Amount of rainfall results in the maximum number of mosquitoes is 4 centimeters.
m(r) = -r(r-4)
m(r) = -r² + 4r
let's find the derivative of m(r) with respect to r:
m'(r) = -2r + 4
To find the critical points, we set m'(r) = 0 and solve for r:
-2r + 4 = 0
-2r = -4
r = 2
m''(r) = -2
Evaluating m''(2), we get
m''(2) = -2
the function m(r) has a maximum at r = 2.
Putting the value 2 we get
m(2) = -2² + 4(2)
m(2) = - 4 + 8
m(2) = 4
Therefore, the amount of rainfall that results in the maximum number of mosquitoes is 4 centimeters
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The question is incomplete the complete question is :
The number of mosquitoes in Brooklyn (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by m(r) = -r(r - 4) What amount of rainfall results in the maximum number of mosquitoes?
A line has equation 2x + y=20 and a curve has equation y=a+
18/x-3, where a is a constant.
Find the set of values of a for which the line does not intersect the curve
Answer:
we have two equations:
2*x + y = 20
y = a + 18/x - 3
We want to find the values of a such that the graphs of the equations do not intersect.
The first step is to isolate y in the first equation.
now we get:
y = 20 - 2*x
Then we have the system of equations:
y = 20 - 2*x
y = a + 18/x - 3
If the line intersects the curve at a point (x, y), then at that point both functions have the same value of y, then:
20 - 2*x = y = a + 18/x- 3
We want to find a value of such that this does not happen.
Let's solve that equation and see what we can find.
20 - 2*x = a + 18/x - 3
20 + 3 = a + 18/x + 2*x
23 = a + 18/x + 2*x
(23 - a) = 18/x + 2*x
if we multiply all values by x, we get:
(23 - a)*x = 18 + 2*x^2
Then we have a quadratic equation, we can write this as:
2*x^2 - (23 - a)*x + 18 = 0
Now, remember that if the determinant of the quadratic function is smaller than zero, then the function does not have any real solution, then we need to find a such that the determinant of this quadratic equation is smaller than zero.
Remember that for a quadratic equation:
a*x^2 + b*x + c = 0 is:
b^2 - 4*a*c
In this case, the determinant is:
(-(23 - a))^2 - 4*2*18
(23 - a)^2 - 144
And this must be smaller than zero, then:
(23 - a)^2 - 144 < 0
23^2 - 2*23*a + a^2 - 144 < 0
529 - 46*a + a^2 - 144 < 0
a^2 - 46*a + 385 < 0
Notice that the function has a positive leading coefficient, then the arms of the function go upwards, then the region of the function that is smaller than zero is the values of a that are between both roots of a.
Then we need to solve:
a^2 - 46*a + 385 = 0
We can use the Bhaskara's equation to find the roots, the roots are given by:
[tex]a = \frac{-(-46) +- \sqrt{(-46)^2 - 4*1*385} }{2*1} = \frac{46 +-24}{2}[/tex]
Then the two roots are:
a₁ = (46 + 24)/2 = 35
a₂ = (46 - 24)/2 = 11
Then for all the values of a suc that:
11 < a < 35
The line does not intersect the curve.
¿Por qué creen que la cantidad de almidones es
la misma si el cereal se come solo o con leche? ayuda :(
Answer:
mira aveces el cereal se come con leche y aveces se come con yogurt a quienes lo hacen así claro el cereal tiene almidones
I need help please
And if u don’t know the answer don’t comment because i'm really looking for help! ):
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The points form a right triangle. The circumcenter is the midpoint of the hypotenuse of a right triangle. Here, that is the midpoint of AC:
O = (A +C)/2
O = ((1, 1) +(10, 8))/2 = (11, 9)/2 = (5.5, 4.5)
The circumcenter is (5.5, 4.5).
3 positive integers numbers that add up to 10
Help please
Answer:
3+2+5
Step-by-step explanation:
word problem that represents 8 times -0.25
Answer:
If bob buys 8 choclates, which each of them are 0.25 dollars each, how much money does he have if he has 0 dollars?
Step-by-step explanation:
PLZ HELP!!! WILL GIVE HIGHEST POINTS IF THE ANSWER IS CORRECT!!!
Answer:
ab multiplied by ( A -B)
Step-by-step explanation:
HELP! ITS EASY BUT I CANT DO IT!! Find the volume of a rectangular prism with length = 8.4mm, width = 3.5mm and height = 5.6mm. Length = 8.4mm
Answer:
164.64
Step-by-step explanation:
you just have to multiply
8.4 x 3.5= 29.4 then you do 29.4 x 5.6 = 164.64
4. Margo is shopping for art supplies. She has a budget of $50 to spend. She buys 8 packages of
construction paper and receives $33.12 in change. Which equation could be used to find the
price of one package of construction paper?
A. 50 - 8x
B. 50- 33.12+8x
C. 33.12 = 8x
D. 50+ 33.12 - 8x
Answer:
I'm not sure but maybe try B
Paula is going to hire a makeup artist for a fashion show and is comparing prices. Shelley charges $40 as a booking fee and an additional $30 per hour. Ezra charges $35 per hour, plus a booking fee of $30. Depending on the length of the show, the cost could end up being the same for either artist. What would the cost be?
Answer:70
Step-by-step explanation:
The cost of booking was $100 as obtained by the length of the show.
What are linear and non-linear functions?A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.
Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.
An example of a non-linear function is a quadratic function.
From the given information the two linear equations can be formed as,
30x + 40 and 35x + 30.
The cost would be the same when we'll equate these two equations.
30x + 40 = 35x + 30.
30x - 35x = 30 - 40.
- 5x = - 10.
5x = 10.
x = 10/5.
x = 2, So at two hours the cost would be the same and the total cost is,
$30(2) + 40.
$60 + 40.
= $100.
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A metallic cylinder of diameter 14 cm and height 49 cm is melted and cast into cubes with side 22 7 cm. How many cubes will be formed
Answer:
22 cubes are formed.
Step-by-step explanation:
Given that,
The diameter of the cylinder, d = 14 cm
Height of the cylinder, h = 49 cm
The side of the cube, a = 7 cm
Let there are n cubes formed. So,
[tex]n=\dfrac{\text{volume of cylinder}}{\text{side of cube}^3}\\\\=\dfrac{\pi r^2 h}{a^3}\\\\=\dfrac{\dfrac{22}{7}\times (7)^2 \times 49}{(7)^3}\\\\n=22[/tex]
Hence, there are 22 cubes that are formed.
Andy learns in school that plants grow best when they receive an optimal range of water, sunlight, and nutrients. He decides to do an experiment with bean plants to test this idea. Over the course of a month, he is planning on giving five bean plants different amounts of water. His watering schedule is outlined below.
Plant
Amount of Water
Every Week
A
0 mL
B
10 mL
C
100 mL
D
1,000 mL
E
10,000 mL
What will be the most likely result of his experiment?
Question 2 options:
A. Plant A will die, while all of the other plants will flourish.
B. There will be no difference between the plants by the end of the fourth week.
C. Plant A and Plant E will die.
D. Plant E will grow faster than all of the other plants.
Question 3 (1 point)
Answer:
C. Plant A and Plant E will die.
Step-by-step explanation:
A0 mL
B 10 mL
C 100 mL
D 1,000 mL
E 10,000 mL
Plant A will get no water so it will Die
Plant E will be overwatered so it will rot and die
PLEASE HELP I WILL MARK BRAINLIEST
3y + 7 = x
Solve for y and x.
Answer:
x=3y+7
y=1/3x-7/3
Step-by-step explanation:
Answer:
y=6 x=25
Step-by-step explanation:
brainliest plz
Find the value of x, Round to the nearest tenth.
19
16
X
A 133.5 kg crate, sliding on the floor, is brought to a stop by a 54.5 N force. What is the deceleration of the crate?
Answer:
0.40m/s^2
Step-by-step explanation:
Given data
Mass= 133.5kg
Force F= 54.5N
The expression for the force acting is
F=ma
substitute
54.5=133.5*a
]Divide both sides by 133.5
a= 54.5/133.5
a= 0.40 m/s^2
Hence the acceleration is 0.40m/s^2
in order to use an expert from a movie in your history class you must pay a royalty fee. the base fee is 50 and an additional .25 cents per minute of the film. the equation for this is?
Answer:
.50=.25x x= Minutes of watching the film.
Step-by-step explanation:
Photos fast charges a fee of $2.50 plus $0.05 for each picture developed. Photos quick charges a fee of $3.70 plus $0.03 for each picture developed. for how many will the total cost be the same at each shop?
The total cost will cost be the same at each shop for 60 pictures.
What is word problem?Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement.
Let for x number of picture, the total cost will cost be the same at each shop.
Total cost of x number of picture on Photos fast shop = $ (2.50 + 0.05x)
Total cost of x number of picture on Photos quick shop = $ (3.70 + 0.03x)
according to the question:
(2.50 + 0.05x) = (3.70 + 0.03x)
0.05x - 0.03x = 3.70 - 2.50
0.02x = 1.20
x = 1.20 ÷ 0.02
x = 60
Hence, for 60 number of picture, the total cost will cost be the same at each shop.
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pls hurry i need the answer
9514 1404 393
Answer:
slope: 9/5
graph: C
Step-by-step explanation:
In a proportional relationship, the slope is the ratio of y to x. Here, that is ...
slope = y/x = 9/5
__
The graph of a proportional relationship goes through the origin. (eliminates graph B)
For this relationship, y is greater than x. (eliminates graph A)
The appropriate graph for y = 9/5x is graph C.
Sara uses 7.6 pints of blue paint and white paint to paint her bedroom walls. 3 4 of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?
Answer:
1.9
Step-by-step explanation:
7.6/4= 1.9
1.9*1= 1.9
ans is 1.9 pints
Work out the percentage change to 2 decimal places when a price of £220 is decreased to £210.
Answer:
the answer is 4.54%
While walking past a flag pole, Tommy looked down and noticed his shadow. Use the diagram below to
find the length of his shadow.
PLS HELP
Answer: 30ft
Step-by-step explanation:
Write the equation in slope-intercept form.
y−1=45(x+5)
Answer:
y=45x+226
Step-by-step explanation:
hope that's what you're looking for
have a nice day!!!
Answer:
Step-by-step explanation:
Slope intercept form of a line is y=mx+b so we need to solve for y.
y-1=45(x+5) first expand right side
y-1=45x+225 now add 1 to both sides.
y=45x+226
Help me to find two chords.
Answer:
I dont understand how to sorry
Answer:
the answer is 77
Step-by-step explanation:
a= b+c/2
78+76/2 = 77
Chen rode his skateboard 3 1/4 miles in 1/2 of an hour. What was his average speed in miles per hour.
Answer:
6.5 MPH
Step-by-step explanation:
Since he rode his skateboard for half an hour, you must multiply 2, that way he rode 1 hour. Since you multiply the 1/2 hour, you must also multiply 3 1/4, to get 6 1/2, or 6.5. Even though we know he didn't ride a full hour, if he had, and at the same rate, he would have rode 6.5 miles per hour.
Hope this helps! ;)
please help asap!!!!
Answer:
The area is 60. Thats all I know TwT
Step-by-step explanation:
A computer store bought a program at $10 and sold it at a selling price of $12 find the percent makup
Answer:
20%
Step-by-step explanation:
12-10=2
changed ÷ original x 100
2 ÷ 10 x 100
=20%
How many squares are there in this diagram?
Answer:
well sense you got the answer now, ima just take the points.
Step-by-step explanation:
its a 4x4 square with 16 squares
STEW Merlin made 7
−
8
gallon of stew. Then he
ate 3
−
4
gallon of stew. How much stew was left over?
-x + 4 = -9 Solve the equation.
Answer:
-13
Step-by-step explanation:
Subtract 4 from both sides of the equation
+ 4 = − 9
+ 4 − 4 =− 9 − 4
Simplify
Solution:
= − 1 3
Answer:
x = -13
Step-by-step explanation:
I hope it helps you, sorry if it is wrong.
5. Find 7568 more than 16498.
16498 + 7568 = 24066.So, the correct answer is 24066 To find 7568 more than 16498, we can perform the following calculation:
16498 + 7568 = 24066.
We can perform sum via many ways:
Place value: This approach adds numbers by using their place values. For instance, we would arrange the numbers according to their decimal places and add each place value column separately to get the sum of 23 and 45. 68 would be the total.
Comparable to place value addition, but with the integers arranged in columns, is the column addition technique. For adding higher numbers, this can be useful. For instance, we would arrange the numbers in columns and add each column separately to equal 234 + 567. 801 would be the total.
Mental addition: To add numbers quickly, utilize this technique. For instance, we may consider about 23 as 20 + 3 and 45 as 40 to add 23 and 45.
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The number in front of a variable or term is called a .
Answer:
Coefficient. For example, in the term -3x, -3 serves as the coefficient of x.
The number in front of a variable or term is called a coefficient.
The coefficient represents the numerical factor by which the variable or term is multiplied. In an algebraic expression, the coefficient is the number that appears directly in front of the variable.
For example, in the expression 5x, the coefficient of x is 5. Similarly, in the expression 3y², the coefficient of y² is 3. The coefficient helps determine the magnitude or scale of the variable or term within the expression.
Therefore, the number in front of a variable or term is called a coefficient.
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