The expression for the area of the rectangle inscribed in a circle of radius 9, in terms of n, is:
Area = n * √(81 - n^2)
To find an expression for the area of a rectangle inscribed in a circle of radius 9, we need to use the terms "rectangle" and "circle."
First, let's denote the length of the rectangle as "n" and the width as "w." Since the rectangle is inscribed in a circle with a radius of 9, its diagonal is equal to the diameter of the circle, which is 2 * 9 = 18.
Using the Pythagorean theorem for the right triangle formed by half of the diagonal, the length, and the width, we can write the equation:
(1/2 * 18)^2 = n^2 + w^2
81 = n^2 + w^2
Now, we need to express w in terms of n. To do this, we'll isolate w from the equation:
w^2 = 81 - n^2
w = √(81 - n^2)
The area of the rectangle can be calculated as the product of its length and width:
Area = n * w
Area = n * √(81 - n^2)
So, the expression for the area of the rectangle inscribed in a circle of radius 9, in terms of n, is:
Area = n * √(81 - n^2)
learn more about "Area":-https://brainly.com/question/25292087
#SPJ11
Consider the vector field.
F(x, y, z) =
5ex sin(y), 9ey sin(z), 2ez
sin(x)
(a) Find the curl of the vector field.
curl F =
(b) Find the divergence of the vector field.
div F =
(a) To find the curl of the vector field F(x, y, z), we first find its component functions:
F(x, y, z) = (5ex sin(y), 9ey sin(z), 2ez sin(x))
Then, we use the formula for the curl of a vector field:
curl F = (∂Fz/∂y - ∂Fy/∂z, ∂Fx/∂z - ∂Fz/∂x, ∂Fy/∂x - ∂Fx/∂y)
Plugging in the component functions of F(x, y, z), we get:
curl F = (2ez cos(x), -5ex cos(y), 9ey cos(z))
(b) To find the divergence of the vector field F(x, y, z), we use the formula for the divergence of a vector field:
div F = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z
Plugging in the component functions of F(x, y, z), we get:
div F = 5e^x sin(y) + 9e^y sin(z) + 2e^z sin(x)
(a) To find the curl of the vector field F(x, y, z) = (5e^x sin(y), 9e^y sin(z), 2e^z sin(x)), we need to compute the cross product of the del operator (∇) and F:
curl F = ∇ x F
curl F = ( (∂/∂y)(2e^z sin(x)) - (∂/∂z)(9e^y sin(z)), (∂/∂z)(5e^x sin(y)) - (∂/∂x)(2e^z sin(x)), (∂/∂x)(9e^y sin(z)) - (∂/∂y)(5e^x sin(y)) )
After computing the partial derivatives, we get:
curl F = ( 0, 5e^x cos(y) - 2e^z cos(x), 9e^y cos(z) - 5e^x cos(y) )
(b) To find the divergence of the vector field F(x, y, z), we need to compute the dot product of the del operator (∇) and F:
div F = ∇ ⋅ F
div F = (∂/∂x)(5e^x sin(y)) + (∂/∂y)(9e^y sin(z)) + (∂/∂z)(2e^z sin(x))
After computing the partial derivatives, we get:
div F = 5e^x sin(y) + 9e^y sin(z) + 2e^z sin(x)
learn more about vector field here: brainly.com/question/16180391
#SPJ11
Review Questions
1. A washer and a dryer cost $1004 combined. The washer costs $54 more than the dryer. What is the cost of the dryer?
Please use your work.
The calculated cost of the dryer is $475.
What is the cost of the dryer?Let's assume that the cost of the dryer is x dollars.
According to the problem, the cost of the washer is $54 more than the dryer.
Therefore, the cost of the washer is (x + $54).
We are given that the combined cost of the washer and the dryer is $1004. So we can set up the equation:
x + (x + $54) = $1004
Simplifying the equation:
2x + $54 = $1004
2x = $950
x = $475
Therefore, the cost of the dryer is $475.
Read more about expression at
https://brainly.com/question/15775046
#SPJ1
If a data set has many very large data values, then the mean wil be
the median
a larger than
b. the same as
c. equal to
d. smaller than
A data set has many very large data values, then the mean will be larger than the median. The correct option is a.
In a dataset with large values, the mean is influenced by outliers and extreme values, whereas the median is not. The median is the value that divides the data into two equal halves, while the mean is calculated by summing up all values and dividing by the total number of values.
Thus, in a skewed dataset with large values, the mean tends to be pulled towards the larger values, resulting in a larger mean than the median. This effect is more pronounced in datasets with a high variance. Therefore, option (a) is the correct answer.
To know more about mean, refer here:
https://brainly.com/question/31101410#
#SPJ11
Larijah is creating a circular board game with a spinner with four regions that players use to determine what happens on their turns. she wants to meet these requirements: - exactly a quarter of the circle should contain the ""lose a turn"" region. - ""move one space"" should be three times the angle as ""move two spaces"". - ""move two spaces"" should be twice the angle as ""trade places with any opponent"". what is the measure of the ""trade places with any opponent"" region?
The measure of the trade places with any opponent region is 30°
Let the measure of the trade places with any opponent = x
Move two space is twice the angle as trade places with any opponent
Move two space = 2x
Move one space is three times the angle as moving two spaces
Move one space = 3(2x)
Move one space = 6x
Lose your turn is a quarter
Lose your turn = 90°
The sum of a complete angle = 360°
90 + x + 2x + 6x = 360°
9x = 360 - 90
9x = 270
x = 30
The measure of the trade places with any opponent region is 30°
To know more about measure click here :
https://brainly.com/question/4725561
#SPJ4
Given that 3 is a primitive root modulo 25; Find a primitive root modulo 250
The primitive root modulo 250 is 103, as 3 is a primitive root modulo 25 we tested if it is also a primitive root modulo 250.
To find a primitive root modulo 250, we need to first factor 250 as 2 x 5³. Since 3 is a primitive root modulo 25, we can test if it is also a primitive root modulo 250.
Using Euler's totient function, we know that [tex]\phi(250)[/tex] = 100. Therefore, we only need to check if [tex]3^{20[/tex] (which is [tex]3^{\phi(250)/2[/tex]) is congruent to -1 modulo 250.
Calculating [tex]3^{20[/tex] modulo 250 gives us 1. Since [tex]3^{20[/tex] is not congruent to -1 modulo 250, 3 is not a primitive root modulo 250.
To find a primitive root modulo 250, we can use a common method called the "index cycling" method. We can start with a primitive root modulo 5³ = 125 and then test the other primitive roots modulo 2³ = 8 until we find a primitive root modulo 250.
Using a computer or calculator, we can find that 2 is a primitive root modulo 125. To find a primitive root modulo 250, we can test the numbers 2, 2 + 125, 2 + 2125, and 2 + 3125 until we find a primitive root.
Testing these numbers, we find that 2 + 3*125 = 377 is a primitive root modulo 250. Therefore, 377 is a primitive root modulo 250.
Learn more about the primitive root modulo at
https://brainly.com/question/14766413
#SPJ4
And 7/8 hours Greg reads 2/3 chapters. What is the unit rate in chapters per hour? Write your answer in simplest form
The unit rate for chapters per hour is calculated as 16/21
How to find the unit rateIn order to find the unit rate for the number of chapters Gregory reads in an hour, we must firstly divide the total amount of chapters read by the amount of hours devoted to the activity:
= 2/3 chapters ÷ 7/8 hours
= 2/3 chapters × 8/7 hours
= 16/21 chapters per hour
Consequently, the unit rate for chapters per hour is calculated as 16/21, which already exists in its most simplified form.
Learn more about unit rate at
https://brainly.com/question/19493296
#SPJ1
What is the cost of 0. 7 kg of apples, if 1 kg of apples cost 89. 50
In the proportion, the cost of 0.7kg apple is Rs.62.65 .
What is proportion?
A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.
Here cost of 1kg apples = 89.50
Then cost of 0.7 kg apple = x.
Now using proportion,
=> 1 = 89.50
0.7= x
=> x = [tex]\frac{89.50\times0.7}{1}[/tex]
=> x = 62.65.
Hence the cost of 0.7kg apple is Rs.62.65 .
To learn more about proportion refer the below link
https://brainly.com/question/13604758
#SPJ4
The function h is given by h(x)=log_2(x^2 -6). For what positive value of x does h(x)=4?
The function h is given by h(x)=log2(x² -6). The positive value of x that makes h(x) equal to 4 is approximately 4.69
We have the function:
h(x) = log2(x² - 6)
We want to find the value of x that makes h(x) equal to 4:
h(x) = 4
log2(x² - 6) = 4
We can rewrite this equation as:
2⁴ = x² - 6
16 = x² - 6
x²= 22
x = √22 (because we are looking for a positive value of x)
Therefore, the positive value of x that makes h(x) equal to 4 is approximately 4.69 (rounded to two decimal places).
Learn more about logarithm function at https://brainly.com/question/4563843
#SPJ11
Answer Immeditely Please
Answer:
it's ither 1 2 or 4 I'm still thinking but I'm pretty sure it's one of those answers
A hotel offers two activity packages. One costs $192 and includes 3h of horseback riding and 2h of parasailing. The second costs $213 and includes 2h of horseback riding and 3h of parasailing. What is the cost for 1h of each activity?
Answer:
Step-by-step explanation:
Step-by-step explanation:
let's assumed that
x = 1h of horseback
y = 1h of parasailing
3h of horseback = 3x
2h of parasailing = 2y
and
2h of horseback = 2x
3h of parasailing = 3y
if
3x + 2y = 192
2x + 3y = 213
to find y we have to remove the x
(3x + 2y = 192) × 2
(2x + 3y = 213) × 3
6x + 4y = 384
6x + 9y = 639
___________ -
-5y = -255
y = 51
substitute y to any equation to find x
3x + 2y = 192
3x + 2(51) = 192
3x + 102 = 192
3x = 192 - 102
3x = 90
x = 30
so the answers are 1h of horseback = $30 and 1h of parasailing = $51
#CMIIWAnswer this question please
This question can be answered as follows:
-4 + 12 = 8
How to answer the questionTo answer this question, we can begin by searching for the number whose addition to -4 will yield 8 and the answer is 12. To determine the answer, we can first begin by assigning the figure x to the unknown variable. Thus, we will have:
-4 + x = 8
We collect like terms:
x = 8 + 4
= 12
So, the number that when added to -4 will yield 8, is 12. So, to find a missing number, we assign it a variable and equate to the specified end result.
Learn more about addition and subtraction here:
https://brainly.com/question/25421984
#SPJ1
how does the area of a rectangle help you find the area of a triangle, rhombus, and parallelogram???
The area of a rectangle can be used to find triangle, rhombus and parallelogram since the shapes are related to one another
How does the area of a rectangle help you find the area of a triangle, rhombus, and parallelogram?The area of a rectangle can be used to determine the area of a triangle, rhombus and parallelogram because these figures are somewhat similar to a rectangle.
When we join two triangles together at opposite end or we cut transversally between a rectangle from the diagonal, we would have two triangle.
When a rhombus is split across it's diagonal, it will produce two congruent triangles.
When a parallelogram is divided across it's diagonals, it produces two congruent triangles.
Learn more on area of a rectangle here;
https://brainly.com/question/2607596
#SPJ1
Determine the intercepts of the line.
Do not round your answers.
5x − 9 = −8y − 3
Please help
The intercepts of the line are (6/5, 0) and (0, -3/4).
We have,
To find the x-intercept, we need to set y = 0 and solve for x:
5x - 9 = -3
5x = 6
x = 6/5
So the x-intercept is (6/5, 0).
To find the y-intercept, we need to set x = 0 and solve for y:
-9 = -8y - 3
8y = -6
y = -3/4
So the y-intercept is (0, -3/4).
Therefore,
The intercepts of the line are (6/5, 0) and (0, -3/4).
Learn more about the equation of a line here:
https://brainly.com/question/23087740
#SPJ1
El mastil de un velero se halla unido a la proa y a la popa por dos cables que forman con la cubierta, angulo de 45 grados y 60 grados, respectivamente. si el barco tiene una longitud de 25m, ¿cual es la altura del mastil?
La altura del mástil es de aproximadamente 20.87 metros.
How to find mast height?Para resolver el problema, se puede utilizar la ley de cosenos para encontrar la longitud del mástil:
c² = a² + b² - 2ab cos C
Donde:
c es la longitud del mástil (lo que se busca)
a es la longitud de la parte delantera del barco (25m)
b es la longitud de la parte trasera del barco (también 25m)
C es el ángulo entre a y b, que se puede calcular utilizando la tangente: tan C = 1.5 (pues tan 60° = √3, y tan 45° = 1)
Resolviendo para c:
c² = 25² + 25² - 2(25)(25)cos(arctan 1.5)
c = √(25² + 25² - 2(25)(25)(1/√(1+(1.5)²)))
c ≈ 31.08 m
Por lo tanto, la altura del mástil es de aproximadamente 31.08 metros.
Learn more about Para
brainly.com/question/23402398
#SPJ11
Esteban has `3` kittens. According to the vet, each kitten is born with blue eyes and there is a `50\%` chance of it changing color once they reach three months.
Esteban decides to run a simulation using `3` coins, where heads represent the eyes changing color.
The table shows the results of his simulation.
Estimate the probability that at least one of Esteban’s kittens will still have blue eyes at three months old
There is an estimated probability of 0.875 (or 87.5%) that at least one of Esteban's kittens will still have blue eyes at three months old.
Let's use the complement rule to estimate the probability that at least one kitten will still have blue eyes at three months old:
P(at least one kitten with blue eyes) = 1 - P(no kitten with blue eyes)
To estimate P(no kitten with blue eyes), we can use the results of Esteban's simulation. We can see from the table that all three coins came up tails (representing no color change) in row 8, so that's one outcome where no kitten has blue eyes. There are a total of 2^3 = 8 possible outcomes, so the estimated probability of no kitten having blue eyes is:
P(no kitten with blue eyes) = 1/8 = 0.125
Therefore, the estimated probability that at least one kitten will still have blue eyes at three months old is:
P(at least one kitten with blue eyes) = 1 - P(no kitten with blue eyes) = 1 - 0.125 = 0.875
So, there is an estimated probability of 0.875 (or 87.5%) that at least one of Esteban's kittens will still have blue eyes at three months old.
To learn more about probability visit: https://brainly.com/question/30034780
#SPJ11
The function f(x)=8x+3x^−1 has one local minimum and one local maximum.
This function has a local maximum at x= With a value of =
This function has a local minimum at x = With a value of =
The function f(x) = 8x + 3x^(-1) has a local maximum at x = 2 with a value of f(2) = 19, and a local minimum at x = -2 with a value of f(-2) = -19.Explanation:
To find the local extrema of a function, we need to find the critical points of the function, which are the points where the derivative is either zero or undefined. In this case, the derivative of f(x) is f'(x) = 8 - 3x^(-2), which is undefined at x = 0.Setting the derivative equal to zero, we get:8 - 3x^(-2) = 0Solving for x, we get:x = ±2
These are the critical points of the function. To determine whether each critical point is a local maximum or a local minimum, we need to examine the second derivative of the function.
The second derivative of f(x) is f''(x) = 6x^(-3), which is negative for x > 0 and positive for x < 0.Therefore, x = 2 is a local maximum of the function with a value of f(2) = 19, and x = -2 is a local minimum of the function with a value of f(-2) = -19. These are the only local extrema of the function, since the function is increasing for x < -2 and decreasing for -2 < x < 0, and then increasing again for x > 0.
For more similar questions on topic local maximum
brainly.com/question/7805334
#SPJ11
Researchers pose a question can pant sizes be predicted from a man's height? A random sample of 20 males and their pant size versus height
Answer:
Yes, there is evidence at the 10% significance level, but not at the 5% level
Step-by-step explanation:
Look at the p-value in bottom left corner (in the Height row).
It is less than 0.1, but greater than 0.05. Thus, Yes, there is evidence at the 10% significance level, but not at the 5% level. Got it right.
Fill in the boxes 3(n+7) = (3)( ) + (3)( ) = +
the final result will be 3n + 21
what is ditribustion propety?
The Distributive Property is a mathematical property that states that when a single term is multiplied by a sum or difference, the result can be expressed as the sum or difference of the products of the term multiplied by each term inside the parentheses. It is often used to simplify expressions and equations in algebra. 3(x + 2) = 3x + 32 (distributing the 3 over the parentheses) = 3x + 6 (simplifying the products) This property is very useful when dealing with expressions containing variables or unknowns, as it allows us to simplify complex expressions and solve equations more easily.
using distribution propety
3(n + 7)
= (3)(n) + (3)(7)
= 3n + 21
Hence the final result will be 3n + 21
Learn more about ditribustion propety, by the following link
https://brainly.com/question/2807928
#SPJ4
A teacher asked three different students to write the conditions that would result in a triangle. Which of the following students listed conditions that would result in more than one triangle?
The condition that will result in more than one triangle is C. Student III.
How the conditions will result in more than one triangleThe conditions listed by the third student will result in more than one triangle because we are given all three angles. As a rule in math, some conditions will determine if there is more than one triangle. One of them is this:
Rule 1:
If all three angles of the triangle are given and they all add up to exactly 180°, it is possible to get more than one triangle. In the third option, we are given angles 62°, 36°, and 82°, so different triangles can be constructed. Also, they all add up to give 180°. The condition is satisfied.
Rule 2:
Also, as a rule, if we have two angles that do not add up to 180° and one side, then only one unique triangle can be obtained. This is the case for student A who is given angles A and B and a side length of 5cm. (ASA)
Rule 3:
Student 2 will also produce a unique triangle because there are three sides that meet the triangle inequality theorem. (SSS)
Learn more about triangles here:
https://brainly.com/question/1058720
#SPJ1
Pls answer this asap
Answer:
(C) Neither
Step-by-step explanation:
You want to know if the function values in the table represent an even function, and odd function, or neither.
SymmetryAn Even function is symmetrical about the y-axis:
f(-x) = f(x)
An Odd function is symmetrical about the origin:
f(-x) = -f(x)
ApplicationThe attached graph of the given points shows the function has no symmetry at all.
The table represents neither an even nor odd function.
Answer:
Neither
Step-by-step explanation:
In an even function, f(x) = f(-x).
Look at x = 2 and x = -2.
f(2) = -4; f(-2) = 2
Since f(2) ≠ f(-2), the function is not even.
In an odd function, f(x) = -f(-x).
Look at f(2) and f(-2).
f(2) = -4; f(-2) = 2
Since f(2) ≠ -f(-2), the function is not odd.
Answer: C Neither
The answer to this math problem please.
Answer:
C) 6
Step-by-step explanation:
n=6
6( 6 + 1) + 3 =45
36 + 6 + 3 = 45
36 + 9 = 45
Subtract 1/4- 5/14 = type an integer or fraction
Answer:
-3/28
Step-by-step explanation:
In order to subtract fractions you first have to get a common denominator. The common denominator between 4 and 14 is 28 since 4(7) = 28 and 14(2) = 28. Then multiply the top and bottom of (1/4) by (7/7) and (5/14) by (2/2). This gives a common denominator and since you multiply by a fraction equal to 1, it doesn't change the value. Therefore, we get 7/28 - 10/28 = -3/28.
A boy cycles 5km from his home to school and 8km from his home to the market. The chief's camp is closer to the boys home than the market but further than the school. Write a compound inequality to show the distance from the boys home to the chief's camp.
A compound inequality to show the distance from the boys home to the chief's camp is 5 < d < 8
How to explain the inequalityThe distance from the boy's home to the school is 5km.
The distance from the boy's home to the market is 8km.
The chief's camp is closer to the boy's home than the market, but further than the school
The chief's camp is closer to the boy's home than the market, so the distance from the boy's home to the chief's camp is less than 8km.
Putting these together, we can write a compound inequality to show the possible distances d from the boy's home to the chief's camp:
distance from home to school < distance < home to maket
5 < d < 8
The inequality is 5 < d < 8.
Learn more about Inequalities on
https://brainly.com/question/24372553
#SPJ1
A cross section of the cylinder with the cone removed is a ring. To find the area of the ring, find the area of the outer circle and of the inner circle. Then subtract the area of the inner circle from the outer circle.
The area of the outer circle and of the inner circle is : πr² and, πx².
Then subtract the area of the inner circle from the outer circle is :
π (r - x) (r+x)
Here, we have,
Given:
Let the radius of outer circle i.e CA be r
Let the radius of inner circle i.e CB be x
The diagram is given below as attachment.
We know that,
area of circle = πR²
Then subtract the area of the inner circle from the outer circle is:
The area of the outer circle - area of the inner circle
= πr² - πx²
= π (r² - x²)
=π (r - x) (r+x)
So, we get
Then subtract the area of the inner circle from the outer circle is:
π (r - x) (r+x)
Hence, The area of the outer circle and of the inner circle is : πr² and, πx².
Then subtract the area of the inner circle from the outer circle is :
π (r - x) (r+x)
Learn more about circle here:
brainly.com/question/11833983
#SPJ1
Fred goes to Old Navy and buys two pairs of jeans for $17. 99 each, three shirts at $5. 99 each, and a pack of socks for $3. He has a coupon for 25% off his entire purchase. Sales tax is 6. 5%. What is the total cost after the discount and tax?
A: $43. 07
B: $39. 95
C: $45. 49
D: $60. 65
The total cost after discount and tax is $46.28.
To find the total cost after the discount and tax, we need to first find the subtotal before tax.
Fred bought two pairs of jeans for $17.99 each, so the cost of the jeans is $17.99 x 2 = $35.98.
He also bought three shirts at $5.99 each, so the cost of the shirts is $5.99 x 3 = $17.97.
The pack of socks costs $3.
The subtotal before discount is $35.98 + $17.97 + $3 = $57.95.
With the 25% off coupon, Fred gets a discount of $57.95 x 0.25 = $14.49.
The new subtotal after discount is $57.95 - $14.49 = $43.46.
Finally, we need to add the 6.5% sales tax.
The sales tax is $43.46 x 0.065 = $2.82.
The total cost after discount and tax is $43.46 + $2.82 = $46.28.
Therefore, the closest answer is C: $45.49.
Learn more about Profit and Loss: https://brainly.com/question/9281343
#SPJ11
Jane completed 8 homework problems in class. The function p(m) relates the
time (in minutes) Jane spent on her homework at home to the total number
of problems she completed. The input is the number of minutes worked. The
output is the number of problems completed.
p(m)= m/5+8
Which equation represents the inverse function m(p), which uses problems
completed as the input and gives minutes worked as the output?
Answer:
Step-by-step explanation:
5p-40
Help please! solve problem in the photo
Check the picture below.
[tex]6^2=[4+(2x+5)](4)\implies 36=(9+2x)(4)\implies \cfrac{36}{4}=9+2x \\\\\\ 9=9+2x\implies 0=2x\implies \cfrac{0}{2}=x\implies 0=x~\hfill \stackrel{ 2(0)+5 }{{\Large \begin{array}{llll} GH=5 \end{array}}}[/tex]
Find the properties for the ellipse with the equation x^2/169 + y^2/144 = 1
latus rectum =
a. 288/13
b. 328/12
c. 288/12
The latus rectum of an ellipse is 288/13 when the ellipse equation is given as [tex]x^2/169 + y^2/144 = 1[/tex]. Option A is correct.
The standard form of an ellipse equation is given as
[tex](x2/a2) + (y2/b2) = 1[/tex]
where :
a = lengths of the semi-major axes
b = length of semi-minor axes
The length of the chord through one of the foci that are perpendicular to the major axis is defined as the latus rectum of an ellipse.
From the given data the equation of the ellipse is given as :
x² / 169 + y² / 144 = 1
By comparing the standard equation and the given equation of the ellipse we get :
a² = 169
a = √169
[tex]a = 13[/tex]
b² = 144
b = √144
[tex]b = 12[/tex]
The distance between the center and one of the foci is given by
c = √(a² - b²)
= √(13² - 12²)
= 5
We can find the latus rectum by substuting a and b values in the latus rectum of an ellipse formula,
= 2×b²/a
= 2 × 12² / 13
= 288/13
Therefore, the latus rectum of an ellipse is 288/13.
To learn more about the latus rectum of an ellipse :
https://brainly.com/question/30017551
#SPJ4
What is the max/min of the quadratic equation in factored form: f(x) = 0. 5(x+3)(x-7)? Is it a maximum or a minimum? Show your workor explain your reasoning.
The quadratic equation in factored form: f(x) = 0. 5(x+3)(x-7) have a minimum point. The minimum value of the function is -11.
To find the maximum or minimum of the quadratic equation in factored form f(x) = 0.5(x+3)(x-7), we need to convert it to standard form by expanding the terms:
f(x) = 0.5(x² - 4x - 21)
f(x) = 0.5x² - 2x - 10.5
The coefficient of x² is positive, so the parabola opens upwards and we have a minimum point.
To find the x-coordinate of the minimum point, we can use the formula x = -b/2a, where a = 0.5 and b = -2:
x = -(-2)/2(0.5) = 2
So the minimum point is at x = 2. To find the y-coordinate, we can substitute x = 2 into the equation:
f(2) = 0.5(2)^2 - 2(2) - 10.5 = -11
Therefore, the minimum value of the function is -11.
Learn more about minimum point at https://brainly.com/question/29288315?
#SPJ11
The area of the region under the curve of a function f(x)= ax+b on the interval [0,4] is 16 square units. (A,b) ≠
There are infinitely many solutions to this equation. For example, one possible solution is a = 2, b = 0. Another possible solution is a = 1, b = 2.
How to find the area?To find the area, we need to use the definite integral formula to calculate the area under the curve:
∫[0,4] f(x) dx = ∫[0,4] (ax + b) dx = 1/2 * a * x² + b * x |[0,4]
Substituting the limits of integration, we get:
1/2 * a * 4² + b * 4 - (1/2 * a * 0² + b * 0) = 16
Simplifying, we get:
8a + 4b = 16
Dividing by 4, we get:
2a + b = 4
Since (a,b) ≠ (0,0), there are infinitely many solutions to this equation. For example, one possible solution is a = 2, b = 0. Another possible solution is a = 1, b = 2.
Learn more about area
brainly.com/question/30307509
#SPJ11