Answer:
16 ÷ 8 = 2
Step-by-step explanation:
It was really simple actually
Answer:
16 - 8 = 8
Step-by-step explanation:
16 divided by 8 = 2
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
PLS HELP AND ANSWER QUICK PLZ
Answer:
X = 90° , Y = 45°, Z = 45°
Step-by-step explanation:
Need help 15 points pls help me
5 1/2 feet is the base of window.
Answer:
area of parllelogram =base×height
25 2/3=base×4 2/3
77/3=base×14/3
77/3×3/14=base
base=77/14=11/2=5 1/2feet
The length of a rectangle is x feet more than its width. The area of the rectangle is 5x + 25. What is the width of the rectangle?
Answer:
w = [tex]l + \frac{25 - l^{2}}{l - 5}[/tex]
(Anyone can correct me if I'm wrong)
Step-by-step explanation:
Before we start the solving, we can make the following statements:
Area = l x w
Area = 5x + 25
therefore,
l x w = 5x + 25
Since the question states that the length is x more than the width, so we can make the following statement:
w = l + x
With this, we can substitute it to the first statement we made, l x w = 5x + 25,
l x (l + x) = 5x + 25
[tex]l^{2}[/tex] + lx = 5x + 25
lx - 5x = 25 - [tex]l^{2}[/tex]
x(l - 5) = 25 - [tex]l^{2}[/tex]
x = [tex]\frac{25 - l^{2}}{l - 5}[/tex]
From this, we can find w by substituting it in the statement we made earlier, w = l + x,
w = [tex]l + \frac{25 - l^{2}}{l - 5}[/tex]
The logarithm of a number to the base V2 is k. What is its logarithm to the base 2v2 ?
Answer:
[tex]log_{2\sqrt 2} X = \frac{1}{3}k[/tex]
Step-by-step explanation:
Given
Let the number be X
From the first statement, we have:
[tex]log_{\sqrt 2} X = k[/tex]
Required
Find [tex]log_{2\sqrt 2} X[/tex]
[tex]log_{\sqrt 2} X = k[/tex]
using the following law of logarithm
[tex]log_ab = n, b=a^n[/tex]
So:
[tex]log_{\sqrt 2} X = k[/tex]
[tex]X = \sqrt{2}^k[/tex]
Substitute: [tex]X = \sqrt{2}^k[/tex] in [tex]log_{2\sqrt 2} X[/tex]
[tex]log_{2\sqrt 2} X = log_{2\sqrt 2} ( \sqrt{2}^k)[/tex]
[tex]log_{2\sqrt 2} X = klog_{2\sqrt 2} \sqrt{2}[/tex]
Apply the following law:
[tex]log_ab = \frac{log\ b}{log\ a}[/tex]
[tex]log_{2\sqrt 2} X = k\frac{log\ \sqrt 2}{log\ {2\sqrt 2}}[/tex]
Express the square roots as power
[tex]log_{2\sqrt 2} X = k\frac{log\ 2^\frac{1}{2}}{log\ {2 * 2^\frac{1}{2}}}[/tex]
[tex]log_{2\sqrt 2} X = k\frac{log\ 2^\frac{1}{2}}{log\ {2^\frac{3}{2}}}[/tex]
using the following law of logarithm
[tex]log_ab = n, b=a^n[/tex]
[tex]log_{2\sqrt 2} X = k\frac{\frac{1}{2}log\ 2}{\frac{3}{2}log\ 2}}[/tex]
[tex]log_{2\sqrt 2} X = k\frac{\frac{1}{2}}{\frac{3}{2}}}[/tex]
Rewrite as:
[tex]log_{2\sqrt 2} X = k * \frac{1}{2} \div\frac{3}{2}[/tex]
[tex]log_{2\sqrt 2} X = k * \frac{1}{2} *\frac{2}{3}[/tex]
[tex]log_{2\sqrt 2} X = k * \frac{1}{1} *\frac{1}{3}[/tex]
[tex]log_{2\sqrt 2} X = \frac{1}{3}k[/tex]
What is the common denominator of 3 5 and 4 10
Answer:
3 and 5, 15; 4 and 10, 20
Step-by-step explanation:
The lowest number divided by 3 and 5 is 15. Same for 4 and 10. The lowest number they can both be divided by is 20.
If one pair of supplementary angles is a right angle, the other angle must also be a right angle true or false?
Answer: True
Step-by-step explanation:
A supplementary angle refers to the angles that has a sum of 180° when they're added together.
We should note that a right angle equals to 90°, therefore the other angle in the supplementary angle will be:
= 180° - 90°
= 90°
Since a right angle equals 90°, then the other angle must be a right angle.
Therefore, the answer is TRUE.
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.
HElP ME 5th grade math
Answer:
(4.80 x 0.05) + 4.80
Step-by-step explanation:
If 65% of Americans are overweight, how many people would be overweight in a city of 1.5 million?
Answer:
hey There
Step-by-step explanation:
This compares with 27.5 percent of those age 55 to 64 and 25.6 percent of those age 65 to 74. With respect to being overweight, 31.8 percent of the individuals 75 and older were such, while 37.9 percent of 55 to 64 year olds and 37.8 percent of individuals age 65 to 74 were overweight (figure 1).
Answer:
66.9%
i hope thats right
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:
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]
can someone help having trouble solving this question
Answer:
if you pit the shape in a straight line it would be 180 degrees now take 180 take 130 and 100 and subtract those add that to the other 30 then take 180 divided by 60
Answer:
x = 50°
Step-by-step explanation:
sum of exterior angles is always equal to 360°
so, we can add all the given numbers and set them equal to 360° to find x:
130° + 30° + 100° + x° + x° = 360°
260° + 2x = 360°
2x = 100°
x = 50°
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
if f(x)=5x-7,what isf(3)?
Answer:
Explanation:
f ( − 3 ) basically means substitute − 3 for x in the function − 5 x
f
(
−
3
)
=
−
5
(
−
3
)
−
7
f
(
−
3
)
=
15
−
7
f
(
−
3
)
=8
Step-by-step explanation:
Investigate the patern “13/1 family” of fractions. Use plenty of space to show what you find.
Answer:
2/1 of a family
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:
Which transformation could NOT be used to prove that two circles are congruent to one another?
Answer: D
Step-by-step explanation:
PLEASE PLEASE PLEASE HELP ME!
Answer:
I dont see the question...
Step-by-step explanation:
what is the slope of the line passing through the points (4,7) and (-2,10)?
Answer:
-1/2
Step-by-step explanation:
Answer:
the answer is the slope is -1/2
(Urgent) Worth 15 points 7.3
Answer: 20790
Step-by-step explanation:
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
Helps, is it 64 111 or 90?
Answer:
111
Step-by-step explanation:
please OMG I DONT UNDERSTAND
Answer:
ANSWER
Step-by-step explanation:
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?
Need the answer ASAP
Answer:
63
Step-by-step explanation:
To find the area of a trapezoid you have to use the formula
a+b/2 h
So we would substitute them
3 + 15 / 2 x 7
Which would equal
63
Hope this helps :)
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 :)
Find X please help me with test corrections due midnight tonight!
If HBN is congruent to LYR.
Answer:
the answer is
x=22..........
Use similar triangles to solve for the missing lengths below.
If you know how to work this out please help:)
Answer:
x = 14
y = 18
Step-by-step explanation:
By the property of similar triangles,
If two triangles are similar their corresponding sides will be proportional.
[tex]\frac{AB}{EF}= \frac{AC}{GE}[/tex]
[tex]\frac{5}{10}=\frac{7}{x}[/tex]
x = [tex]\frac{70}{5}[/tex]
x = 14
Similarly, [tex]\frac{AB}{EF}= \frac{CB}{GF}[/tex]
[tex]\frac{5}{10}=\frac{9}{y}[/tex]
y = [tex]\frac{90}{5}[/tex]
y = 18