Area of circular pipe in terms of pi is found as [tex]100 \pi[/tex] square centimeter
Solution:
Given that an engineer is going to install a new water pipe. The diameter of this circular pipe is, d = 20 cm
We have to find the area 'A' of the circular cross-section of the pipe.
Given, diameter of the circular section is:
diameter = 20 cm
Let us find the radius
[tex]radius = \frac{diameter}{2}\\\\r = \frac{20}{2} = 10[/tex]
Thus radius = r = 10 cm
The area 'A' of the circular cross-section of the pipe measn we can use the area of circle formula
The area of circle is given as:
[tex]area = \pi r^2[/tex]
Where "r' is the radius of circle
We have to find area in terms of pi
[tex]area = \pi (10)^2\\\\area = \pi \times 10 \times 10\\\\area = 100 \pi[/tex]
Thus area of circular pipe in terms of pi is found as [tex]100 \pi[/tex] square centimeter
9.
The surface area of the right square pyramid shown is 129.5 cm. The base is 4.5 cm. Determine the slant height, s, of this
pyramid, rounded to the nearest tenth
Answer:
Slant height (s)= 12.1 cm
Step-by-step explanation:
Given: Base= 4.5 cm.
Surface area of right square pyramid= 129.5 cm.
First, calculating slant height (s) of right square pyramid.
Surface area of square pyramid= [tex](a^{2} +2\times a\times s)[/tex]
a= side of square base.
s= slant height
∴ [tex]129.5= (4.5^{2} + 2\times 4.5\times s)[/tex]
⇒ [tex]129.5= (20.25+2\times 4.5\times s)[/tex]
⇒ [tex]129.5= (20.25+9\times s)[/tex]
Now, opening the parenthesis and subtracting both side by 20.25.
⇒ [tex]109.25=9\times s[/tex]
cross multiplying both side
∴ Slant height (s)= 12.1
Final answer:
To find the slant height of the right square pyramid, subtract the base area from the total surface area, divide by four to find the area of one triangular side, and then solve for the slant height using the triangle area formula. The calculated slant height is = 12.1 cm
Explanation:
The student is asking how to find the slant height of a right square pyramid when given the surface area and the base length. To solve this, we need to take into account the formula for the total surface area of a right square pyramid, which is the sum of the base area and the area of the four triangles forming the sides. We know the total surface area is 129.5 cm2 and the base length is 4.5 cm. The area of the base is simply the square of the base length since it's a square base.
Base area = base length2 = (4.5 cm)2 = 20.25 cm2
Total area of four triangular sides = 129.5 cm2 (total surface area) - 20.25 cm2 (base area) = 109.25 cm2
Area of one triangular side = 109.25 cm2 / 4 = 27.3125 cm2
Now, using the formula for the area of a triangle, A = 1/2 × base × height, we can substitute the area of one triangular side and the base length to solve for the slant height:
27.3125 cm2 = 1/2 × 4.5 cm × slant height (s)
Slant height (s) = (2 × 27.3125 cm2) / 4.5 cm = 12.139 cm
Rounded slant height = 12.1 cm
Which table of ordered pairs, when plotted, will form a straight line? Select two answers.
Answer:
B
Step-by-step explanation:
Provide the reason for Step 4 in the following proof.
A) Additive Inverse Property
B) Commutative Property of Addition
C)Definition of Subtraction
D)Identity Property of Addition
Prove :
Answer:
The Correct option is
A) Additive Inverse Property .
Step-by-step explanation:
Identity Property of Addition :
In math, an identity is a number, n, that when added to other numbers, gives the same number, n.
The additive identity is always zero.
This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.
Statement Reasons
1. -(a+b)+a = -a+(-b)+a 1.Distributive Property
= -a+a+(-b) 2.Commutative Property of Addition
= 0+(-b) 3. Additive Inverse Property
= -b 4. Identity Property of Addition
You and your friend each collect rocks and fossils. Your friend collects three times as many rocks and half as many fossils as you. You collect 25 objects. Your friend collects 15 objects. How many rocks and how many fossils do each collect
Answer:
Number of rocks and fossils collected by you is 1 and 24 respectively
Number of rocks and fossils collected by your friend is 3 and 12 respectively
Step-by-step explanation:
Let the number of Rocks you collect be x
Let the number of Fossils you collect be y
Then the total number pf objects you collected will be
x + y = 25
x = 25 - y------------------------------(1)
Your friend collects three times as many rocks and half as many fossils as you.
This can be written as
[tex]3x + y(\frac{1}{2}) = 15[/tex]
[tex]3x + (\frac{y}{2}) = 15[/tex]-------------------(2)
Substituting (1) in (2)
[tex]3(25 -y) + (\frac{y}{2}) = 15[/tex]
[tex] 75 - 3y + (\frac{y}{2}) = 15[/tex]
Grouping the like terms we get,
[tex] 75 - 15 = 3y - (\frac{y}{2})[/tex]
[tex] 60= \frac{6y-y}{2})[/tex]
[tex] 60 \times 2= 6y-y[/tex]
[tex] 120= 5y[/tex]
[tex] y = \frac{120}{5}[/tex]
y= 24
Substituting y value in equation(1) we get
x = 25 - 24
x= 1
Friends collects 3 times rock
so collects 3x =3(1) = 3rocks
Also he collects half as many fossils
That is
[tex]\frac{y}{2} = \frac{24}{2} =12 fossils[/tex]
You collect 1 rock and 24 fossils, while your friend collects 3 rocks and 12 fossils.
Explanation:Let's assign variables to represent the number of rocks and fossils that you and your friend collect.
Let x represent the number of rocks you collect.
Since your friend collects three times as many rocks as you, we can represent the number of rocks your friend collects as 3x.
Let y represent the number of fossils you collect.
Since your friend collects half as many fossils as you, we can represent the number of fossils your friend collects as y/2.
From the information given, we know that you collect 25 objects, so we have the equation:
x + y = 25
We also know that your friend collects 15 objects, so we have the equation:
3x + y/2 = 15
Simplifying the second equation by multiplying both sides by 2, we get:
6x + y = 30
We now have a system of equations:
x + y = 25
6x + y = 30
Solving this system of equations, we can subtract the first equation from the second equation to eliminate y:
(6x + y) - (x + y) = 30 - 25
5x = 5
x = 1
Substituting the value of x into the first equation, we find:
1 + y = 25
y = 24
Therefore, you collect 1 rock and 24 fossils, while your friend collects 3 rocks and 12 fossils.
Write a quadratic function f whose zeros are -9 & -1
Step-by-step explanation:
This is most easily solved by writing the factored form:
[tex]f(x) = (x + 9)(x + 1)[/tex]
Notice how, if we were to substitute -9 for x, the left part would be -9 + 9 = 0. Since (x + 1) × 0 = 0, this makes the function 0. The same logic applies for the right part.
Final answer:
A quadratic function with zeros at -9 and -1 can be written as f(x) = (x + 9)(x + 1) or f(x) = x^2 + 10x + 9 when expanded.
Explanation:
In mathematics, an expression is a combination of numbers, symbols, and/or operators that represents a mathematical phrase or statement. Expressions can consist of variables, constants, arithmetic operations (such as addition, subtraction, multiplication, and division), exponents, and functions.
To write a quadratic function f with zeros at -9 and -1, we use the fact that a quadratic function f(x) can be represented in the form f(x) = a(x - r1)(x - r2), where r1 and r2 are the zeros of the function and a is a nonzero coefficient. In this case, our zeros are -9 and -1, giving us f(x) = a(x + 9)(x + 1). To keep the function in simplest form, we can choose a = 1, which gives us the quadratic function f(x) = (x + 9)(x + 1) or f(x) = x2 + 10x + 9 after expanding the expression.
Final answer:
A quadratic function with zeros at -9 and -1 can be written as f(x) = (x + 9)(x + 1) or f(x) = x^2 + 10x + 9 when expanded.
Explanation:
In mathematics, an expression is a combination of numbers, symbols, and/or operators that represents a mathematical phrase or statement. Expressions can consist of variables, constants, arithmetic operations (such as addition, subtraction, multiplication, and division), exponents, and functions.
To write a quadratic function f with zeros at -9 and -1, we use the fact that a quadratic function f(x) can be represented in the form f(x) = a(x - r1)(x - r2), where r1 and r2 are the zeros of the function and a is a nonzero coefficient. In this case, our zeros are -9 and -1, giving us f(x) = a(x + 9)(x + 1). To keep the function in simplest form, we can choose a = 1, which gives us the quadratic function f(x) = (x + 9)(x + 1) or f(x) = x2 + 10x + 9 after expanding the expression.
LAW OF COSINES...BRAINLEST AND EXTRA POINTS
Answer:
In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. Using notation as in Fig. 1, the law of cosines states where γ denotes the angle contained between sides of lengths a and b and opposite the side of length c.
Step-by-step explanation:
Answer:
X = 117.9°
Step-by-step explanation:
Rearranging the cosine rule to obtain C
cosC = [tex]\frac{a^2+b^2-c^2}{2ab}[/tex]
Here C = X, a = 50, b = 55, c = 90
cosX = [tex]\frac{50^2+55^2-90^2}{2(50)(55)}[/tex]
= [tex]\frac{2500+3025-8100}{5500}[/tex]
= [tex]\frac{-2575}{5500}[/tex], thus
X = [tex]cos^{-1}[/tex]( - [tex]\frac{2575}{5500}[/tex] ≈ 117.9°
It is a rectangle and I need to get x and the top is -1+4x and the bottom is 3x+3 I’m in 8th grade geometry
The value of x is 4.
Step-by-step explanation:
Consider a Rectangle ABCD
AB as Top
CD as Bottom
AB = -1 + 4x
CD = 3x + 3
To Find:
x = ?
Solution:
In a Rectangle ABCD
Opposite sides of rectangle congruent,
AB = CD
Top = Bottom
on substituting we get
[tex]-1+4x=3x+3\\\\4x-3x=3+1\\\\x=4\\\therefore x =4[/tex]
The value of x is 4.
Rewrite the expression with a rational exponent as a radical expression.
(4^2/5)^1/4
a.)^10sqrt4
b.)^4sqrt4
c.)^5sqrt4^2
d.)sqrt4^10
sqrt=square root
Answer:
First option is correct.
[tex]\sqrt[10]{4}[/tex]
Step-by-step explanation:
Given:
The given expression is [tex](4^{\frac{2}{5}})^{\frac{1}{4}}[/tex]
We write the given expression with a rational exponent as a radical expression such as.
[tex]=(4^{\frac{2}{5}})^{\frac{1}{4}}[/tex]
Simplify the above equation by multiplication of powers.
[tex]=(4^{\frac{2}{5}\times \frac{1}{4}})[/tex]
[tex]=(4^{\frac{1}{5}\times \frac{1}{2}})[/tex]
[tex]=(4^{\frac{1}{5\times 2}})[/tex]
[tex]=(4^{\frac{1}{10}})[/tex]
[tex]=\sqrt[10]{4}[/tex]
Therefore, The answer is [tex]=\sqrt[10]{4}[/tex].
-
You randomly choose one of the tiles. Without replacing the first tile, you
choose a second tile. Find the probability of the dependent event(s) both
occurring.
1/2/3/4/5/6/7
-
Choosing a 6 and then a prime number
Choosing two odd numbers
Answer:
Choosing a 6 and then a prime number: 2/21
Choosing two odd numbers: 2/7
Step-by-step explanation:
Choosing a 6 and then a prime number:
The probability of choosing 6 out of 1, 2, 3, 4, 5, 6 and 7 is one event divided by number of total events (which is equal to 7). That results in 1/7. Once 6 is chosen, the probability of choosing a prime number (prime number is a number that can only be divided by 1 and itself) out of 1, 2, 3, 4, 5 and 7 is 4/6 (prime numbers are 2, 3, 5, 7 in total there are 4 number and total number of events are 6). Finally, the probability of choosing a 6 and then a prime number is (1/7)*(4/6)=2/21.
Choosing two odd numbers:
The probability of choosing 1st odd number is 4/7 (number of odd numbers is 4 which includes 1, 3, 5, 7 and the number of total events is 7). Once 1st odd number is chosen, the probability of choosing 2nd odd number is 3/6 (number of odd numbers is 3 - because 1 odd number is already chosen and the number of total events is 6). Finally, the probability of choosing two odd numbers in a sequence is (4/7)*(3/6)=2/7.
Select the correct answer from the drop-down menu.
Phoebe runs a T-shirt printing business. She ships the T-shirts to retailers in boxes of 200. She has two automated printing machines that can
print designs on T-shirts. One machine can print 200 T-shirts in 50 minutes. The other machine can print 200 T-shirts in 150 minutes.
If the two machines work at the same time, they can print 200 T-shirts in
minutes.
Answer:
They will work together and print 200 T-shirts in 37.5 minutes.
Step-by-step explanation:
One machine can print 200 T-shirts in 50 minutes.
So, in one minute that machine can print [tex]\frac{200}{50} = 4[/tex] T-shirts.
Again, the other machine can print 200 T-shirts in 150 minutes.
So, in one minute the other machine can print [tex]\frac{200}{150} = 1.33[/tex] T-shirts.
Therefore, working together for one minute both the machines will print (4 + 1.33) = 5.33 number of T-shirts.
Hence, they will work together and print 200 T-shirts in [tex]\frac{200}{5.33} = 37.5[/tex] minutes. (Answer)
Solve 5n^2=5 with the quadratic formula
Answer:
n = 1
Step-by-step explanation:
First, rearrange the equation to standard form 0 = ax² + bx + c, when everything equals 0.
5n² = 5
5n² - 5 = 0
State the variables a, b and c.
a = 5; b = 0; c = -5
Substitute a, b, and c into the quadratic formula.
[tex]n = \frac{-b ±\sqrt{b^{2}-4ac} }{2a}[/tex]
[tex]n = \frac{-0 ±\sqrt{0^{2}-4(5)(-5)} }{2(5)}[/tex] Substitute
[tex]n = \frac{\sqrt{100} }{10}[/tex] Simplify inside the √ and bottom
[tex]n = \frac{10}{10}[/tex] Simplify the top
[tex]n = 1[/tex] Final answer
Therefore the solution is n = 1.
The quadratic formula usually is written with x, but it can be solved with any variable in standard form.
mrs jones attended a southern living Home party she purchased a vase which cost $34.99 The shipping charge was three dollars and 8.25% sale tax was paid on the subtotal which included the shipping charge how much did she pay for the vase
The total amount paid for vase is $ 41
Solution:
Given that
Cost of vase = $ 34.99
Shipping charge = 3 dollars
Sales tax = 8.25 % was paid on the subtotal which included the shipping charge
To find: total amount paid for vase
total amount paid for vase = Cost of vase + Shipping charge + sales tax
Let us first find the sales tax
Given that 8.25 % was paid on the subtotal which included the shipping charge
Subtotal = 34.99 + 3 = 37.99
So 8.25 % of 37.99 was paid as sales tax
[tex]\text{ sales tax } = \frac{8.25}{100} \times 37.99 = 3.1341[/tex]
Therefore sales tax amount paid = $ 3.1341
total amount paid for vase = Cost of vase + Shipping charge + sales tax
total amount paid for vase = 34.99 + 3 + 3.1341 = 41.1241 ≈ 41
Therefore total amount paid for vase is $ 41
B is the midpoint of AC. AB=7x-4 and BC=4x+5. Find AC.
A) 51
B) 68
C) 17
D) 34
Answer:
D) 34
Step-by-step explanation:
Since B is the midpoint, AB = BC
Plug the two in:
7x - 4 = 4x + 5
Solve for x:
3x = 9, x = 3
Find AB + BC
since BC = AB
AC = 4x + 5 + 4x + 5
AC = 8x + 10
AC = 8(3) + 10
AC = 24 + 10
AC = 34
The calculated length of the segment AC is () 34
How to determine the length of the segment ACFrom the question, we have the following parameters that can be used in our computation:
AB = 7x - 4
BC = 4x + 5
B is the midpoint of AC
So, we have
7x - 4 = 4x + 5
Evaluate
3x = 9
So, we have
x = 3
This means that
AC = 2 * (7 * 3 - 4)
Evaluate
AC = 34
HEnce, the length of the segment AC is () 34
Read more about midpoint at
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Math Question Time! Grade:6
A teacher asked her students to create an algebraic expression with only subtraction by only getting the answer. The answer given was 3. What is one algebraic expression that it can be?
Rewards for completing problem correctly: 15 points (maybe even Brainliest!)
Explanation has to be provided! Good luck!
Answer:
lol
Step-by-step explanation:
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is
the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation
x+y=24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
The test contains 4 three-point questions and 20 five-point questions
The test contains 10 three-point questions and 14 five-point questions
The test contains 14 three-point questions and 10 five-point questions.
The test contains 20 three-point questions and 8 five-point questions.
Answer: 10 three points questions and 14 five points questions
Step-by-step explanation: Please see attachment for explanation.
Name two coordinates that are on the line: [tex]y = 12[/tex]
Name two coordinates that are on the line: [tex]x = -5[/tex]
Write the equation of the line that passes through the point (3, -5) and is perpendicular to the line x = 4.
60 Point offer.
(1, 12)
(420, 12)
Any coordinate with a y value of 12 lies on the line y = 12.
-----
(-5, 69)
(-5, 13)
Any coordinate with an x value of -5 lies on the line x = -5.
-----
Since the equation must be perpendicular to the line x = 4, which is a vertical line, it must also be written in the form x = a.
Since the x coordinate is 3, the equation of the line is simply x = 3.
help me pleaseeee!!!!!
Because she needs 3 blankets and it takes 15 day per blanket(rate is given), she needs 3x15 or 45 days. She has 60 days so she can volunteer at most 15 days.
answer: s≤15
a clothing distributor sold an $80 coat at a selling price of $73 what was the percentage of discount for the coat
Answer:
91 1/4%
Step-by-step explanation:
To find the percentage of the discount, just divide the new selling price cost from the previous selling price over 100
73/80*100 = 91 1/4%
in a 45-45-90 right triangle if the length of the legs is 2 units the length of the hypotenuse will be
Answer:
[tex]2\sqrt{2}\ units[/tex]
Step-by-step explanation:
we know that
In a 45-45-90 right triangle, the length of the two legs are equal
so
Applying the Pythagorean Theorem
[tex]c^2=a^2+b^2[/tex]
where
c is the hypotenuse
a and b are the legs
we have
[tex]a=2\ units\\b=2\ units[/tex]
substitute
[tex]c^2=2^2+2^2[/tex]
[tex]c^2=4+4[/tex]
[tex]c^2=8[/tex]
[tex]c=\sqrt{8}\ units[/tex]
simplify
[tex]c=2\sqrt{2}\ units[/tex]
What is 20 times 4 and add 5?
20 times 4 add 5 is
20*4+5
20*4=80
80+5=85
85 is your answer
Answer: 85.
Step-by-step explanation: 20 times 4 equals 80, add 5 to that makes 85.
And the equation in mathematical form: ( 20 X 4 ) = 80 + 5 = 85.
Hope this helps, if not, comment below please!!!!!
The rules concerning the age a of a soccer player in a recreational league mandate that a player be 17 years of age or older. Which inequality BEST represents this situation?
A. a > 17
B. a ≤ 17
C. a ≥ 17
D. a < 17
Answer:
It can be represented by a ≥ 17.
Step-by-step explanation:
The rules concerning the age of a soccer player in a recreational league mandate that a player is 17 years of age or older.
Therefore, if the age of a player is a years, then the condition for a soccer player to participate in the league is that a must be equal to 17 or more than 17 years old.
Hence, mathematically it can be represented by a ≥ 17. (Answer)
Explain how to find the number of comic books you could buy with $25.00
Answer:
$25 - c(p)
Step-by-step explanation:
C = amount of comic books
P = price of comic books
$25 - c(p)
Hope this helps :)
Answer:
depends on the price of each book
Step-by-step explanation:
For instance if you have ...
one book sold for $5
you divide the total ($25) by the cost for each book ($5) and you will get the number of comic books (25/5 = 5 comic books)
You're designing an experiment that looks at the effect of different types of newly
developed fish food on the growth rate of three species of fish: tiger fish, guppies,
and goldfish. The treatments are new food #1, new food #2, and old food. For a
randomized block design, blocked on species of fish, how many treatment groups
would you have? (Think of "old food" as one of the treatments.)
I need this answer too, did you figure it out?
If the point (1,5) lies on a circle whose center is at the origin, what is the equation of the circle?
Answer:
x^2 + y^2 = 26.
Step-by-step explanation:
The center is at (0, 0) and the radius is sqrt (1^2 + 5^2) = sqrt 26
The general form is
x^2 + y^2 = r^2 so here it is:
x^2 + y^2 = 26.
Final answer:
The equation of the circle whose center is at the origin and passes through the point (1,5) is x² + y² = 25 since the radius of the circle is the distance from the origin to the point, calculated as 5.
Explanation:
If the point (1,5) lies on a circle whose center is at the origin, the equation of the circle can be found using the distance formula which is derived from the Pythagorean theorem. Since the distance from the center (0,0) to the point (1,5) is the radius of the circle, we calculate the radius as follows:
√((x-0)² + (y-0)²) = √((1-0)² + (5-0)²) = √(1 + 25) = √26 = 5.
Therefore, the radius of the circle is 5. The equation of the circle with a radius of 5, centered at the origin, is:
x² + y² = r²
x² + y² = 5²
x² + y² = 25
four times a number decreased by 6 is less than -2. Define a variable, write an inequality, and solve for the number
Final answer:
The variable x represents the unknown number, and the inequality is 4x - 6 < -2. Solving it step-by-step, we find that x < 1, which means any number less than 1 satisfies the inequality.
Explanation:
To solve the inequality 'four times a number decreased by 6 is less than -2', let's define a variable x as the number. Expressing the given condition as an inequality, we get 4x - 6 < -2. To solve for x, follow these steps:
Add 6 to both sides of the inequality to isolate the term with the variable: 4x - 6 + 6 < -2 + 6, which simplifies to 4x < 4.
Divide both sides of the inequality by 4 to solve for x: 4x/4 < 4/4, which gives us x < 1.
Check the answer to ensure it is reasonable. Since multiplying a number by four and subtracting six should result in a number less than -2, a number less than 1 seems reasonable.
Therefore, any number less than 1 satisfies the inequality.
ANSWER ASAP PLS <3
Write the point-slope form of the equation of the line with a slope of -2 and an x-intercept of -1.
Answer:
y = -2(x + 1)
Step-by-step explanation:
x-intercept of -1 means y=0 when x=-1, so you have your (x₁, y₁) value of (-1, 0).
Slope is -2 so m=-2.
Plug into point-slope formula:
y = m(x - x₁) + y₁
y = (-2)(x - (-1)) + (0)
y = -2(x + 1)
How many miles could Kenja travel in 1 hour. Is this the same number of hours it takes kenja to travel 1 mile? Explain your answer
Answer:
Kenja could travel a certain number of miles in 1 hour depending the speedometer. So, it is not necessary that she may always take the same number of hours it takes to travel 1 mile.
For example, If Kenja has traveled 120 miles in three hours. It means it would take 5 hours to travel 200 miles. The reason is that her unit rate is 40 miles per hour. So, it would take her 1/40 hours to travel one mile.
Step-by-step explanation:
Kenja could travel a certain number of miles in 1 hour depending the speedometer.
If she is traveling at the rate of 5 miles per hour, it would take her 12 minutes to travel one mile. The only way she can take the same number of hours to travel 1 miles if she travels at the rate of 1 mile per hour.
For example, if Kenja has traveled 120 miles in three hours. It means it would take 5 hours to travel 200 miles. The reason is that her unit rate is 40 miles per hour.
As
[tex]\frac{120}{3} = 40 mph[/tex]
So, if the unit rate is 40 mph, then it would take her 1/40 hours to travel one mile.
So, it is not necessary that she may always take the same number of hours it takes to travel 1 mile.
Keywords: miles per hour, speed, unit time
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Financial Math question....
What is the monthly payment for a $4,000 3 year loan with an APR of 7.50%
Answer:
$124.42
Step-by-step explanation:
look at the attachment for the formula I used
Find the minimum or maximum value of f(x) = x2 + 6x +11 .
Answer:
Therefore the Minimum value of f(x) is 2.
Step-by-step explanation:
Given:
[tex]f(x)=x^{2} + 6x+11[/tex]
To Find:
minimum or maximum value of f(x)
Solution:
To find minimum or maximum value of f(x)
Step 1 . Find f'(x) and f"(x)
[tex]f(x)=x^{2} + 6x+11[/tex]
Applying Derivative on both the side we get
[tex]f'(x)=\dfrac{d(x^{2})}{dx}+\dfrac{d(6x)}{dx}+\dfrac{d(11)}{dx}[/tex]
[tex]f'(x)=2x+6+0[/tex]
Again Applying Derivative on both the side we get
[tex]f''(x)=\dfrac{d(2x)}{dx}+\dfrac{d(6)}{dx}[/tex]
[tex]f''(x)=2[/tex]
Step 2. For Maximum or Minimum f'(x) = 0 to find 'x'
[tex]2x+6=0\\\\2x=-6\\\\x=\dfrac{-6}{2}=-3[/tex]
Step 3. IF f"(x) > 0 then f(x) is f(x) is Minimum at x
IFf"(x) < 0 then f(x) is f(x) is Maximum at x
Step 4. We have
[tex]f''(x)=2[/tex]
Which is grater than zero
then f(x) is Minimum at x= -3
Therefore the Minimum value of f(x) is 2.
The minimum value is 2 when x = -3.
The minimum or maximum value of the function f(x) = x^2 + 6x +11, we need to complete the square or use the vertex formula for a quadratic function.
The function is a parabola that opens upwards (since the coefficient of the x2 term is positive). To complete the square, we group the x-terms and add and subtract the square of half the coefficient of x:
f(x) = (x^2 + 6x + 9) + 11 - 9
f(x) = (x + 3)^2 + 2
The minimum value of this parabola occurs at the vertex, which is (-3, 2).
Solve q = {(s+t) for t.