The population of a community of foxes is observed to fluctuate on a 10-year cycle due to variations in the availability of prey. When population measurements began (t=0, the population was 35 foxes. The growth rate in units of foxes>>year was observed to be P′(t)=5+10sinπt/5
a. What is the population 15 years later? 35 years later?
b. Find the population P(t) at any time t≥0.
Answer:
Population 15 years later P(15) = 100 + 50/π
Population 35 years later P(35) = 200 + 50/π
Population any t ≥ 0 P(t) = 35 + 50 /π + 5*t + 10*cos(π*t/5)
Step-by-step explanation:
P´(t) = 5 + 10*sinπt/5 ⇒ dP/dt = 5 + 10*sinπt/5
dP = ( 5 + 10*sinπt/5 ) *dt
P(t) = ∫ ( 5 + 10*sinπt/5 ) dt
P(t) = 5*t + 10 * ∫ sinπ*t/5* dt
P(t) = 5*t - 10*5/π *cos πt/5 + k
To determine k t = 0 P(t) = 35
P(0) = 5*0 - 50/π (1) + k
35 = - 50/π + k
k = 35 + 50/π and
P(t) = 5*t + 10*cos(π*t/5) + 35 + 50/π
b)P(t) = 35 + 50 /π + 5*t + 10*cos(π*t/5) (1)
a) Population 15 years later
P(15) = 35 + 50/π + 5*15 - 10
P(15) = 100 + 50/π
Again from equation (1)
P(35) = 35 + 50 /π + 5*35 + 10*cos(35*π/5)
P(35) = 35 + 50/π + 175 + 10*cos (7*π )
P(35) = 210 + 50/π - 10
P(35) = 200 + 50/π
Simplify the expression: 12x+3x+4x
Answer:
19x
Step-by-step explanation:
12+3+4=19
19x
Answer:
12x+3x+4x=19x
Step-by-step explanation:
Help me pls pls pls
Answer:
omg I'm doing the same thing
If 200 of the 550 reptiles in as you are on display what percent of the reptiles are on display
Answer:
200/550×100%
=20000/550
=36.37%
A thrill at an amusement park travels 55 miles per hour.Round to the nearest hundredth,how many feet per second is this?
9514 1404 393
Answer:
80.67 fps
Step-by-step explanation:
1 mi/h = 22/15 ft/s
Multiplying this equation by 55, we get ...
55 mi/h = 1210/15 ft/s = 80 2/3 ft/s ≈ 80.67 ft/s
A 3 slope:3/2
B 3 slope -3/2
C -3 slope 3/2
D -3 slope -3/2
Answer:
C. y-intercept: -3
slope: 3/2
Step-by-step explanation:
✔️The line cuts across the y-axis at y = -3. Therefore the y-intercept = -3.
✔️Slope of the line using two points on the line, (0, -3) and (2, 0):
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-3)}{2 - 0} = \frac{3}{2} [/tex]
Slope = ³/2
Solve x2 − 7x = −12. (6 points) Question 8 options:
1) x = 2 and x = 6
2) x = 6 and x = −2
3) x = −4 and x = −3
4) x = 4 and x = 3
Which best describes a difference between SALT I and SALT II?
SALT I limited weapons, while SALT II limited launchers.
SALT I expanded the production of arms, while SALT II limited production.
SALT I allowed the sides to trade weapons, while SALT II expanded this practice.
SALT I limited military forces of each country, while SALT II allowed their growth.
The difference between SALT I and SALT II is SALT I limited weapons, while SALT II limited launchers. So, correct option is A.
The Strategic Arms Limitation Talks (SALT) were a series of negotiations between the United States and the Soviet Union to limit and reduce the number of nuclear weapons and delivery systems.
SALT I was signed in 1972 and focused on limiting the number of ballistic missiles and bombers each side could possess. It also established a system for verifying compliance with the treaty.
SALT II was signed in 1979 but was never ratified by the U.S. Senate due to increased tensions between the two countries. SALT II aimed to further reduce the number of strategic nuclear weapons and delivery systems, but unlike SALT I, it focused on limiting the number of launchers rather than weapons themselves.
Therefore, the correct answer is A.
To learn more about SALT click on,
https://brainly.com/question/29569705
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Answer:
I just took the test and I can confirm that the answer is A
Step-by-step explanation:
Mei runs 93.24 miles in 3 weeks. If she runs 6 days each week, what is the average distance she runs each day?
Answer:
5.18 miles each day
Step-by-step explanation:
3 weeks × 6 days = 18 days
93.24 miles in 18 days gives an average of 93.24 ÷ 18 = 5.18 miles per day
Simplify using order of operations.
7(6 + 3) - 4 x 5
Answer:
7 × 9 - 4 × 5
63-20= 43
Step-by-step explanation:
we start with () then multiplication then subtract we use the BEDMAS method in order.
B: brackets
E: exponents (powers)
D: divide
M: multiply
A:addition
S: subtract
Points!
( you cant respond from the last 2 i did)
have a nice day :)
Answer:
Thank youuuu!!
(x-8)2 – 7 = 25
Factored
Answer:
x = 8 ± 4√2
Step-by-step explanation:
(x - 8)² - 7 = 25
Add 7 to both sides.
(x - 8)² = 32
Take the square root for both sides.
x - 8 = ±√32
Add 8 to both sides.
x = 8 ±√32
Simplify √32
√32 = √16 · √2
√32 = ±4√2
x = 8 ± 4√2
there are 12 ribbons all of them equal 3 feet how long is each ribbon?
Answer:
i think
12 x 3 = 36 feet long
Answer:
36 feet and maybe check me out on sou-ndcloud and spo-tify and rate a sound I made "Jealousy is a bltch I hate her" might wanna turn down ur headphones and audio in general
Step-by-step explanation:
Anyone know the answer to this help me out please
Answer:
C.
Step-by-step explanation:
< is less than the one with the line is less than equal to
Answer:
D
Step-by-step explanation:
Since there's a circle on -3 then it's not considered on the graph and a dot on 4 so it's considered.
[tex] - 3 < x \leqslant 4[/tex]
5x-3=12x+11
Algebra problem, pls help
Answer:
hope this helps \(owo)\
Step-by-step explanation:
Answer:
x= -2
Step-by-step explanation:
5x-3=12x+11
5x=12x+14
-7x=14
x= -2
solve the question below, please.
Answer:
Adam: 52.26°
Step-by-step explanation:
Use Cosine Rule, [tex] Cos(C) = \frac{a^2 + b^2 - c^2}{2ab} [/tex], to find the angle of both players.
✔️Angle of Carlos:
Let the angle be C,
a = 50 ft
b = 40 ft
c = 24 ft
Plug in the values into the equation
[tex] Cos(C) = \frac{50^2 + 40^2 - 24^2}{2*50*40} [/tex]
[tex] Cos(C) = \frac{3,524}{4,000} [/tex]
[tex] C = Cos^{-1}(\frac{3,524}{4,000}) [/tex]
C = 28.24° (nearest hundredth)
✔️Angle of Adam:
Let the angle be C,
a = 30 ft
b = 22 ft
c = 24 ft
Plug in the values into the equation
[tex] Cos(C) = \frac{30^2 + 22^2 - 24^2}{2*30*22} [/tex]
[tex] Cos(C) = \frac{808}{1,320} [/tex]
[tex] C = Cos^{-1}(\frac{808}{1,320)} [/tex]
C = 52.26° (nearest hundredth)
Which number line best shows how to solve this? please help quickly thank you!
Answer:
Step-by-step explanation:
I attached the work and answer below, take a look!
Find the missing endpoint if the midpoint is at (2,-5) and one endpoint is at (12,-5).
O (2,-5)
O(-8,-5)
O(10-8)
O (12,-5)
Answer:
The answer is (-8,-5)
Step-by-step explanation:
Since the midpoint is (2, -5), the 2 endpoints should be equidistant from each other. Since the endpoint that is given (12, -5), is 10 points to the right of the midpoint, the second midpoint should be 10 points to the left of it. 2-10=-8
Therefore, the other midpoint is (-8,-5)
Please help this is worth 30 points
Please help it’s due in 10 minutes
I will also venmo you $5
Answer:
[tex] \arc{PNM} = 222 [/tex]
Step-by-step explanation:
Central angle = measure of the arc it subtends
Therefore:
[tex] \arc{PN} = \arc{PM} = 138 [/tex]
A full circle = 360°
So,
[tex] \arc{PN} + \arc{PM} + \arc{NM} = 360 [/tex]
Plug in the values
[tex] 138 + 138 + \arc{NM} = 360 [/tex]
[tex] 276 + \arc{NM} = 360 [/tex]
[tex] \arc{NM} = 360 - 276 [/tex] (subtraction property of equality)
[tex] \arc{NM} = 84 [/tex]
[tex] \arc{PNM} = \arc{NM} + \arc{PN} [/tex]
Plug in the values
[tex] \arc{PNM} = 84 + 138 [/tex]
[tex] \arc{PNM} = 222 [/tex]
Consider the figure below.
part a- Determine sin(g)
part b- Determine tan(z)
part c- Determine cos(z)
part d- Determine sin(M)
Answer:
A) 77/427
B) 77/420
C) 420/427
Step-by-step explanation:
Sin= Opposite/Hypotenuse
Opposite always make a 90° with the Adjacent. adjacent and the Hypotenuse are across each other.
Cos= Adjacent/Hypotenuse
Tan= Opposite/Adjacent
Answer:
part a: 420/427
part b: 420/77
part c: 77/427
Anyone know the answer to 2? I really need answers :(
Answer:
1
Step-by-step explanation:
16 cups of water - 4 cups of paper
4 cups of water - [tex]\frac{4}{16}[/tex] × 4 cups of paper = 1 cup of paper
Answer:
1.
Step-by-step explanation:
16/4=4 and 4/4=1. 4/1 is the unit rate of 16/4. hope that helps
I will give brainliest out to anyone who answers correctly please helpmeeee
Answer:
4,5,9
8,9
35
Step-by-step explanation:
hope this helps
Jayla paints a book case. She uses 1 5/6 cups of paint on the outside of the book case and 3/8 cup of paint on the inside. How many cups of paint does Jayla use altogether
Answer:
Answer: Kayla used 2&5/24 cups of paint all together.
Step-by-step explanation:
Kayla paints a bookcase by using
1 5/6 cups of paint on the outside of the bookcase. Converting 1 5/6 cups to improper fraction, it becomes 11/6 cups of paint.
She also used 3/8 cup of paint on the inside.
Therefore, the total number of cups of paint that Kayla used all together would be cups of paint:
[tex]11/6 + 3/8 = (44 + 9)/24 = 53/24[/tex]
Converting to mixed fraction, it becomes
2 and 5/24 cups of paint
Please help I might flunk
please help i am really struggling
Answer:
greater than...
equal
Step-by-step explanation:
welcome
Solve for x -6x+14<-28 AND 3x+28<=25
Answer:
-6x+14<-28
x = x > 7
3x+28<=25
x = x less than or equal to -1
Step-by-step explanation:
Find The Amount Of Time
I = $60, P = $750, r = 4%
Answer:need help with what question?
Step-by-step explanation: what question?
A = {3,5,7,9}
B = {2, 4, 6, 8, 10)
C = {12, 14, 18, 20, 24}
D = {21, 26, 31, 36}
Given the sets above, fill-in the blank: 7 €
-4 (4x + 12)= -2(8x+24)