Answer:
c. dP/dt = (1/5)P
Step-by-step explanation:
Given that the rate of change of population with respect to time dP/dt is directly proportional to the population, P, we have
dP/dt ∝ P
dP/dt = kP
Given that dP/dt = 2 million insects per day and P = 10 million insects after 5 days, So,
2 = k × 10
k = 2/10
k = 1/5
So, dP/dt = kP
dP/dt = (1/5)P
The option C is correct
DifferentiationThe rate of change of a function with respect to the given variable.
How to get the option?The rate of change of population with respect to time is directly proportional to the population P. We have
[tex]\dfrac{\mathrm{d} P}{\mathrm{d} t} \propto P\\\\\dfrac{\mathrm{d} P}{\mathrm{d} t} = kP[/tex]
[tex]\dfrac{\mathrm{d} P}{\mathrm{d} t}[/tex] is 2 million insects per day and P = 10 million insects after 5 days. So
[tex]\begin{aligned} \dfrac{\mathrm{d} P}{\mathrm{d} t} &= kP\\2 &= 10k\\k &= \dfrac{1}{5} \\\end{aligned}[/tex]
Then
[tex]\dfrac{\mathrm{d} P}{\mathrm{d} t} = kP\\\\ \dfrac{\mathrm{d} P}{\mathrm{d} t} = \dfrac{1}{5} P[/tex]
Thus, option C is correct.
More about the Differentiation link is given below.
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What is the value of 3 in the figure shown below?
с
4.3
D
61
3
3
53
A
4.3
9514 1404 393
Answer:
66
Step-by-step explanation:
Angle D (x°) is the same measure as angle A. The measure of angle A is that required to make the total of angles in ΔABC be 180°.
∠A = 180° -61° -53° = 66°
The value of x is 66.
For parallelogram ABCD, find the value of x
Answer:16
Step-by-step explanation:
Your car repair bill was $390. You were charged $215 for parts and $35 per hour for labor.
How many hours did the repairs take?
Answer:
5 hours
Step-by-step explanation:
subtract 390 by 215 to get 175 then divide 175/35 to get 5
Which is the correct order of the numbers from least to greatest? -4/5, 3, 0.4, -1, -5/4
Answer:
-5/4, -1, -4/5, 0.4, 3
Step-by-step explanation:
Answer:
-4/5 -1 -5/4 .4 3
Step-by-step explanation:
Roger is 71.5 inches tall. How many centimeters tall is she?
1 inch = 2.54 cm
Do not use a label - just numbers.
Answer:
181.61 centemeters
Step-by-step explanation:
Answer:
181.61
Step-by-step explanation:
Make a proportion:
1 inch = 2,54 cm
71,5 inches = x cm
x = 71,5 * 2,54 = 181,61 cm
Shrina has read 10% of the books that are in the library. She has now read 327 books.
How many books are there in the library?
The length l of a 200-square-foot rectangular vegetable garden is 4 feet less than twice the width w. Find the length and width of the garden.
Answer:
L=18.1, W=11.0
Step-by-step explanation:
Oliver said, "To the nearest hundred, I’ve attended drama club for 900 days of my life!” Write three numbers that could be the actual number of days Oliver has attended drama club.
A. 743, 970, 933
B. 870, 933, 780,
C. 780, 849, 761,
D. 867, 870, 933
Omg Plzzzzz helpppp!!!!!
Answer:
D
Step-by-step explanation:
[tex]-5+2(7b+6)\geq 10b+7(1+11b)\\-5+14b+12\geq 10b+7+77b\\70b\leq 0\\b\leq 0[/tex]
The line plot above shows the height of the baby giraffes at the zoo. What is the difference in height (in inches) between the shortest and the tallest baby giraffes?
Answer:
3.5 inches
Step-by-step explanation:
Height of tallest baby giraffe = 42.75 inches
Height of shortest baby giraffe = 39.25 inches
Difference in height between the tallest and the shortest baby giraffes = 42.75 - 39.25 = 3.5 inches
What is the initial value of the exponential function
represented by the table?
-2
1
3
-1
1
4
0
1
2
1
1
1
2
2
Answer:
o943
Step-by-step explanation:
Which is a better estimate for the weight of a double-decker bus
Step-by-step explanation:
Coaches are typically sized to a height of 4.38 meters, whereas 'high-bridge' vehicles are usually around 20 centimeters higher. At an average height of 18.65 metres, integrated double-deckers are often permitted .
x-1=y what is the answer plz give me the answer
Answer:
X = 0Y = 1First of all, observe that this is a line, since you can rewrite the equation as y−x+1=0 , which follows the pattern of the generic line ax+by+c=0 .
To draw a line you need two of its points, which you can connect.
To find two points, you can plug any value for one variable, and solve for the other.
For example, let's choose
x=0 . The equation becomes
0−1=y , and so y=−1 .
The first point is thus (0,−1).
Then, let's choose
x=1 . The equation becomes 1−1=y , and so y=0 . The first point is thus
(1,0).
Now you only need to draw the points
(0,−1)
Step-by-step explanation:
Hope it is helpful...
Line___is a transversal.
Answer:
C
Step-by-step explanation:
Line A is Parallel to Line B
Line C intersects Line A and B
Answer:
line C
Step-by-step explanation:
Yesterday, there were 80 problems assigned for math homework. Jenna did 45% of them correctly. How many problems did Jenna get right?
Answer:
36 questions was answered correctly
Step-by-step explanation:
80 x .45 = 36
Hope this helps
Have a great day :D
which graph represents exponential decay
Y=-2x+6 what is the y intercept
Answer:
the Y intercept is 6
Step-by-step explanation:
the Y intercept of a linear equation like that equation
any equation formed as: y=mx+b
B of the equation would always be the Y intercept
The y-intercept of the equation y = -2x + 6 is 6. It means that the line intersects the y-axis at the point (0, 6), where the y-coordinate is 6.
In the equation y = -2x + 6, the y-intercept represents the value of y when x is equal to zero.
To find the y-intercept, we substitute x = 0 into the equation:
y = -2(0) + 6
y = 0 + 6
y = 6
Therefore, the y-intercept of the equation y = -2x + 6 is 6. It means that the line intersects the y-axis at the point (0, 6), where the y-coordinate is 6.
To know more about coordinate:
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Solve.
5t ≤ –15
a. t ≤ 3
b. t ≥ 3
c. t ≤ –3
d. t ≥ –3
Answer:
c. t ≤ –3
Step-by-step explanation:
Solve for the following proportion for v.
Answer:
20/ 11 and if u want it in decimal it's 1.818182
Answer:
v =5÷11×4
v=20÷11=
Step-by-step explanation:
1.82 is your answer may be it is wrong
[1 and [2 are vertical angles. [2 has a measure of 31°. What is the measure of [1?
Answer:
x+31°=180°
180°-31°=149°
answer
help pls :)
how many real and complex roots does the graph have?
a. 2 real and 2 complex
b. 2 real and 4 complex
c. 4 real
b. 2 real
a or d dont read this heiejebdyueneidyebjwow isi ehbr
What is an equation of the line that passes through the points (4, -8) and (-4, 2)?
Put your answer in fully reduced form.
AHHH HELP
An aquarium holds 11.94 cubic feet of water, and 2.6 feet long and 1.4 feet wide. What is its depth? Round your answer to the nearest whole number.
Answer:
The depth of the aquarium is 3 feet.
Step-by-step explanation:
From the formula for the volume of a bar we find that [tex]V=whl[/tex], where [tex]w[/tex] is the width, [tex]h[/tex] is the height (depth), and [tex]l[/tex] is the length of the bar (which in this case is the aquarium). So [tex]h=\frac{V}{wl}[/tex] and by substituting [tex]V=11.94[/tex], [tex]w=1.4[/tex] and [tex]l=2.6[/tex] we can see that [tex]h=\frac{V}{wl} = \frac{11.94}{2.6 \cdot 1.4} = 3.2802... \approx 3[/tex] feet (rounding to the nearest whole number).
So the depth of the aquarium is 3 feet.
Which one of the following are rational numbers?
8
0
10/3
7
Answer:
eight and zero...
Step-by-step explanation:
hope I help
The population of a certain species of insect is given by a differentiable function P, where P(t) is the number of insects in the population, in millions, at time t, where t is measured in days. When the environmental conditions are right, the population increases with resect to time at a rate that is directly proportional to the population. Starting August 15, the conditions were favorable and the. population began increasing. On August 20, five days later, there were an estimated 10 million insects and the population was increasing at a rate of 2 million insects per day.
Required:
What is the differential equation that models this situation?
Answer:
[tex]\frac{dP}{dt} \ =\ \frac{1}{5}P[/tex]
Step-by-step explanation:
Given
Variation: Directly Proportional
Insects = 10 million when Rate = 2 million
i.e. [tex]P = 10\ million[/tex] when [tex]\frac{dP}{dt} = 2\ million[/tex]
Required
Determine the differential equation for the scenario
The variation can be represented as:
[tex]\frac{dP}{dt} \ \alpha\ P[/tex]
Which means that the rate at which the insects increase with time is directly proportional to the number of insects
Convert to equation
[tex]\frac{dP}{dt} \ =\ k * P[/tex]
[tex]\frac{dP}{dt} \ =\ kP[/tex]
Substitute values for [tex]\frac{dP}{dt}[/tex] and P
[tex]2\ million = k * 10\ million[/tex]
Make k the subject
[tex]k = \frac{2\ million}{10\ million}[/tex]
[tex]k = \frac{2}{10}[/tex]
[tex]k = \frac{1}{5}[/tex]
Substitute [tex]\frac{1}{5}[/tex] for k in [tex]\frac{dP}{dt} \ =\ k * P[/tex]
[tex]\frac{dP}{dt} \ =\ \frac{1}{5}* P[/tex]
[tex]\frac{dP}{dt} \ =\ \frac{1}{5}P[/tex]
Which equation represents the line that passes through the point (3,-1) and is perpendicular to the graph of x+4y=10
Answer:
Step-by-step explanation: The given equation is in standard form, so it must be converted to slope-intercept form: y = mx + b to discover the slope is –2/3. To be perpendicular the new slope must be 3/2 (opposite reciprocal of the old slope).
4x - y = 13 represents the line that passes through the point (3,-1) and is perpendicular to the graph of x+4y=10.
What is perpendicular equation?A perpendicular line is a straight line through a point. It makes an angle of 90 degrees with a particular point through which the line passes.
Given
x + 4y = 10
∴ 4y = -x + 10
∴ y = [tex]\frac{-1}{4} x + \frac{5}{2}[/tex]
so y = 4x + b pass through the point (3, -1)
⇒ -1 = 4 × 3 + b
⇒ -1 = 12 + b
⇒ b = -1 - 12
⇒ b = -13
∴ y = 4x -13
4x - y = 13
Hence, 4x - y = 13 represents the line that passes through the point (3,-1) and is perpendicular to the graph of x+4y=10.
Find out more information perpendicular equation here
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The sum of 8 times b and twice g is equal to 32
Help me pls I don’t want to fail math
Answer: They are proportional.
Explanation: To determine whether a table is proportional just simply notice if there is a number you can get to the next number.
Example: on the x values you multiply from left to right by 2 and get the next number. on the y values you multiply by 1. This table is proportional
WILL GIVE BRAINLIEST. ARE THOSE EQUATIONS THE SAME
Answer:
no
Step-by-step explanation:
m+m+m = 3m
m+3=m+3
they are not equal
Hope it helps!
Answer:
yes because there is 3 m so m plus 3 is equivalent to it
Step-by-step explanation:
The shaded area on the grid represents the part of a rectangular wall that was painted. Each small square on the wall has the same dimensions. What percentage of the wall was painted?
Answer:
68
Step-by-step explanation:
There are total of 5*5 = 25 rectangles on the wall. 17 of these are painted.
17 / 25 = 17*4 / 100
17 * 4 = 68
Answer 68%
Step-by-step explanation:
