Population y grows according to the equation dy/dt=ky, where k is a constant and t is measured in years. if the population doubles every 10 years, then the value of k is
Given that the population doubles every ten years, k may be found using the population growth equation dy/dt=ky by computing ln(2)/10, or roughly 0.0693 annually.
We begin by thinking about the solution to the differential equation dy/dt = ky, where the population doubles every ten years, in order to determine the value of k. This differential equation can be solved generally as y(t) = y(0)e^kt, where y(0) is the beginning population.
Since there are ten years between population doubling, we can write: y(10) = 2y(0) = y(0)e^10k.
The result of dividing both sides by y(0) is 2 = e^10k.
We get: ln(2) = 10k by taking the natural logarithm on both sides.
After calculating k, we have k = ln(2)/10 ≈ 0.0693.
Thus, k's value is around 0.0693 per year.
multiply and simplify 12 and 2 / 3 3 + 1 / 4
Apply the distributive property to create an equivalent expression. 2(3-8y)
Answer:
An equivalent expression is [tex]6 - 16y[/tex]
Step-by-step explanation:
The distributive property consists in removing the parenthesis. For this problem, it is done by multiplying the number outside the parenthesis by each term inside the parenthesis and then performing a subtraction between the results because of the minus sign inside.
For the expression [tex]2(3-8y)[/tex], when applying the distributive property, you would get:
[tex]2\times 3 - 2\times 8y[/tex]
[tex]6 - 16y[/tex]
Thus, an equivalent expression is [tex]6 - 16y[/tex].
The distributive property to remove the parentheses in the expression 2(3 - 8y) is 6 - 16y
Using the distributive property to remove the parenthesesFrom the question, we have the following parameters that can be used in our computation:
2(3 - 8y)
When the expression is expanded, we have the following
2(3 - 8y) = 2 * 3 - 2 * 8y
Evaluate the products
This gives
2(3 - 8y) = 6 - 16y
Lastly, we have
2(3 - 8y) = 6 - 16y
Hence the expression when simplified is 6 - 16y
Read more about expression at
brainly.com/question/30492964
#SPJ6
Suppose you have 15 days until your field trip and you need to raise $900 there are 10 students going on the field trip they will each help fundraise how much should each student have raised in 1 week?
Steven, a tailor, got an order to make a blazer. The customer specifically asked him to save 5/6 of a foot of the given cloth to make a pocket square. However, Steven accidentally saved 5/12 of a foot. What is the difference between the requested cloth and the saved cloth? A. 0.1466' B. 0.4166' C. 0.4265' D. 04066'
Which equations represent inverse variation? Check all that apply.
y = 2x
pv = 13
z = (2/x)
4 = (y/x)
h = (9g/5)
Answer:
B and C
Step-by-step explanation:
which equation represents a proportional situation?
A. y = 9x
B. y = -2x + 23
C. y = - 3x + 4
D. y = 3x - 12
Find dy/dx by implicit differentiation. 8 cos x sin y = 6
find the volume of this prism
Which is the best approximation for the solution of the system of equations
Answer:
Solution of the system of the equations is (0.882, 0.647)
Step-by-step explanation:
As shown in the figure equations are [tex]y=-\frac{2}{5}x+1[/tex] and y = 3x - 2
Solution of the system of equations will be the common point or point of intersection of these lines.
To get the point of intersection we will solve these equations.
We will equate these equations to get the value of x.
[tex]-\frac{2}{5}x+1=3x-2[/tex]
[tex]-2x+5=15x-10[/tex]
15x + 2x = 10 + 5
17x = 15
[tex]x=\frac{15}{17}[/tex]
x = 0.882
By putting x = 0.882 in y = 3x - 2
y = 3(0.882) - 2
y = 0.647
So the solution of systems of equations is (0.882, 0.647)
How do you solve 3x^3+6x^2=72x
PLEASE HELP PLEASE WILL GIVE BRAINLIEST !!!!! Freya is training for a track race. She starts by sprinting 200 yards. She gradually increases her distance
Answer:
A. [tex]a_n=200+(n-1)5[/tex]
Step-by-step explanation:
Given,
The initial sprinting of Freya = 200 yards,
Also, She gradually increases her distance by 5 yards per day,
So, in second day her sprinting = 200 + 5 = 205 yards,
In third day = 205 + 5 = 210 yards,
In fourth day = 210 + 5 = 215 yards,
...................., so on,.....
Hence, the sequence that shows the given situation,
200, 205, 210, 215, .........
Which is an A.P.
That having first term, a = 200,
Common difference, d = 5,
Thus, the explicit formula for the given situation is,
[tex]a_n=a+(n-1)d[/tex]
[tex]\implies a_n=200+(n-1)5[/tex]
Option A is correct.
Answer:
Option A.
Step-by-step explanation:
The explicit formula of an AP is
[tex]a_n=a+(n-1)d[/tex] .... (1)
where,
a is the first of the AP,
d is common difference.
It is given that Freya starts by sprinting 200 yards and she gradually increases her distance, adding 5 yards a day.
200, 205, 210,..., 305
Here,
First terms = 200
Common difference = 5
Substitute a=200 and d=5 in equation (1), to find the required explicit model
[tex]a_n=200+(n-1)5[/tex]
Therefore, the correct option is A.
Find the value of each variable.
∆FGH , the measure of <H=90, FH=48,GF=73,and, HG=55 What is the value of the sine of <F to the nearest hundredth
Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.
write a polynomial (x+6)(x-2)(x-1)
A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1.3 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? (That is, find the angle's rate of change when the bottom of the ladder is 8 ft from the wall.)
The angle's rate of change when the bottom of the ladder is 8ft from the wall is
[tex]\dfrac{-1.3}{6} rad/s[/tex]
It is given the Length of Ladder [tex](h)[/tex] is [tex]10ft.[/tex]. and the distance between the bottom of the ladder to the wall [tex](r)[/tex] is [tex]8ft.[/tex] as shown in the below figure.
By using the Pythagoras Theorem
[tex]b=\sqrt{10^{2}-8^{2} }\\=\sqrt{36} \\=6ft.[/tex]
and
[tex]cos(\theta)= r/h\\cos(\theta)=r/10[/tex]
Differentiating both sides with respect to [tex]'t'[/tex] by using the chain rule
[tex]-sin(\theta)\dfrac{\mathrm{d}\theta }{\mathrm{d} t}=\dfrac{1}{10} \dfrac{\mathrm{d}r }{\mathrm{d} t}\\\\\dfrac{\mathrm{d}\theta }{\mathrm{d} t}=\dfrac{1}{10} \dfrac{\mathrm{d}r }{\mathrm{d} t} \dfrac{1}{-sin(\theta)} } ......(eq. 1)[/tex]
given
[tex]\dfrac{\mathrm{d}r }{\mathrm{d} t}=1.3ft./s\\sin(\theta)=\frac{6}{10}[/tex]
putting this in eq.1, we get
[tex]\dfrac{\mathrm{d} \theta}{\mathrm{d} t} = \dfrac{1.3}{10} (\dfrac{1}{-\frac{6}{10} }) \\\dfrac{\mathrm{d} \theta}{\mathrm{d} t} =\dfrac{-1.3}{6} rad/s[/tex]
So the angle's rate of change when the bottom of the ladder is 8ft from the wall is[tex]\dfrac{-1.3}{6} rad/s[/tex].
Know more about Pythagoras Theorem here:
https://brainly.com/question/15190643?referrer=searchResults
A player shoots a basketball from a height of 6 feet. The equation, h = -16t 2 + 25t + 6, gives the height, h , of the basketball after t seconds. Describe the height, rounded to the nearest tenth of a foot, of the basketball after 1.5 seconds, assuming no other player touches the ball.
Answer:
The height of the ball after t =1.5 second is 7.5 feet.
Description:
The basket ball shoots from a height of 6 feet, it increase the height 1.5 feet after 1.5 seconds.
Therefore, the basketball thrown at the rate of 1 feet/per second.
Step-by-step explanation:
Given: A player shoots a basketball from a height of 6 feet. The equation,
h(t) = [tex]-16t^2 + 25t + 6[/tex]
We need to find the height of the ball when t = 1.5 and describe the height.
plug in t = 1.5 in h(t) = [tex]-16t^2 + 25t + 6[/tex]
h(1.5) = [tex]-16(1.5)^2 + 25(1.5) + 6[/tex]
Simplifying the above expression, we get
h(1.5) = -36 + 37.5 + 6
h(1.5) = -36+43.5
h(1.5) = 7.5 feet
The height of the ball after t =1.5 second is 7.5 feet
Description:
The basket ball shoots from a height of 6 feet, it increase the height 1.5 feet after 1.5 seconds.
Therefore, the basketball thrown at the rate of 1 feet/per second.
Can a right triangle have two angles that measure 25 and 65
the perimeter of a semi circle is 20.56 MM. What is the semicircle of radius?
The sum of 5 consecutive numbers is 135
Answer:
Step-by-step explanation:
The answer is 25+26+27+28+29=135
Is the correct answer I basically divided 135 by 5 and got 27 then I just worked around that number to get the answer.
help me with this because I'm a little rusty on ths
which values are solutions to the inequality below? check all that apply
According to Coldwell Banker Real Estate Corporation, a home selling for $189,000 in Austin, Texas, would sell for $437,850 in Denver, Colorado. How much would a $350,000 home in Denver sell for in Austin? Round to the nearest $1000.
x * 1 + x/1 = _______.
Which of the following graphs represents the equation x >-3y+9
Consuela earns a salary of $40,000 per year plus a commission of $1,00 for each car she sells. Write and solve an equation that shows the number of cars Consuela must sell in order to make $60,000 in one year.
Answer:
y = $1,000/car x + $40,000
20 cars
Step-by-step explanation:
Let
x = number of cars sold
y = total earnings
The relationship between y and x can be expressed through a linear equation.
y = mx + b
where,
m is the slope
b is the y-intercept
The slope is how much she earns per car sold, that is, the commission of $1,000/car (I think you meant this number instead of $1,00).
The y-intercept is what she earns even if she does not sell any car, i.e. a salary of $40,000.
The resulting equation is
y = $1,000/car x + $40,000
If she is to make $60,000 in one year (y = $60,000), the number of cars sold is:
$60,000 = $1,000/car x + $40,000
$20,000 = $1,000/car x
x = 20 car
Use the parabola tool to graph the quadratic function f(x)=x^2+10x+24.
Graph the parabola by first plotting its vertex and then plotting a second point on the parabol
Answer:
See the attachment
Step-by-step explanation:
You want a graph of the parabola defined by f(x) = x² +10x +24.
VertexWe can add and subtract the square of half the x-coefficient to put the equation into vertex form:
f(x) = x² +10x +24 . . . . . . . . . . given
f(x) = x² +10x +25 +24 -25 . . . . add and subtract (10/2)² = 25
f(x) = (x +5)² -1 . . . . . . . . . write in vertex form
Comparing to the vertex form equation f(x) = (x -h)² +k, we see that ...
(h, k) = (-5, -1).
These are the coordinates of the vertex.
Another pointThe coefficient of x² is 1, so another point can be found by adding (1, 1) to the vertex. That means a second point on the parabola is ...
(-5, -1) +(1, 1) = (-4, 0)
GraphThe attached graph shows the parabola with vertex (-5, -1) through point (-4, 0).
__
Additional comment
When the coefficient of x² is not 1, the process is a little different. If you start with f(x) = ax² +bx +c, you can factor 'a' from the first two terms to help you get vertex form.
f(x) = a(x² +(b/a)x) +c
f(x) = a(x² +(b/a)x +(b/(2a))²) + c - a(b/(2a))²
f(x) = a(x +b/(2a)x)² +(c -b²/(4a))
The vertex is (-b/(2a), c -b²/(4a)).
The second point can be found by adding (1, a) to the vertex coordinates.
Larry used a pattern of colors to make a cube train he use Red Cube a blue cube a Red Cube and another Red Cube before he started the pattern again he use 15 cubes how many red cubes did Larry use
What is the probability that a unit chosen at random has between four and six rooms?