Step-by-step explanation:
= 2³ + x ³ + 3(2)²x + 3(2)x²
= 8 + x³ + 12x + 6x²
= x³ + 6 x² + 12 x + 8
Let c be a positive number. A differential equation of the form dy/dt=ky^1+c where k is a positive constant, is called a doomsday equation because the exponent in the expression ky^1+c is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term My^1.01. If 2 such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?
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
3. $595 refrigerator; 22% discount.
Show the work
Answer:
Discount: $130.90
Total cost after discount: $464.10
Step-by-step explanation:
Since I don't know what the actual question is, I will solve for the discount:
595 × 22%
Convert percentage into decimal
595 × 0.22
130.9
Discount is 130.9
Now I'll solve for how much that will take off from the original price:
595 - 130.9
464.1
On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, of planted seeds will germinate. A random sample of seeds is chosen. If these seeds are planted according to the instructions, find the probability that of them germinate. Do not round your intermediate computations, and round your answer to three decimal places.
Complete question:
On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, 63% of planted seeds will germinate. A random sample of 9 seeds is chosen. If these seeds are planted according to the instructions, find the probability that 4 of them germinate.
Answer:
[tex]P(x = 4) = 0.1376[/tex]
Step-by-step explanation:
Given
[tex]n = 9[/tex]
[tex]p = 63\%[/tex] --- proportion that germinates
[tex]p = 0.63[/tex]
Required
P(x = 4)
This question follows a binomial distribution:
[tex]P(x) = ^nC_x*p^x*(1-p)^{n-x[/tex]
When x = 4;
[tex]P(x = 4) = ^9C_4*0.63^4*(1-0.63)^{9-4[/tex]
[tex]P(x = 4) = ^9C_4*0.63^4*(0.37)^5[/tex]
[tex]P(x = 4) = 126*0.63^4*0.37^5[/tex]
[tex]P(x = 4) = 0.13763895392[/tex]
[tex]P(x = 4) = 0.1376[/tex]
there are 144 microscopes in boxes at a school. each box has 24 microscopes which equation could be used to find b, the number of boxes of microscopes at this school
A. 24+144= b
B. 144-b= 24
C. B divided by 24= 144
D. 24 x b= 144
A rectangle has vertices at P (16,16), Q(16,-16), R(-16,-16) and S(-16,16). The origin is the center of dilation and the rule of a dilation is (x,y)→(1/4x, 1/4y) What is P' of the dilated image, PQ’R’S’?
Answer:
(4, 4)
Step-by-step explanation:
So you're trying to find what P' is, and P' would be the dilation of P. This means that you apply the rule (x, y) --> (1/4x, 1/4y) with the coordinate point (16, 16). This would be:
(16, 16) --> (1/4 * 16, 1/4 * 16) = (4, 4)
Ralph opened up his checking account with $100. On Monday, he withdrew $45 to purchase a pair of jeans. On Wednesday, he deposited a $25 check he received for his birthday from his uncle. On Friday, he used his debit card to buy a $98 football ticket. What is the balance in Ralph's checking account?
Answer:
The answer is -18
Step-by-step explanation:
He starts off with $100 in his account. He then take so $45 to purchase a pair of jeans, so we have to subtract 45 from 100 and that gives us $55. He now has $55 in his account, he then adds another $25 to his account, so we have to add 25 to 55 and that will give us $80 in his account. Finally on Friday he takes out $98 of his checking account. He takes out more than he has in his checking account so we have to subtract $80 from $98 and we will get $18, but since he takes out more than what he has in his account the answer will be negative and we end up with -18 dollars in his checking account.
Answer:72
Step-by-step explanation:
Explain why (x+1)(3x-6) is NOT a complete factorization of 3x^2-3x-6
Answer:
The real answer is:
3x^2 -6x+3x-6
Step-by-step explanation:
Mariel says that a jewelry box that is 3 inches high, 4 1/2 inches wide, and 5 inches long has a volume of 67 1/2 inches. Katie says that answer is not quite correct. What is the error in Mariel's answer?
Answer: inside width, length and heights may be smaller
Step-by-step explanation. Walls of box have certain thickness, assume 0.1 inches. Then inner measures would be 2.8 in, 4.3 in and 4.8 in. You need to reduce thickness of wall from both sides.
2. What is the solution to the inequality
--4x > 132? Show your work
Answer:
x < -33 ( mark me as the brainliest )
Step-by-step explanation:
1) -4x > 132
2) -4x/4 > 132/-4
3) x < -33
1) Find the missing angle.
31°
949
? + 31° + 94° = 180°
? + 125° = 180°
? = 180° - 125°
? = 55°
Answer: 52°
Step-by-step explanation:
Angles in a triangle always add up to 180°.
So to work out what the missing angle is, you would have to add 34 and 94 together.
34+94=128
Then you would have to take 128 away from 180.
180-128=52°
Hope this helps :)
Which answer best describes the shape of this distribution?
uniform
skewed left
bell-shaped
skewed right
An untitled line plot from 35 to 49. The plot displays the following values as dots above the corresponding value on the number line. One dot at 36. One dot at 37. One dot at 38. One dot at 40. Two dots at 41. One dot at 42. Three dots at 43. Four dots at 44. Five dots at 45. Three dots at 46. Two dots at 47. One dot at 48.
Answer:
huh what am i looking at
Step-by-step explanation:
step-by-step explanation
Answer:
its skewed left if you are in k12
Step-by-step explanation:
Helpppp!!!!!! I need this nowwwww
2/6+1/4
Show work please
And no links
Answer:
7/12
Step-by-step explanation:
1/3+1/4
convert to twelfths
4/12+3/12
7/12
Answer:
7/12
Step-by-step explanation:
2/6 + 1/4
Change the denomintors to be alike (Change the denominators to 12) 4/12 + 3/12
Multipy the top and bottom
Add
Get 7/12
Brainliest?
please help sarie this is the rest of the questions and i need help
Well what's the question? I got a buncha graphs and no question!
²³√∛·×÷±≈≠≤≥βα∞∨∧∉∈⇔,⇒≅≡ΔπФω↑↓∵∴↔→←⇵∀⊅⊄⊇⊆⊃⊂∑∫⇆⇄⇅°∠∡⊥∪∩∅¬⊕║∦∝㏑㏒∞
What do all of these symbols stand for?
Answer:
Mathematical symbols used for different calculations?
Alexa uses the binomial theorem to correctly expand (x + 2)^4. Which is one of the terms in Alexa's
answer?
24x^2
6x^2
16x
2x^4
Answer:
24x^2
Step-by-step explanation:
When expanded (x+2)^4= x^4+8x^3+24x^2+32x+16
The only term that matches with these is 24x^2
Answer:
24x^2
Step-by-step explanation:
HELPPP PLEASE YOU’LL GET 10 POINTS
Answer:
angle y and angle x
Step-by-step explanation:
Hello! I was trying to Do 69x24 but it is sadly not giving helpful tips so I was wondering if you can help me step by step?
Which expression is equivalent to sqrt -108 - sqrt -3?
A) 5 sqrt 3i
B) 6 sqrt 3i
C) 7 sqrt 3i
D) 8 sqrt 3i
Anybody can tell me How to solve |8|+|-6|?
The radio of boys to girls at a middle school is 3 : 2 what is the ratio of girls to all students.
Answer:
2:5
Step-by-step explanation:
because the total students are 5 and just girls are 2
also u wrote radio but i think its ratio
pls mark brainlest let me know if u got it right?
The radius of a circle is 3.9 in. Find the circumference to the nearest tenth.
Answer:
24.5
Step-by-step explanation:
ANSWER THIS PLZZ I WILL GIVE TOP COMMENT :)!!!!!
Answer:
D, -42 multiply 6 on both sides
D. because when it is multiplied, the inequality is no longer true.
What is the value of x in the equation 2/3x = 12
Answer:
x = 8
The value of 'x' is 8
Step-by-step explanation:
2/3(8)=12
2/(24)=12
Good luck!!
x
What is the angle of elevation of the sun when a 50-ft
mast casts an 18ft shadow? Round to the nearest
whole number.
Tano
50
Tan 0 =
18
0=
Opposite Leg
Adjacent Leg
Submit
50ft
How do I solve this please it’s the last problem
Answer:
[tex]\theta \approx 1.23^\circ[/tex]
Step-by-step explanation:
The expression has been given as:
[tex]tan(\theta) = \frac{50}{18}[/tex]
Required: Find [tex]\theta[/tex]
Simplify the fraction
[tex]tan(\theta) = 2.7778[/tex]
Take arc tan of both sides
[tex]\theta = tan^{-1}(2.7778)[/tex]
[tex]\theta \approx 1.23^\circ[/tex]
The data is shown below:
91, 48, 86, 49, 77, 86, 64, 78
What is the median?
a. 72.37
b. 74
c. 86
Answer: 72
Step-by-step explanation: Its in the middle
What is the probability of flipping a coin 85 times and getting tails 30 times or
fewer?
A. 99.8%
B. 33.2%
C. 95.9%
D. 0.4%
Answer:
C
Step-by-step explanation:
Answer:
0.4
Step-by-step explanation:
what is the answer to 1\2÷3
Answer:
0.16666666666
Step-by-step explanation:
1/2 ÷ 3
1/2/3
0.16666666666
Or
1/2 = 0.5
0.5 ÷ 3
0.16666666666
3/2 or 1.5. You have to multiply by the reciprocal.
Is it a function yes or no
Answer:
no
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
Simplify the following expression completely, where x 20.
x5xy* + 405x’y* - 180x’y4
O xy2 5x + xy? V405x – xy2/80x
0 6xyV5x
-3xy 5x + xy? J405x
O 6xy ſ5x}
Answer:
Option B is your answer
Step-by-step explanation:
hope it helps
have a great day!!
Answer:
A.) -80X^8 + 40x^7 -5x^6 -3x^2
Its OPTION A
Step-by-step explanation: