Determine the whether the quadratic equation below has a maximum or minimum.
y = 4x² – 3x - 43
Answers
Answer:
Minimum
Need to know:
Derivative power rule: d/dx xⁿ = nxⁿ⁻¹
Derivative constant rule: d/dx c = 0
Step-by-step explanation:
A way to determine whether the quadratic equation has a maximum or a minimum is by graphing it.
If we look at the image below, we notice that the graph does not go to the bottom infinitely, but it keeps going up infinitely. This means there is a minimum to this graph.
Another way to determine this is through calculus.
First, we have to find the point of extremum
Find the derivative of the given equation
d/dx 4x² - 3x - 43
You can separate the terms and solve them individually
d/dx 4x² = 4(2)(x²⁻¹) = 8x
d/dx -3x = -3(1)(x¹⁻¹) = -3(1)(1) = -3
d/dx -43 = 0
y' = 8x - 3
Set y' to equal 0
8x - 3 = 0
Add 3 to both sides
8x - 3 = 0
+ 3 + 3
8x = 3
Divide both sides by 8
8x/8 = 3/8
x = 3/8
There is only one point of extremum
Now we have to test whether the equation changes from negative to positive or positive to negative
If it changes from negative to positive, that point is a minimum
If it changes from positive to negative, that point is a maximum
To find this, pick a number less than 3/8 and plug it in the place of x in the derivative equation. We'll use 0.
y' = 8(0) - 3 = -3
Now we will do the same for a number larger than 3/8. We'll use 1
y' = 8(1) - 3 = 5
Since the lesser side of 3/8 is negative and the larger side of 3/8 is positive, that means it changes from negative to positive. This point is a minimum.
Related Questions
What is the total finance charge for a $4,250 loan at 13. 25% interest compounded monthly for 24 months? a. $25. 47 b. $202. 55 c. $611. 20 d. $4,861. 20 Please select the best answer from the choices provided A B C D.
Answers
The total finance charge for a $4,250 loan at 13. 25% interest compounded monthly for 24 months is $670.54.
What is Compound Interest?
Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
A is the final amount, P is the Initial principal balance, r is the interest rate, n is the number of times interest is applied per time period, t is the number of time periods elapsed.
As it is given that the principal amount is $4,250 while the interest rate is 13.25% compounded monthly and the principal amount is taken for 24 months, therefore,
[tex]A = P(1 + \frac{r}{n})^{nt}\\\\A = 4,250(1 + \frac{0.1325}{12})^{24 \times 2}\\\\A = 5,531.54[/tex]
Now, the total amount that is needed to be paid is $5,531.54, while $4,250 was the principal amount therefore, the finance charge or the interest is,
Financial Charge = Final amount - Principal amount
Financial Charge = $5531.54 - $4861 = $670.54
Hence, the total finance charge for a $4,250 loan at 13. 25% interest compounded monthly for 24 months is $670.54.
Learn more about Compound Interest:
https://brainly.com/question/25857212
HELP ME OUT PLEASE!! UR THE BEST AND PLS DONT ADD IRRELEVANT ANSWERS
Mark the Following statement as True or False and provide an explanation for your
choice:
"If the price of Hula Hoops is set below its market equilibrium price there will be a
surplus of Hula Hoops in the market."
Hula Hoop Market
Answers
The figure shows the measurements, in inches, of a rectangular prism.
A rectangular prism has a height of 8 inches, length of 7 inches and a width of 7 inches.
What is the volume of the prism?
Answers
Answer:
8×7×7 diameters should be accurate
What is the 7th term in the geometric sequence described by this explicit
formula?
an = 800 - (0.5)(n-1)
Answers
Answer:
a₇ = 797
Step-by-step explanation:
substitute n = 7 into the explicit formula
a₇ = 800 - 0.5(7 - 1) = 800 - 0.5(6) = 800 - 3 = 797
What is the unit rate for mason's run?
Answers
Answer:
Picture or graph? I need a graph to answer.
What are the values of a and b?
Answers
Answer:
A=44 B=68
Step-by-step explanation:
There are two congruent sides, therefore the corresponding angles are also congruent.
Answer:
a and b both are 56 degree
Step-by-step explanation:
this is due to it's isosceles triangle. So, we take (180-68):2
What is the greatest common factor of 24 and 60
Answers
Answer:
12 is the GFC.
Step-by-step explanation:
24 - 8, 3, 4, 6, 2, 12, 1, 24
60 - 10, 6, 2, 30, 20, 3, 5, 12, 4, 15
The greatest common factor of 24 and 60 is 12
What is greatest common factor?The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
For us to find the greatest common factor we need to find the common factors between the numbers.
The factors of 24 = 1,2,3,4,6,8,12 and 24
The factors of 60 = 1,2,3,4,5,6,12,15,30 and 60.
The common factors are ;
1,2,3,4,6 and 12
And the greatest common factor is 12. because it is the highest factor.
learn more about greatest common factor from
https://brainly.com/question/219464
#SPJ6
Help me with this problem please.
Answers
Answer:
1.23, -4.8
Step-by-step explanation:
-3.57 - 1.23 = -4.8
Hope this helps :)
Need these also any help
Answers
==============================
Explanation:
For problem 1, we will plot a closed circle at x = -2 to include this value in the shaded solution set. We include it because of the "or equal to". The shading is to the right because of the "greater than". So we're describing all x values that are either equal to -2 or larger than -2. You could say "x is -2 or larger".
---------------------
In problem 2, we'll exclude the endpoint since we don't have "or equal to". We shade to the left to visually show all values smaller than 3.
---------------------
In problem 3, we follow the same idea as the last problem. We have an open hole to exclude the endpoint and shade to the right of 12 to describe all values larger than 12.
---------------------
With problem 4, we now include the endpoint again. This is similar to problem 1. We shade to the left to describe x values that are either -15 or smaller.
239 students went on a field trip. Six
buses were filled and 17 students traveled
in cars. How many students were in each
bus?
Answers
Answer:
37
Step-by-step explanation:
239-17=222
222/6=37
37
If z = x² + y² , prove that:
[tex]{ \large{ \rm{ {x}^{2} \: {\frac{ {∂}^{2}z }{∂ {x}^{2} } + 2xy \frac{ {∂}^{2}z }{∂x∂y} } + {y}^{2} \frac{ {∂}^{2}z }{∂ {y}^{2} } = 2z}}}[/tex]
_____________
Don't Spam
Well explained answers needed
Answers
Answer:
Given That:
[tex]{ \large\longrightarrow { \rm{z = {x}^{2} + {y}^{2} }}}[/tex]
Partial differentiating both sides with respect to x, we get:
[tex]{ \large\longrightarrow { \rm{ \frac{∂z}{∂x} = 2x}}}[/tex]
Partial differentiating again with respect to x, we get:
[tex]{ \large\longrightarrow {{ \rm{ \frac{ {∂}^{2}z }{∂ {x}^{2} } \: = 2 \: \: \: \: \quad -(i) }}}}[/tex]
Consider again:
[tex]{ \large\longrightarrow {{ \rm{ z = {x}^{2} + {y}^{2} }}}}[/tex]
Partial differentiating both sides with respect to y, we get:
[tex]{ \large\longrightarrow { { \rm{ \frac{∂z}{∂y} = 2y}}}}[/tex]
Now, partial differentiating both sides with respect to x, we get:
[tex]{ \large\longrightarrow{ \rm{ \frac{ {∂}^{2}z }{∂x \:∂y } = 0 \: \: \: \quad - (ii) }}}[/tex]
Consider again:
[tex]{ \large\longrightarrow { \rm{ \frac{∂z}{∂y} = 2y}}}[/tex]
Partial differentiating both sides with respect to y, we get:
[tex]{ \large\longrightarrow{ \rm{ \frac{ {∂}^{2}z }{∂ {y}^{2} } = 2 \: \: \: \: \: \quad - (iii) }}}[/tex]
Now, consider Left Hand Side, we get:
[tex]{ \large{ \rm{ \longrightarrow {x}^{2} \frac{ {∂}^{2}z }{∂ {x}^{2} } + 2xy \frac{ {∂}^{2} x}{∂x \:∂y } + {y}^{2} \frac{ {∂}^{2}z }{∂ {y}^{2} } }}}[/tex]
From Equation (i),(ii) and (iii), we can write:
[tex]\longrightarrow{ \large{ \rm{ {2x}^{2} + 0 + {2y}^{2} }}}[/tex]
[tex]\longrightarrow \: { \large{ \rm{2( {x}^{2} + {y}^{2} ) }}}[/tex]
[tex]\longrightarrow{ \large{ \rm{2z}}}[/tex]
Therefore,
[tex]{ \large{\longrightarrow \: { \rm{{x}^{2} \frac{ {∂}^{2} z}{∂ {x}^{2} } + 2xy \frac{ {∂}^{2}x }{∂x \:∂y } + {y}^{2} \frac{ {∂}^{2}z }{∂ {y}^{2} } = 2z }}}}[/tex]
Hence Proved!!
[tex] \: [/tex]
Learn More:-[tex]\boxed{\begin{array}{c|c}\bf f(x)&\bf\dfrac{d}{dx}f(x)\\ \\ \frac{\qquad\qquad}{}&\frac{\qquad\qquad}{}\\ \sf k&\sf0\\ \\ \sf sin(x)&\sf cos(x)\\ \\ \sf cos(x)&\sf-sin(x)\\ \\ \sf tan(x)&\sf{sec}^{2}(x)\\ \\ \sf cot(x)&\sf-{cosec}^{2}(x)\\ \\ \sf sec(x)&\sf sec(x)tan(x)\\ \\ \sf cosec(x)&\sf-cosec(x)cot(x)\\ \\ \sf\sqrt{x}&\sf\dfrac{1}{2\sqrt{x}}\\ \\ \sf log(x)&\sf\dfrac{1}{x}\\ \\ \sf{e}^{x}&\sf{e}^{x}\end{array}}[/tex]
Refer to the attachments for answer
Used Concept :- [tex]{\boxed{\bf{\dfrac{d}{dx}(x^n)=nx^{n-1}}}}[/tex]Helppp meeeee with question 1 or can the all pleaseeee !!!
Answers
Answer:
1. 2c+9=m
Step-by-step explanation:
A small regional carrier accepted 22 reservations for a particular flight with 20 seats. 14 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 42% chance, independently of each other.
a. Find the probability that overbooking occurs.
b. Find the probability that the flight has empty seats.
Answers
The probabilities for each case are:
a) P = 0.012b) P = 0.937How to get the probability?
There are 8 reservations for passengers that may go or not, such that the probability of arriving to the flight is P = 0.42, and the probability of not arriving is Q = 0.58
a) There will be overbooking if 7 or more passengers go to the flight, the probability that the 8 attend is:
P(8) = (0.42)^8
The probability that 7 attend is:
P(7) = 8*(0.42)^7*(0.58)
(where the factor 8 is because there are 8 permutations)
The total probability is:
P = P(8) + P(7) = 0.012
b) Will be empty seats if less than 6 people go.
The probability that exactly 6 of these people go to the flight is:
P(6) = (28)*(0.42)^6*(0.58)^2
Where there are 28 permutations, that is why we used that factor.
Then, the probability of having empty seats is:
P = 1 - P(6) - P(7) - P(8) = 0.937
If you want to learn more about probability, you can read:
https://brainly.com/question/251701
What is y+3=-(x-5) written in standard form
Answers
Answer:
the answer would be 3x+y-15
Which products result in a difference of squares? check all that apply. (5z 3)(–5z – 3) (w – 2.5)(w 2.5) (8g 1)(8g 1) (–4v – 9)(–4v 9) (6y 7)(7y – 6) (p – 5)(p – 5)
Answers
Option second [tex]\rm (w-2.5)(w+2.5)[/tex] and option fourth [tex]\rm (-4v-9)(-4v+9)[/tex] are the products that result in a difference in squares.
It is required to identify which products result in a difference in squares.
What is polynomial?Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.
We know that:
[tex]\rm (a^2-b^2)=(a+b)(a-b)[/tex]
In option first:
[tex]\rm = (5z+3)(-5z-3)\\\rm = -(5z+3)(5z+3)\\\rm = -(5z+ 3)^2[/tex]
Which is not the difference between squares.
In option second:
[tex]\rm=(w-2.5)(w+2.5)\\\rm =(w^2-2.5^2)[/tex]By using [tex]\rm (a^2-b^2)=(a+b)(a-b)[/tex]
It is the difference between squares.
Similarly, in option third:
[tex]\rm =(8g+1)(8g+1)\\\rm =(8g+1)^2[/tex]
It is not the difference between squares.
Similarly, in option forth:
[tex]\rm = (-4v-9)(-4v+9)\\\rm = (4v+9)(4v-9)\\\rm = (4v)^2-9^2[/tex]
It is the difference between squares.
Similarly, in option fifth:
[tex]\rm = (6y+7)(7y-6)\\\rm = 42y^2+13y-42[/tex]
It is not the difference between squares.
Similarly, in option sixth:
[tex]\rm =(p-5)(p-5)\\\rm =(p-5)^2[/tex]
It is also not the difference between squares.
Thus, option second and option fourth are correct.
Learn more about polynomial here:
brainly.com/question/17822016
How much do you earn per week if your annual salary is $40,716?
Answers
Answer:
783
Step-by-step explanation:
There are 52 weeks in a year. Divide 40,716/52 and you get $783 weekly.
What is 7/10 + 3/5 answer
Answers
Answer:
■○■•♤•♤♤•》•♤~♤~♤~♤~♤♤~♤•♤○♤~
helppppppppppppppppp
Answers
Answer:
Step-by-step explanation:
2: 4/2 is 2
3: 4/3 is 1 1/3
4: 4/4 is 1
5: 4/5 is .8
x y y/x
2 2 4/2
3 1 1/3 or 1.333... 4/3
4 1 4/4
5 4/5 or 0.8 4/5
Hope this Helped! :)
-SGO
Please I need some steps!
Answers
Answer:
98.875
Step-by-step explanation:
Just add all the hours worked.
Hope this helps! :)
Evaluate.
x² + 2
for x = 5.1
Answers
Answer:
28.01
Step-by-step explanation:
Since x = 5.1
Substitute
5.1² + 2
=26.01+2
Add the numbers
=28.01
Hence, Answer = 28.01
~Learn with Lenvy~
Carly made her uncle a quilt. The width is 7 2 5 ft and the length is 5 1 2 ft. What is the area of the quilt?
Answers
Answer:
2474
Step-by-step explanation:
(725 x 2) + (512 x 2)
(1450)+(1024)
=2474
Please help I need this before 8:00
Answers
Answer:
c/d = 5x/3
Step-by-step explanation:
Given :-
c/d - a/b = x
a = 2c
b = 5d
To Find :-
Value of c/d in terms of x
Solving :-
Substitute value of a and b.
c/d - 2c/5d = x
3c/5d = x
c/d = 5x/3
Solution :-
c/d = 5x/3
Please help me, I don't know this one.
Answers
please can you help me with this question.
thank you.
Answers
Answer:
Follow the steps shown below.
Step-by-step explanation:
12cos(30)+2tan(60)
[tex]12*\frac{\sqrt{3} }{2} + 2\sqrt{3}[/tex]
[tex]6\sqrt{3} + 2\sqrt{3}[/tex]
[tex]8\sqrt{3}[/tex]
[tex]\sqrt{64*3}[/tex]
[tex]\sqrt{192}[/tex]
30. Felipe va a hacer un banderín para su equipo de fútbol, con las medidas que se indican en la figura. ¿Cuánta tela ocupará para elaborar el banderín?
A) 930 cm2
B) 961 cm2
C) 1 860 cm2
D) 1 922 cm2
Answers
Veremos que el area del banderín es 930cm^2, entonces la opción correcta es A.
¿Que area tiene el banderin?Luego de una pequeña busqueda online, pude ver que el banderin es un triangulo isósceles con base de 31cm y altura de 60 cm.
Recordar que para un triangulo de base b y altura h, el area es:
A = b*h/2
Entonces el area del banderín va a ser:
A = (31cm)*(60cm)/2 = 930cm^2
Entonces la opción correcta es A.
Sí quieres aprender más sobre triangulos, puedes leer:
https://brainly.com/question/2217700
What is the other factor of 6x2 – 7x 2? 3x – 2 3x – 1 3x 1 3x 2.
Answers
The quadratic polynomial 6x² – 7x + 2 has factors (3x – 2) and (2x – 1). Then the correct option is A.
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
The quadratic polynomial is 6x² – 7x + 2.
On factorization, we have
6x² – 7x + 2
6x² – (4 + 3)x + 2
6x² – 4x – 3x + 2
2x(3x – 2) –1(3x – 2)
(3x – 2)(2x – 1)
The factor is (3x – 2).
More about the factorization link is given below.
https://brainly.com/question/6810544
whats the equation 2+2 yo
Answers
Answer: is 4 you dontiy noweok
Step-by-step explanation: beacouse 2 + 2 is for silli sdlkfjasñldkas
sadfjlñsakdfjñsldfk
sdfsdlfksjañdlkfj234
23
42
34
23
4234
4
56
6
345
.
A project is graded on a scale of 1 to 5. If the random variable, X, is the project grade, what is the mean of the probability
distribution below?
Probability Distribution
PX)
OND
.li.
Answers
Complete question:
A project is graded on a scale of 1 to 5. If the random variable, X, is the project grade, what is the mean of the probability
distribution below?
Grade(X)_____ 1_____2_____3_____4_____5
Frequency____3 _____5____ 9 ____ 5 ____ 3
P(X) : _______ 0.1 ___0.2 ___0.4 ___ 0.2 __0.1
Answer:
3
Step-by-step explanation:
Given the probability distribution :
Grade(X)_____ 1_____2_____3_____4_____5
Frequency____3 _____5____ 9 ____ 5 ____ 3
P(X) : _______ 0.1 ___0.2 ___0.4 ___ 0.2 __0.1
The mean of the distribution :
Σ(X * P(X)) :
(1*0. 1) + (2 * 0.2) + (3 * 0.4) + (4 * 0.2) + (5 * 0.1)
0.1 + 0.4 + 1.2 + 0.8 + 0.5
= 3
Answer:
the mean is 3
answer choice D
the function g(x) is a transformation of the quadratic parent function, f(x) = x^2. What function is g(x)
Answers
Answer:
Option (C)
Step-by-step explanation:
Quadratic parent function has been given as,
f(x) = x²
If we reflect this function across the x-axis and vertically stretched by a scale factor of 'k',
g(x) = -kx²
This quadratic function passes through a point (1, -4),
g(1) = -k(1)²
-4 = -k
k = 4
Therefore, the new function after transformation will be,
g(x) = -4x²
Option (C) will be the correct option.
The function g(x) is [tex]\rm g(x) = -4x^2\\[/tex].
Given that,
The function g(x) is a transformation of the quadratic parent function,
[tex]\rm f(x) = x^2[/tex]
We have to determine,
What function is g(x)?
According to the question,
The function f(x) is a transformation of the quadratic parent function,
[tex]\rm f(x) = x^2[/tex]
In the given figure the function g(x) reflect across the x-axis and is vertically stretched by a scale factor of 'k',
Then, The function g(x) is,
[tex]\rm g(x) = -kx^2[/tex]
Therefore,
The quadratic equation passes through the point (1,4),
[tex]\rm g(x) = -kx^2\\\\g(1) = -k(1)^2\\\\-4 = -k\\\\k= 4[/tex]
Therefore,
The function g(x) is,
[tex]\rm g(x) = -kx^2\\\\g(x) = -4x^2[/tex]
Hence, The required function g(x) is [tex]\rm g(x) = -4x^2\\[/tex].
For more details refer to the link given below.
https://brainly.com/question/411998
You need a new computer for college that costs $1200. You
have worked all summer and earned $960. You will have to ask
your aunt if you can borrow the rest. What percent of the
computer's cost do you ask your aunt to pay?
Answers
Answer: 20%
Step-by-step explanation: $1200 - $960 = $240
20% of 1200 is 240.