Answer:
a) The expression for the height, 'H', of the plant after 't' day is;
[tex]H = \dfrac{30}{1 + 5\cdot e^{-(2.02732554 \times 10^{-3}) \cdot t}}[/tex]
b) The height of the plant after 30 days is approximately 19.426 inches
Step-by-step explanation:
The given maximum theoretical height of the plant = 30 in.
The height of the plant at the beginning of the experiment = 5 in.
a) The logistic differential equation can be written as follows;
[tex]\dfrac{dH}{dt} = K \cdot H \cdot \left( M - {P} \right)[/tex]
Using the solution for the logistic differential equation, we get;
[tex]H = \dfrac{M}{1 + A\cdot e^{-(M\cdot k) \cdot t}}[/tex]
Where;
A = The condition of height at the beginning of the experiment
M = The maximum height = 30 in.
Therefore, we get;
[tex]5 = \dfrac{30}{1 + A\cdot e^{-(30\cdot k) \cdot 0}}[/tex]
[tex]1 + A = \dfrac{30}{5} = 6[/tex]
A = 5
When t = 20, H = 12
We get;
[tex]12 = \dfrac{30}{1 + 5\cdot e^{-(30\cdot k) \cdot 20}}[/tex]
[tex]1 + 5\cdot e^{-(30\cdot k) \cdot 20} = \dfrac{30}{12} = 2.5[/tex]
[tex]5\cdot e^{-(30\cdot k) \cdot 20} = 2.5 - 1 = 1.5[/tex]
∴ -(30·k)·20 = ㏑(1.5)
k = ㏑(1.5)/(30 × 20) ≈ 6·7577518 × 10⁻⁴
k ≈ 6·7577518 × 10⁻⁴
Therefore, the expression for the height, 'H', of the plant after 't' day is given as follows
[tex]H = \dfrac{30}{1 + 5\cdot e^{-(30\times 6.7577518 \times 10^{-4}) \cdot t}} = \dfrac{30}{1 + 5\cdot e^{-(2.02732554 \times 10^{-3}) \cdot t}}[/tex]
b) The height of the plant after 30 days is given as follows
[tex]H = \dfrac{30}{1 + 5\cdot e^{-(2.02732554 \times 10^{-3}) \cdot t}}[/tex]
At t = 30, we have;
[tex]H = \dfrac{30}{1 + 5\cdot e^{-(2.02732554 \times 10^{-3}) \times 30}} \approx 19.4258866473[/tex]
The height of the plant after 30 days, H ≈ 19.426 in.
What is the surface area of the solid
Answer:
189
Step-by-step explanation:
each of the triangles has a area of 35 cm, so 35x4=140, then the square is 49 cm so its 140+49=189.
sqrt x^7 ...........
What about the sqrt{x^7}?
Do you need to simplify?
Let me see.
sqrt{x^6} • sqrt{x}
Answer: (x^3)sqrt{x}
Note: sqrt{x} cannot be further simplified.
For the two right triangles above, explain why
.
What trigonometric ratio is also equal to the two given ratios?
Answer:
we cant see the triangles
Step-by-step explanation:
Question 9 of 10
On a unit circle, the terminal point of θ is
(√3/2,1/2)
What is θ?
A. π/2 radians
B. π/6 radians
C. π/4 radians
D. π/3 radians
Answer:
30° or π/6 rad
Step-by-step explanation:
Imagine or draw a right triangle with horizontal side (√3)/2 and vertical side 1/2. Verify that the hypotenuse of this triangle is 1 (which it must be, since the circle is a unit circle): [(√3)/2)^2 + (1/2)^2 = r^2, which leads to r = 1.
The tangent function tan x = opp/adj takes on the following values here:
tan x = 1/2 over √(3/2)/2, or 1/√3. Using a calculator or a table of trig function values, we find that the angle x is π/6 radians, or 30°
Answer:
B. π/6 radians
Step-by-step explanation:
a company has a storewide sale and discounts every item in the store by 24% you buy an item originally priced at $180 what is the price after the discount
Answer:
43.20
Step-by-step explanation:
x/180 = 24% or 24/100
Multiply 180 times 24 and get 4,320
Divide 4320 by 100
and get 43.20
What percent of computers sold on weekdays were sold on Tuesday? Round to the nearest percent.
Answer:
there isn't a difference they both have 20 so it will be the same
What is the expression in simplest form
Answer:
It would be option A
Step-by-step explanation:
ARE U HAVING A GOOD DAY
Answer:
Yup
Step-by-step explanation:
Answer:
Yes yes yes
Step-by-step explanation:
Which solution set is graphed on the number line?
-4 -3 -2
-1
0
1
2
3
4
"x21
C
X> 1
x < 1
X31
Answer:
for this one option C will be your answer
Step-by-step explanation:
identify the domain and range of the relation
{(4, 2), (1, 3), (0, 0), (-1, -1), (1, -3)
Answer:
So, the domain are:
[tex]x = 4,1,0,-1[/tex]
The range are:
[tex]y = 2,3,0,-1,-3[/tex]
Step-by-step explanation:
Given:
[tex]\{(4, 2), (1, 3), (0, 0), (-1, -1), (1, -3)\}[/tex]
Required
The domain and the range
In relation, we have:
[tex]\{(x_1, y_1), (x_2, y_2), ......, (x_n, y_n)\}[/tex]
Where the x values are the domain and the y values represent the range.
So, the domain are:
[tex]x = 4,1,0,-1[/tex]
The range are:
[tex]y = 2,3,0,-1,-3[/tex]
Find the value of x.
Step-by-step explanation:
hope this will help you plz check and tell me
I need help on finding the height of a triangular pyramid
if there’s no work, I don’t get credit
I will give Brainliest
Answer:
20 in
Step-by-step explanation:
The formula for the volume of a triangular pyramid is V=1/3 x B x H, in which B is the area of the base and H is the height. You're given the volume and area of the base so you can just plug that into the formula. You will get 120 = 1/3 x 18 x H. You can multiply the 1/3 and 18 so you will get 120 = 6H. In this case, you are solving for H so you need to isolate the variable. You can do this by dividing both sides by 6. You will end up eith 20 = H.
what is the proportion of 22/3
Answer:
not to sure but is it 733.333333333333%
Step-by-step explanation:
help me please i need help
Answer:
k= 70
Step-by-step explanation:
Find the 100th term to 1,3,9,27
Answer:
The n-th term of this sequence appears to be
3
n
−
1
,
n
≥
1
.
Step-by-step explanation:
These are powers of
3
ordered from
3
0
=
1
to
3
a
(for an integer
a
≥
1
). However, the first convenient value for
n
is
1
, not
0
(imagine saying the 0th term of a sequence). Because of that, since the first term is actually
3
0
, we need to start from the first term (
n
=
1
) being
3
1
−
1
. The next is
3
2
−
1
,
3
3
−
1
...
3
n
−
1
.
what is the value of
(8+3k)²-(-k-6)²¹ if k=5
Answer:=530
Step-by-step explanation:
One angle of an isosceles triangle measures 32°. Which other angles could be in that isosceles
triangle?
Answer:
32° and 116°
Step-by-step explanation:
An isosceles triangle has two equal angles and the other angle is found by subtracting the sum of the two equivalent angles from 180°.
Since, one of the angles are given in the problem, one of the angles is 32°.
To find the other angle, we subtract the two angles from 180°.
180° - 32° - 32°
116°
The other two angles are: 32° and 116°
The area: is about? UHH anyone know this??!!
Answer:
1.77 ft.^2
Step-by-step explanation:
What we know: diameter of circle is 1.5
What we need: the radius to find the area of a circle
What we can do: Divide 1.5 by two to get the radius(since the diameter is twice the radius : radius x 2 = diameter)
Math --> 1.5 divide by 2 = .75
What we need to know: Formula of finding Area of Circle is A=(pie)r^2
Insert what we know: A=(pie).75^2
Work out problem(do radius to the second power first)#1: .75^2 = .5625(unrounded)
Work out problem(multiply number by pie))#2: .5625 multiplied by (pie) = 1.7671458676442586966352369030947
Round Answer to nearest hundredth: 1.77 ft.
Note: I use the pie sign for this problem. So I used : 3.1415926535897932384626433832795
I used a scientific calculator for the calculations.
^2 is added after the unit to show Area.
To the second power is multiplying the number by itself. Example: 4^2 = 16 = 4 x 4
A game company asked people at the mall which game console they owned. They recorded the results in the bar graph below. How many more people owned a Xbox 360 than owned a Gameboy?
Answer:
Option (4)
Step-by-step explanation:
From the bar graph given in the picture,
Number of people who owned a Xbox 360 = 8
Similarly, number of people who owned Gameboy = 1
Therefore, difference in the number of people having Xbox 60 and Gameboy = 8 - 1
= 7
Option (4) is the correct option.
The dot plot below shows the number of students on a classroom honor roll for one or more weeks. According to the dot plot how many students were on the classroom honor roll of 5 or more weeks
3
Here is a formula.
V = 1/2 X2 h
Work out the value of V when
(1 Point)
X = 11 and h = 6
Enter your maths answer
11
Answer:
if V=½X2h then
V=½(11)(2×6)
V=(11/2)(12)
V=66
Use the equation √4x+15 - 3√x How many potential solutions are there?
Answer:
potential solutions- 1
extraneous solutions- 0
solution to equation- x=3
Step-by-step explanation:
Solve and check
please please help i will mark u as a brill it is easy please
Answer:
B=25
Step-by-step explanation:
Help??????? Anyone.
Answer: if the second angle is vertical to the first one, then they will both have the same degrees which is 131°
Step-by-step explanation:
the bar graph shows the results of spinning a spinner 100 times. use the bar graph to find the experimental probability of the event.
Spinning a 2
Answer:
you will have an 18% chance of rolling a 2.
Step-by-step explanation:
18/100 = 18
The probability of spinning an even number is 39/10
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, we have,
to determine the probability of spinning an even number.
The missing bar chart is added as an attachment
The bar chart (see attachment) represents the graph that would be used to calculate the required probability
On the bar chart, we have the sample size of the even number
Even number = 18 + 21
Even number = 39
So, we have
P(Even) = Even/Total
By substitution. we have
P(Even) = 39/100
Hence, the probability is 39/100
Read more about probability at
brainly.com/question/251701
#SPJ2
Put smallest to largest
4.3 4.303 4.03 4.33 4.033 4.003
Are ZK and 2B corresponding angles? Explain.
Answer:
No
Step-by-step explanation:
When two lines are crossed by another line, the angles in matching corners are called corresponding angles. <K and <B do not match this definition, so they are not corresponding angles.
Answer:
NO!
Step-by-step explanation:
K and B are not corresponding angles
They are supplementary angles
In the image there is an example of correspodning angles
The integer 4 more than -5 is??
Answer:
-1
Step-by-step explanation:
Add 4 to -5
-5 + 4 = -1
Start at -5 on the number line and count 4 units to the right.
-4, -3, -2, -1
We end up at -1.
Answer: -1
You can also add -5 + 4 = -1.
Either way you will get -1.
Belle deposited money into a savings account. This table gives the value of her account for the first 14 months after the initial deposit. The data can be modeled using an exponential function.
Years 2 4 6 8 10 12 14
Account value $106 $113 $119 $126 $135 $143 $152
Based on the data, which amount is closest to the value of the account 24 months after the initial deposit?
$180
$200
$240
$280
Answer:
The answer is B 200
Step-by-step explanation:
i just took the test so yah :)
Jaden and Cali start doing chores at 9:15 AM. Jaden finishes his chores 60
minutes later. Cali finishes his chores 30 minutes after Jaden. When does Cali
finish his chores?
Answer:
10:45 am
Explanation:
9:15 + 60 = 10:15
10:15 + 30 = 10:45
Answer:
cali finished 10:45
Step-by-step explanation:
60 min=1hour
9:15 + 1h = 10:15
10:15 + 30 min = 10:45