8. [-/1 Points) DETAILS HARMATHAP12 10.4.003.MI. MY NOTES ASK YOUR TEACHER PRA The profit per acre from a grove of orange trees is given by x(210 - x) dollars, where x is the number of orange trees per acre. How many trees per acre will maximize the profit? trees per acre Need Help? Read It Master It
Answers
To maximize the profit per acre from the orange grove, we need to find the value of x (number of orange trees per acre) that yields the highest profit. The profit function is given by P(x) = x(210 - x).
To find the maximum profit, take the derivative of P(x) with respect to x:
P'(x) = (210 - x) - x
Set P'(x) to 0 to find the critical points:
0 = (210 - x) - x
2x = 210
x = 105
So, to maximize the profit, you should plant 105 trees per acre. To maximize profit, we need to find the maximum value of the function x(210 - x). We can do this by finding the vertex of the parabola that represents the function.
The vertex of a parabola with equation ax^2 + bx + c is given by (-b/2a, c - b^2/4a). In this case, a = -1, b = 210, and c = 0, since the function is x(210 - x).
So the x-coordinate of the vertex is -b/2a = -210/-2 = 105. This means that the maximum profit occurs when there are 105 trees per acre.
To check that this gives the maximum profit, we can plug x = 105 into the profit function: 105(210 - 105) = 11025
So the maximum profit per acre is $11,025 when there are 105 orange trees per acre.
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Related Questions
let f be the function defined by f(x)=2x 3e−5x, and let g be a differentiable function with derivative given by g′(x)=1x 4cos(5x). it is known that limx→[infinity]g(x)=[infinity]. the value of limx→[infinity]f(x)g(x) is
a. 0
b. 1/2
c. 1
d. none existent
Answers
Thus, the value of limit(x→∞) f(x)g(x) is 0, which corresponds to answer choice (a). 0
Given the functions f(x) = 2x * 3e^(-5x) and g'(x) = (1/x) * 4cos(5x), we are asked to find the value of lim(x→∞) [f(x)g(x)].
Since lim(x→∞) g(x) = ∞, we can use L'Hôpital's rule to evaluate the limit of the product f(x)g(x) as x approaches infinity.
To apply L'Hôpital's rule, we need to find the derivatives of both f(x) and g(x). We already have g'(x). Now let's find f'(x).
f'(x) = d/dx [2x * 3e^(-5x)] = 2 * 3e^(-5x) - 10x * 3e^(-5x) (by applying product and chain rule)
Now, let's apply L'Hôpital's rule:
lim(x→∞) [f(x)g(x)] = lim(x→∞) [f'(x)g'(x)]
Since both f'(x) and g'(x) go to 0 as x approaches infinity, the limit can be evaluated as:
lim(x→∞) [f'(x)g'(x)] = 0
Therefore, the value of lim(x→∞) f(x)g(x) is 0, which corresponds to answer choice (a).
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a restaurant offers a choice of 4 salads, 10 main courses, and 4 desserts. how many possible meals are there?
Answers
Answer:
160
Step-by-step explanation:
4 × 10 × 4 = 160
(Random words to hit the character limit please ignore)
consider the functions below. Match each with its simplified form.
Answers
We are given the following functions:
\(\begin{gathered} P(x)=\frac{2}{3x-1} \\ \\ Q(x)=\frac{6}{-3x+2} \end{gathered}\)We are asked to determine:
\(P(x)\div Q(x)\)This is equivalent to:
\(\frac{P(x)}{Q(x)}\)Substituting the functions:
\(\frac{P(x)}{Q(x)}=\frac{\frac{2}{3x-1}}{\frac{6}{-3x+2}}\)Now, we use the following property:
\(\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}*\frac{d}{c}\)Applying the property we get:
\(\frac{P(x)}{Q(x)}=(\frac{2}{3x-1})(\frac{-3x+2}{6})\)Solving the products:
\(\frac{P(x)}{Q(x)}=\frac{2(-3x+2)}{6(3x-1)}\)Simplifying we get:
\(\frac{P(x)}{Q(x)}=\frac{-3x+2}{3(3x-1)}\)And thus we get the desired expression.
Now, we are asked to determine:
\(P(x)*Q(x)\)This is the product of the functions. Substituting we get:
\(P(x)*Q(x)=(\frac{2}{3x-1})(\frac{6}{-3x+2})\)Solving the products:
\(P(x)*Q(x)=\frac{12}{(3x-1)(-3x+2)}\)Since we can't simplify any further this is the final answer.
What is the circumference of the circle? Use 3.14 pi
Answers
Answer: multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π=3.14)
Step-by-step explanation:
becaue... multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π=3.14)
2(3 + 2) whats the answer lol
Answers
Answer:
10 thats the answer
Step-by-step explanation:
3+2=5×2=10
List the new coordinate of point A' when the figure is reflected over the y-axis.
Answers
The new coordinated after reflection over the y axis are
C' (-4, 2)
A' (-3, -1)
J' (-4, -3)
T' (-5, -2)
How to find the new coordinatesIn geometry, reflection refers to a transformation that flips a figure across a line, known as the line of reflection.
When a figure is reflected, it is essentially mirrored across the line of reflection, so that each point on the original figure is transformed to a corresponding point on the reflected figure that is equidistant from the line of reflection.
The transformation rule for reflection over the y axis is
(x, y) → (−x, y)
The preimage coordinates are
C (4, 2)
A (3, -1)
J (4, -3)
T (5, -2)
Applying the rule results to an image with coordinates
C (4, 2) → C' (-4, 2)
A (3, -1) → A' (-3, -1)
J (4, -3) → J' (-4, -3)
T (5, -2) → T' (-5, -2)
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y=2/3x does this represent a proportional relationship? what is the constant of proportionality?
Answers
Answer: the answered is 12 due to Newton laws of physics
Step-by-step explanation:
Answer:
Yes, \(y = \dfrac{2}{3}x\) does represent a proportional relationship
The constant of proportionality is the coefficient of x:
\(\dfrac{2}{3}\)
Step-by-step explanation:
solve the following problem
Answers
The power rules show that the value of x is equal to 1.
Power RulesThe main power rules are presented below.
Multiplication with the same base: you should repeat the base and add the exponents.Division with the same base: you should repeat the base and subtract the exponents.Power. For this rule, you should repeat the base and multiply the exponents.Exponent negative - For this rule, you should write the reciprocal number with the exponent positive.Zero Exponent. When you have an exponent equal to zero, the result must be 1.For solving this question you should apply the power rules.
\(2^{5x}:2^x=\sqrt[5]{2^{20}}\)
First, you should apply the power rules for the first term. Thus, applying the rule - Division with the same base, you have:
\(2^{5x}:2^x=2^{4x}\)
After, you should convert the given root represented in the second term to power.
\(\sqrt[5]{2^{20}}=2^\frac{20}{5} \\ \\ \sqrt[5]{2^{20}}=2^4\)
Thus,
\(2^{4x}=2^4\)
From the previous equality, you can write:
4x=4
x=1
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Graph the solution set for the inequality
2/5*s +7>=3-4.2s
Answers
The solution of the inequality is:
s ≥ -0.86
And the graph can be seen on the image at the end.
How to find the solution set of the inequality?Here we want to find and graph the solution set of the inequality below:
(2/5)*s + 7 ≥ 3 - 4.2*s
To do so, first we need to isolate s in one of the sides, then let's do that:
(2/5)*s + 7 ≥ 3 - 4.2*s
(2/5)*s + 4.2*s ≥ 3 - 7
(2/5 + 4.2)*s ≥ -4
And we know that 4.2 = 21/5
Then:
(2/5 + 21/5)*s ≥ -4
(23/5)*s ≥ -4
s ≥ -4*5/23
s ≥ -20/23
s ≥ -0.86
The graph of this will something like the one below:
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In a diagram, angle A and angle B are vertical angles, and angle B is a complementary angle with angle C. If angle A = 22°, write an equation
that you can use to solve for angle C. (2 points)
!! Please help!!!
Answers
The value of angle C is 68°.
Describe complementary angles?In geometry, complementary angles are two angles that add up to 90 degrees (a right angle). In other words, when two angles are placed adjacent to each other, and they form a right angle, they are considered complementary angles.
For example, if angle A is 40 degrees, then angle B, which is adjacent to angle A and together they form a right angle, is considered to be a complementary angle. Angle B would be 90 - 40 = 50 degrees.
Complementary angles can be found in many geometric shapes and objects, such as squares, rectangles, and triangles. In a right triangle, the two acute angles (the angles that are not the right angle) are always complementary.
Vertical angles are always congruent, which means that angle B is also 22°.
Since angle B and angle C are complementary, their sum is equal to 90°.
Thus, we can write the equation:
angle B + angle C = 90°
Substituting the known value of angle B, we get:
22° + angle C = 90°
Simplifying the equation, we get:
angle C = 90° - 22°
angle C = 68°
Therefore, the value of angle C is 68°.
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I went out to the hazel wood,
Because a fire was in my head,
And cut and peeled a hazel wand,
And hooked a berry to a thread;
And when white moths were on the wing,
And moth-like stars were flickering out,
I dropped the berry in a stream
And caught a little silver trout.
—“The Song of Wandering Aengus,”
William Butler Yeats
Choose the best visualization of the fishing pole described as “a hazel wand.”
The pole looks like an ordinary pole.
The pole looks like it has mythical power.
The pole looks like it catches only trout.
The pole looks like a trap for white moths.
pls answer this pls in at least in 5 min pls
Answers
Answer:
Shalani Moore? from Mrs.Chastain's class in 6th grade?
Step-by-step explanation:
It's Antonio.
Samir bought snacks for his team's practice. he bought a bag of popcorn for $1.67 and a 24-pack of juice bottles. the total cost before tax was $31.19. write and solve an equation which can be used to determine xx, how much each bottle of juice cost.
Answers
The equation is 1.67 + 24x = 31.19.
In a class of 30 pupils, 12 are boys What percentage of the class are boys?
Answers
no links and no wrong answer please help i'll mark you the brainlest.
What are the domain and range of the function?
domain: {x|x∈R} and range:{y|y∈R}
domain:{x|−2≤x≤2} and range:{y|−10≤y≤10}
domain: {x|x∈R} and range: {y|−6≤y≤6}
domain:{x|−2≤x≤2} and range: {y|−6≤y≤6}
Answers
Answer:
boh
Step-by-step explanation:
9) If point B with coordinates (5, 2) is dilated by a scale factor of 3, what will be the coordinates of the image point B'?
Answers
Answer
Option A is correct.
B' (15, 6) is the answer.
Explanation
To dilate a given coordinate (x, y) about the origin by a scale factor of n, we will obtain (nx, ny).
So, for the given coordinate (5, 2), dilating by the scale factor of 3, we will obtain
B (5, 2) = B' (5×3, 2×3) = B' (15, 6)
Hope this Helps!!!
URGENT plz help
What is the value of y?
A.44°
B.112°
C.68°
D.56°
Answers
Answer:
C. 68
Step-by-step explanation:
Explained in image attached
i need numbers 1,2,3,6,8,10, and 25
Answers
Answer:
What subject is this?. May you please take apicture clear so i can see perfectly
thank you by Tracy Stewart
Step-by-step explanation:
A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume the scenario can be modeled with right triangles. At what rate is the length of the person's shadow changing when the person is 16 ft from the lamppost?
In similar triangles, both the two triangles must satisfy the two properties. One is the side proportional, and the other is equal in angles. There are three criteria in similarity. They are AA similarity, SSS similarity, and SAS similarity. The below one satisfies the AA similarity.
Answers
The length of the shadow is changing rate at 2.69 \(\frac{ft}{sec}\).
What do you mean by length?
The measurement or size of something from end to end is referred to as its length. To put it another way, it is the greater of the higher two or three dimensions of a geometric shape or object. For instance, the length and width of a rectangle define its dimensions.
According to data in the given question,
We have the given information:
The height of the person is 7 ft.
The person is walking away from the post at a rate of 5ft/sec.
The height of the lamppost is 20ft.
Let the person's distance from the bottom of the light post be x ft.
And his shadow's length is y ft.
Form the similar triangles,
\(\frac{x+y}{20}=\frac{y}{7}\\\)
7(x+y) = 20y
7x+7y = 20y
20y-7y = 7x
13y = 7x
y = \(\frac{7}{13}x\)
Now, we will differentiating wrt t,
\(\frac{dy}{dt}=\frac{7}{13}\frac{dx}{dt}................(1)\)
We know that,
\(\frac{dx}{dt}=5\frac{ft}{sec}\)
Putting the value of \(\frac{dx}{dt}\) in equation (1),
\(\frac{dy}{dt}=\frac{7}{13}.5=\frac{35}{13}=2.69\frac{ft}{sec}\)
Therefore, the length of the shadow is changing rate at 2.69 \(\frac{ft}{sec}\).
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what is equivalent 10q - 30
Answers
Answer:
10(q - 3)
Step-by-step explanation:
1) Find the Greatest Common Factor (GCF).
What is the largest number that divides evenly into 10q and - 30?
It is 10.
What is the highest degree of q that divides evenly into 10q and -30?
It is 1, since q is not in every term.
Multiplying the results above,
The GCF is 10.
2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
10 (10q/10 - 30/10)
3) Simplify each term in parentheses.
10(q - 3)
suppose you roll two number cubes and multiply the numbers. what is the probability of getting a multiple of 3 and 4
Answers
For given experiment, the probability of getting a multiple of 3 and 4 is 1/7
In this question we have been given an expreiment of rolling two number cubes and multiply the numbers.
We need to find the probability of getting a multiple of 3 and 4
If two number cubes are rolled and multiply the numbers, the maximum output of multiplication would be 36
So, the sample space:
n(S) = 21
The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36
And the multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36
The number of outcomes for getting a multiple of 3 and 4 are:
12, 24, 36
n(A) = 3
so, the required probability would be,
p(A) = n(A)/n(S)
p(A) = 3/21
p(A) = 1/7
Therefore, the probability of getting a multiple of 3 and 4 = 1/7
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the average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. the number of shoppers is normally distributed. for a random day, what is the probability that there are between 250 and 450 shoppers at the grocery store?
Answers
For a random day with the standard deviation, the probability that there are less than 300 shoppers on a random day, is 0.00585.
Probability is a measure of the likelihood that an event will occur.
Many events cannot be predicted with absolute certainty. We can only predict the probability that an event will occur, i.e. how likely it is to occur, using it.The average total number of shoppers on a grocery store in 1 day is 505; the standard deviation is 115.
Let, X be the random variable denoting the number of shoppers on a random day.
Then, X follows normal with mean 505 and standard deviation of 115.
Then, we can say that,
Z=(X-505)/115 follows standard normal with mean 0 and standard deviation of 1.
We have to find
P (250 <X< 450)
= P {(250-505)/155} < Z < {(450-505)/155}
= P (-1.64 <Z< -0.03)
Where, Z is the standard normal variate.
ρ = -1.64 <ρ< -0.03
Where, ρ is the distribution function of the standard normal variate.
From the standard normal table, this becomes
=0.00585
For a random day, the probability that there are less than 300 shoppers on a random day, is 0.00585.
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the total amount of fiber (in grams) in a package containing x apples and y oranges is given by the equation 5x 10y
Answers
The equation given, 5x + 10y, does not represent the total amount of fiber in a package containing x apples and y oranges.
To calculate the total amount of fiber in a package containing x apples and y oranges, you would need to know the amount of fiber in each apple and orange and the number of apples and oranges in the package.
For example, if each apple contains 3 grams of fiber and each orange contains 2 grams of fiber, and there are x apples and y oranges in the package, the total amount of fiber in the package would be:
Total fiber = (3 grams of fiber per apple)(x apples) + (2 grams of fiber per orange)(y oranges)
Total fiber = 3x + 2y grams
what is number?
A number is a mathematical concept used to represent quantity or magnitude. Numbers can be used to count objects, measure distances or sizes, perform calculations, and describe various other mathematical concepts. The most basic types of numbers are the natural numbers, which include all positive integers (1, 2, 3, ...), and sometimes zero (0) as well. Other types of numbers include fractions, decimals, negative numbers, complex numbers, irrational numbers, and more. Numbers are a fundamental concept in mathematics and are used extensively in many fields, including science, engineering, economics, and finance.
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15/20+16/20 as a mixed number
Answers
Answer: 1 11/20
hope this helps :)
Which of the following is the midsegment of ABC ?
A
С
ОА. А
B. LM
Оооо
Ос. В
O D. MC
SUBMIT
Answers
Answer:
B. LM
Step-by-step explanation:
It is the midsegment of ABC since it is the only answer that lies in the middle of the triangle.
Answer: LM
Step-by-step explanation:
Mid segment is a straight line joining the midpoints of two segments.A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle.In the given triangle ABC ,L and M are midpoints of sides AB and CB.LM is the line joining the midpoints of sides AB and CB.LM is called the midsegment of triangle ABC.
What is the equation of a line with Point A(0, 4) and Point B(2,-6) ?
Answers
9514 1404 393
Answer:
y = -5x +4
Step-by-step explanation:
The slope can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (-6 -4)/(2 -0) = -10/2 = -5
The point (0, 4) tells you the y-intercept is b = 4. So, the equation in slope-intercept form is ...
y = mx +b . . . . . where m is slope and b is y-intercept
y = -5x +4
if a right circular cylinder and oblique cylinder both have a height of 15 inches and diameter of 6 inches, do they have the same volume?
Answers
Answer:
Yes, they both have a volume of 423.9 inches cubed.
Step-by-step explanation:
Both cylinders have the same volume formula V=(pi)(r^2)(h)
d/2=r=3
h=15
so, (3.14)(9)(15)=423.9
The volume of each cylinder is 423.9
Question nine is this answer blue instead of green?
Answers
Answer:
The answer is the blue line
Answer:
The answer is the blue line :)
The sixth-graders at Ashley's school got to choose between a field trip to a museum and a field trip to a factory. 75% of the sixth-graders picked the museum. If there are 96 sixth-graders in all at Ashley's school, how many sixth-graders went on the trip to the museum?
Answers
Answer:
72
Step-by-step explanation:
Sylvester and Lin go to the amusement park. Sylvester plays 5 rounds of mini golf and takes 4 turns in the batting cages for $60. Lin plays 3 rounds of mini golf and takes 6 turns in the batting cages for $45. Use two equations to find the price for each activity. Enter your answers in the boxes.
Answers
Answer:
Mini golf costs: $10.00 per round.
Batting cages cost: $2.50 each turn.
Step-by-step explanation:
Let g= rounds of golf
Let b = batting cage
Sylvester
5g+4b = 60
Lin
3g +6b = 45
We have two equations and two unknowns
5g+4b = 60
3g +6b = 45
Divide the second equation by 3
3/3g +6/3b = 45/3
q+2b = 15
Multiply this equation by -2
-2q -4b= -30
Add this to the first equation
5g+4b = 60
-2q -4b = -30
3q = 30
Divide by 3
3g/3 = 30/3
g = 10
A game of mingolf is 10 dollars
Now we need to find b
q+2b = 15
10 +26 =15
Subtract 10
10-10+2b =15-10
26=5
Divide by 2
2b/2 =5/2
b=25
A turn in the batting cage is 2.50
y = 4x - 3 y = -2x + 9
Answers
Answer:
We all make mistakes, I just make more of them!