/tex]
Simplify
[tex]P(Sum = 9) = \frac{1}{9}[/tex]
The captain of a ship at sea sights a lighthouse which is 120 feet tall. The captain measures the the angle of elevation to the top of the lighthouse to be 16 ^\circ. How far is the ship from the base of the lighthouse? feet
Answer:
As viewed on the deck, the lighthouse is 50-6 = 44 m above. First we need to compute the two distances from the captain and the lighthouse. For point1:
d1 = 44 / tan(60) = 25.403 m
For point2:
d2 = 44 / tan(30) = 76.210 m
The distance traveled by the ship in five minutes is 50.807 m or 0.050807 km. Five minutes is equivalent to 1/12 hours.
The speed is then equal to 0.050807/(1/12) kph = 0.61 kph.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Step-by-step explanation:
Need answer asap, will give brainliest to the correct answer.
Answer:The answer is the 2 one
Step-by-step explanation:
How do you multiply polynomials ??
Answer:
multiply each term in one polynomial by each term in the other polynomial.
add those answers together, and simplify if needed.
Step-by-step explanation:
Use FOIL !
1. multiply each term in one polynomial by each term in the other polynomial
2. add those answers together, and simplify if needed
Multiply polynomials the same way you multiply monomials and bionomials. You can also use symbolab to check if your answer is correct
Good luck! Don't be afraid to comment something below this if you have another specific question.
Select the words that best describe the given equation y=x2-1
Answer:
I'm not completely sure what you're asking, but the equation is slope-intercept form. That's how you'd describe the given equation.
Answer:
the y-value is 1 less than the square of the x-value
Step-by-step explanation:
(1/5)³= help me plz its been like more hours since i fond this site like I got into this site yesterday
To cube a fraction, we simply cube both the numerator and the denominator.
So we have 1^3/5^3 which is 1/125.
It's due in 30 minutes!!
Answer:
Top Left: 40/100 = 2/5 = 40%
Top Right: 52/100 = 13/25 = 52%
Bottom Left: 22/100 = 11/50 = 22%
Bottom Right: 9/100 = 9/100 = 9%
Step-by-step explanation:
I need help solving this
If the average person sleeps 7 hours every day how many days will it be before they have slept 35 hours
Si un número es divisible entre 5, es múltiplo de 10? Expliquen porque por favor.
Answer: No es porque el número podría ser 35
Sam scored 98, 25, 105, 62 and 65 run in 5 matches. What was the
average score per match?
Answer:
75
Step-by-step explanation:
am scored 92,25,105,62,65 in 5 matches
The average score per match is
= total of runs in 5 matches/ 5
= 92+25+105+62+65/5
=355/5
= 71
Answer: the average score per match is 71 maybe try looking around before wasting points but im glad to help
What are some values to make -2x> 10 true ?
Please help ASAP!
Answer:
-6 -7 -8 -9 -10
Step-by-step explanation:
anything that keeps going from there dont do anything like -5 -4 -3 -2 -1 because it would be wrong
any negative number that keeps increasing after -6
how do you graph 3-2i
Answer:
X is first then Y
Step-by-step explanation:
x is up to down
y is side to side
you write it like this (x,y)
Find the value of x.
Pleaseeee I need helppp!!!!!!
Answer:
x = 38
Step-by-step explanation:
The measure of a vertex angle outside a circle = ½(difference of intercepted arcs)
Thus:
m<S = ½(UV - TW)
m<S = 34°
UV = (3x - 2)°
TW = (x + 6)°
Plug in the values into the equation
34 = ½((3x - 2) - (x + 6))
34 = ½(3x - 2 - x - 6)
34 = ½(2x - 8)
Multiply both sides by 2
34*2 = 2x - 8
68 = 2x - 8
68 + 8 = 2x (addition property of equality)
76 = 2x
76/2 = x (division property of equality)
38 = x
x = 38
47 in = ? ft ? in
3 ft 11 in
4 ft 0 in
3 ft 9 in
564 ft 0 in
Answer:
3ft 11 in
Step-by-step explanation:
1 foot equals 12 inches, 12 × 3 = 36 = 3 feet + 11 inches = 47 inches = 3ft 11in
Please help! And make sure to add a let statement!
Answer: See explanation
Step-by-step explanation:
1. Let the small number be x
Then, the bug number will be: x + 25
Therefore, x + x + 25 = 131
2x + 25 = 131
2x = 131 - 25
2x = 106
x = 106 / 2
x = 53
Small number= 53
Big number = x + 25 = 53 + 25 = 78
2. Let the small number be x
Then, the bug number will be: x + 14
x + x + 14 = 58
2x + 14 = 58
2x = 58 - 14
2x = 44
x = 44/2
x = 22
Small number = 22
Bug number = 22 + 14 = 36
The numbers are 22 and 36.
3. Let number of basketball sold be x
Therefore, number of football sold will be x+3.
Therefore, x + x + 3 = 27
2x + 3 = 27
2x = 27 - 3
2x = 24
x = 24/2
x = 12
12 basketball were sold
Number of footballs sold = 12 + 3 = 15
4. Let calories in bowl of soup x
Hamburger = 2 × x = 2x
Therefore, x + 2x = 738
3x = 738
x = 738/3
x = 246
There are 246 calories in bowl of soup
Calories in hamburgers = 246 × 2 = 492 calories
NEED HELP ASAP FREE BRAINLIST
Answer:
G
Step-by-step explanation:
Answer:
now they can have brain
Step-by-step explanation:
Give each side and angle measure rounded to the nearest whole number.
Answer:
Step-by-step explanation:
By applying sine rule in the given triangle,
cos(25°) = [tex]\frac{\text{AC}}{AB}[/tex]
cos(25°) = [tex]\frac{b}{400}[/tex]
b = 400[cos(25°)]
b = 362.52
b = 363 ft
By applying sine rule in the given triangle,
sin(25°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
sin(25°) = [tex]\frac{a}{400}[/tex]
a = 400[sin(25°)]
a = 169.05
a = 169 ft
m∠A + m∠B + m∠C = 180°
25° + m∠B + 90° = 180°
m∠B = 180° - 115°
m∠B = 65°