Jessica is designing a large, circular garden for a neighborhood park. A part of the garden will be occupied by a fountain. If the diameter of the garden is 82 meters and the measure of the angle formed by the fountain is 126°, what will be the approximate length of the garden cover by the fountain?
How can you quickly determine the number of roots a polynomial will have by looking at the equation?
(This is not a math problem simply a question)
The number of roots a polynomial will have can be determined by its degree, assuming that we are considering all possible roots including complex roots and counting each root according to its multiplicity.
For example, a linear polynomial (degree 1) such as [tex]\( ax + b = 0 \)[/tex] will have exactly one root. A quadratic polynomial (degree 2) like [tex]\( ax^2 + bx + c = 0 \)[/tex] will have two roots, which could be real or complex. Similarly, a cubic polynomial (degree 3) will have three roots, and so on.
If the coefficients of the polynomial are real numbers, then any complex roots will occur in conjugate pairs. This means that a real polynomial of odd degree will always have at least one real root.
To summarize, the number of roots of a polynomial equation is equal to the degree of the polynomial, provided that:
1. We include all real and complex roots.
2. We count each root according to its multiplicity (the number of times it is repeated).
3. The polynomial is non-constant (degree greater than 0).
1 question pleasee i need this asap!! thank you :D
An apple farm yields an average of 31 bushels of apples per tree when 17 trees are planted on an acre of ground. each time 1 more tree is planted per acre, the yield decreases by 1 bushel (bu) per tree as a result of crowding. how many trees should be planted on an acre in order to get the highest yield?
To maximize the apple yield from an acre, the optimal number of apple trees to plant is 24 trees.
Explanation:In this problem, we need to maximize the yield of apples from an acre of an apple farm. The yield of apples from an acre is given by the product of the number of trees and the number of bushels per tree. The number of bushels of apples per tree decreases by 1 bushel every time an additional tree is added due to crowding. In mathematical terms, this can be expressed as the equation Y = N * (31 - (N - 17)), where Y is the total yield, and N is the number of trees per acre.
To find the maximum yield, we differentiate this equation with respect to N and set the derivative equal to zero. This gives us N = 24. Therefore, the optimal number of trees to plant per acre in order to maximize apple yield is 24 trees.
Learn more about Maximizing Yield here:https://brainly.com/question/32287841
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To maximize the yield of apples per acre, plant 24 trees. This balances the number of trees and the yield per tree due to crowding.
To find the number of trees that should be planted per acre to get the highest yield, we need to model the yield per acre as a function of the number of trees planted and then find the maximum value of this function.
1. Define the variables:
- Let ( n ) be the number of trees planted per acre.
- The yield per tree decreases by 1 bushel for each additional tree planted, starting from 31 bushels per tree when there are 17 trees planted.
2. Model the yield per tree:
- If ( n = 17 ), the yield per tree is 31 bushels.
- For each additional tree, the yield decreases by 1 bushel, so the yield per tree can be expressed as ( 31 - (n - 17) ).
Simplifying this, we get:
Yield per tree = 31 - n + 17 = 48 - n
3. Model the total yield per acre:
- The total yield ( Y ) per acre is the number of trees ( n ) times the yield per tree.
Y = n × (48 - n)
4. Formulate the quadratic function:
Y = 48n - [tex]n^2[/tex]
5. Find the maximum yield:
- This is a quadratic function of the form [tex]\( Y = -n^2 + 48n \)[/tex], which is a downward-opening parabola. The maximum value of \( Y \) occurs at the vertex of the parabola.
- The vertex of a quadratic function [tex]\( ax^2 + bx + c \)[/tex] occurs at [tex]\( x = -\frac{b}{2a} \)[/tex] . In our case, ( a = -1 ) and ( b = 48 ).
[tex]\[ n = -\frac{48}{2(-1)} = \frac{48}{2} = 24 \][/tex]
So, to get the highest yield, 24 trees should be planted per acre.
How many 1/2 cup servings are in the 7/8 cups of peanut butter
the domain for f(x) is all real numbers greater than or equal to ___ ?
Answer:
The domain of f(x) is all real numbers greater than or equal to -2
Step-by-step explanation:
We have been given that
[tex]f(x)=2(x)^2+5\sqrt{x+2}[/tex]
Domain is the set of x values for which the function is defined.
The given function is the combination of a square and square root function.
Square function is defined for all real values. Whereas, the square root function is defined for only positive values.
Therefore, the function is defined when
[tex]x + 2\geq0[/tex]
Subtract 2 to both sides
[tex]x\geq-2[/tex]
Hence, the domain of f(x) is all real numbers greater than or equal to -2
Marie decides to work all summer rather than going on vacation. She will be able to earn money and learn new skills but will not be able to spend much time with her friends. What is the opportunity cost in this scenario?
The opportunity cost in this scenario is the value of the best alternative that Marie gives up by choosing to work all summer rather than going on vacation.
Explanation:The opportunity cost in this scenario is the value of the best alternative that Marie gives up by choosing to work all summer rather than going on vacation. In this case, the opportunity cost could be the time she could have spent with her friends. By deciding to work, Marie forgoes the opportunity to socialize and spend quality time with her friends.
Opportunity cost is an important concept in economics that highlights the trade-offs we face when making choices. It helps us understand the value of the options we give up when we choose one alternative over another. In Marie's case, the opportunity cost of earning money and learning new skills is the limited time she can spend with her friends.
Dad just had a birthday. Before this birthday, dividing Dad’s age by 2 left a remainder of 1. How do you know that’s Dad’s new age is not a prime number?
Dad's age after his birthday is not a prime number because before his birthday his age was odd, and adding 1 to it made it even. All even numbers greater than 2 are not prime as they are divisible by 2. The new age's prime factors summed with 1 is also divisible by 3, confirming its non-primality.
Before Dad's birthday, dividing his age by 2 left a remainder of 1, which means his age was an odd number. When an odd number has 1 added to it (as occurs on a birthday), it becomes an even number. Since all even numbers except 2 are not prime because they are divisible by 2, we can conclude that Dad's new age cannot be a prime number.
Prime numbers are those that are only divisible by 1 and themselves, and the smallest even prime is 2. Therefore, if Dad's age increased by 1 and became an even number greater than 2, it cannot be prime due to the divisibility rule.
Considering the character of ages having the sum of their prime factors (including one) divisible by 3, and using the modulus operator, we can affirm that the age after the birthday (which is even) conforms to this pattern, hence, verifying its non-primality.
A rocket is launched from atop a 55-foot cliff with an initial velocity of 138 ft/s. a. Substitute the values into the vertical motion formula h = −16t2 + vt + c. Let h = 0. b. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
How would the expression x^2-4 be rewritten using Difference of Squares?
A) (x+2)^2
B) (x-4)^2
C) (x+4)(x-4)
D) (x+2)(x-2)
d.........................
Which of the following best describes the solutions to the inequality shown below?
4c + 5 < 4c + 3
A. All real numbers
B. c < 1/2
C. c > 1/4
D. No solution
show or describe two different ways to complete the comparison using < , > ,or =: 0.26 () 0.4
What is the discount and sale price of a $300 item that has been discounted 10%?
(PLEASE EXPLAIN)
How are experimental and theoretical probability alike?
TIME SENSITIVE
The range of [tex]y= \frac{4}{5} sinx[/tex] for [tex] \pi \leq x \leq \frac{3 \pi }{2} [/tex] is _____.
A hiker is lost in the woods. A search team has created a coordinate grid to represent the woods. Each unit on the grid is one square mile. The hiker was last seen at (4, -9) and could have walked 10 miles in any direction since then. Which equation represents the area the hiker could be in?
A) (x - 4)2 + (y + 9)2 = 102
B) (x + 4)2 + (y - 9)2 = 102
C) (x + 4)2 + (y + 9)2 = 1002
D) (x - 4)2 + (y - 9)2 = 1002
PLEASE HELP ASAP!!!1
PLEASE HELP ME QUICKLY!!
f √6 is the geometric mean between 6 and another number, then the number is
HELLO!!! ^-^
The answer is 1.
If √6 is the geometric mean between 6 and another number, then the number is 1.
(I had the same question and got it right using this answer so yeah) ^-^
Have an amazing day!!! ^-^
Historical Fact:
Back in the older days, the word awful was a word used to praise someone! That is because aw in awful comes from the origin awe which is used when someone is in awe of you!!! For example: You are AWESOME!!!
The new number, 550, is 200 more than the original number. What is the approximate percent change?a The percent change is 33%. b The percent change is 55%. c The percent change is 150%. d The percent change is 175%
The approximate percent change is:
55%
Step-by-step explanation:It is given that:
The new number, 550, is 200 more than the original number.
Let the original number be: x
That means:
550=200+x
x=550-200
x=350
Now, the percent change is calculated as:
[(New number-Original number)/original number]×100
= [tex]\dfrac{550-350}{350}\times 100\\\\=\dfrac{200}{350}\times 100\\\\=57.14\%[/tex]
which is approximately equal to :
55%
Tanya wants to find the height of the tree. She walks away from the base of the tree so the tip of her shadow coincides with the tip of the tree's shadow at point C. BE is two and a half times EC. Tanya is 5 feet, 3 inches tall. How tall is the tree in feet?
The height of the tree is 7.35 feet.
To find the height of the tree, we need to use similar triangles. Here’s the detailed process:
Understand the problem and convert units: Tanya is 5 feet, 3 inches tall. Convert her height to feet.
- 3 inches is 0.25 feet.
- So, Tanya’s height is [tex]\( 5 + 0.25 = 5.25 \)[/tex] feet.
According to diagram
- A tree T with height h.
- Tanya is standing at a point B, with her shadow extending to point E.
- The tree’s shadow extends to point C.
- The tip of Tanya’s shadow coincides with the tip of the tree’s shadow at point C.
- Let E be the point where Tanya’s shadow ends.
- Let EC = x.
- [tex]\( BE = 2.5 \times EC = 2.5x \)[/tex].
Using similar triangles:
[tex]\[ \frac{\text{Tanya's height}}{\text{Length of Tanya's shadow}} = \frac{\text{Tree's height}}{\text{Length of tree's shadow}} \][/tex]
[tex]\[ \frac{5.25}{2.5x} = \frac{h}{3.5x} \][/tex]
Simplify the ratio:
[tex]\[ \frac{5.25}{2.5} = \frac{h}{3.5} \][/tex]
Cross-multiply and solve for h:
[tex]\[ 5.25 \times 3.5 = 2.5 \times h \][/tex]
Calculate [tex]\( 5.25 \times 3.5 \):[/tex]
[tex]\[ 5.25 \times 3.5 = 18.375 \][/tex]
Now, divide by 2.5 to find h:
[tex]\[ h = \frac{18.375}{2.5} = 7.35 \][/tex]
The complete question is
Tanya wants to find the height of the tree. She walks away from the base of the tree so the tip of her shadow coincides with the tip of the tree's shadow at point C. BE is two and a half times EC. Tanya is 5 feet, 3 inches tall. How tall is the tree in feet?
a doctor is using a treadmill to assess the strength of a patients heart. he sets the 48 inch long treadmill at an incline of 10 degrees. how high is the treadmill raised
In this exercise we have to use the knowledge of sine to be able to calculate the triangle values, in this way we can say that:
[tex]h= 8.3[/tex]
So from the values initially given we can describe that the calculation for this triangle will be:
[tex]x / 48 = sin(10)\\ x = 48* .1736\\ x = 8.3335\\ sin 10^0 = h/48\\ h = 48 sin 10^0\\ h = 8.3 inches[/tex]
See more about triangles at brainly.com/question/25813512
Find the slope intercept form for the equation of the line which passes through the point ( -2,15 )and has a slope of -1
The answer is:
y = -x + 13
Work/explanation:
First, we will write the equation in the form of [tex]\sf{y-y_1=m(x-x_1)}[/tex], which is point slope.
Plug in the data
[tex]\large\begin{gathered}\sf{y-15=-1(x-(-2)}\\\sf{y-15=-1(x+2)}\\\sf{y-15=-1x-2}\\\sf{y-15=-x-2}\\\sf{y=-x-2+15}\\\sf{y=-x+13}\end{gathered}[/tex]
Hence, the slope intercept is y = -x + 13.
What perfect squares divide into 337? I only need two!
Multiply. −5m(−2m6+4m4+m−9) Express the answer in standard form. Enter your answer in the box.
Two number cubes are rolled. What is the probability that the sum of the numbers rolled is either 3 or 9?
A.1/6
B.1/13
C.1/18
D.1/162
[tex] |\Omega|=6^2=36\\
|A|=\underbrace{2}_{\text{the sum is 3}}+\underbrace{4}_{\text{the sum is 9}}=6\\\\
P(A)=\dfrac{6}{36}=\dfrac{1}{6}\approx17\% [/tex]
In the graph below, find the coordinate of the image point, P(3, 0). O is the origin and O,90 is a rotation of 90 degrees about the origin. Rx and Ry are reflections around the x- and y-axes.
Rx O,90: (3,0)
(0, 3)
(-3, 0)
(0, -3)
Answer:
Thus, (3,0) Rx O,90° changes to (0,-3)
Step-by-step explanation:
O is the origin and O,90 is a rotation of 90 degrees about the origin. Rx and Ry are reflections around the x- and y-axes.Given: Rx O,90: (3,0)
To determine:
Point P (3,0) rotation about origin (0,0) of 90°
and then Reflection about x-axis.
Rotation of P(x,y) about origin of 90°
P(x,y) changes to P'(y,x)
Therefore, P(3,0) changes to P'(0,3)
Now we take reflection about x-axis
R(x,y) changes to R'(x,-y)
Therefore, P'(0,3) changes to P''(0,-3)
Please see the attachment for both rule.
Thus, (3,0) Rx O,90° changes to (0,-3)
Plot the data for the functions f(x) and g(x) on a grid
If a fair coin is tossed 5 times what is the probability of getting 3 heads in a row
Water flowing at the rate of 15km/hr through a pipe of diameter 14cm into a cuboidal pond which is 50m long and 44m wide. In which time will the level of water in the pond rise 21cm?