The behavior of the graph of the function y = -x^3 - 5x^2 - 3x + 9 at each of its zeros is as follows:
At x ≈ -4.919 and x ≈ -0.488, there are local minima.
At x ≈ 1.752, there is a local maximum.
Let's analyze the behavior of the graph of the function y = -x^3 - 5x^2 - 3x + 9 at each of its zeros in more detail.
To find the zeros of the function, we need to solve the equation -x^3 - 5x^2 - 3x + 9 = 0.
To simplify the calculations, let's use a numerical method like the Newton-Raphson method to approximate the zeros. We'll start with initial guesses and iteratively refine them to improve the accuracy of the solutions.
Initial guess: x_0 ≈ -5
Applying the Newton-Raphson method:
x_1 = x_0 - f(x_0) / f'(x_0)
where f(x) = -x^3 - 5x^2 - 3x + 9
f'(x) = -3x^2 - 10x - 3 (derivative of f(x))
x_1 = -5 - (-5^3 - 5(-5)^2 - 3(-5) + 9) / (-3(-5)^2 - 10(-5) - 3)
≈ -4.919
Initial guess: x_0 ≈ -1
Applying the Newton-Raphson method:
x_1 = x_0 - f(x_0) / f'(x_0)
x_1 = -1 - (-1^3 - 5(-1)^2 - 3(-1) + 9) / (-3(-1)^2 - 10(-1) - 3)
≈ -0.488
Initial guess: x_0 ≈ 2
Applying the Newton-Raphson method:
x_1 = x_0 - f(x_0) / f'(x_0)
x_1 = 2 - (2^3 - 5(2)^2 - 3(2) + 9) / (-3(2)^2 - 10(2) - 3)
≈ 1.752
After iterating through the Newton-Raphson method, we approximate the zeros as follows:
x ≈ -4.919
x ≈ -0.488
x ≈ 1.752
Now, let's analyze the behavior of the graph at each zero:
x ≈ -4.919:
When x is close to -4.919, y is close to zero. Since the coefficient of the leading term (-x^3) is negative, as x approaches -4.919 from the left side, the graph of the function will be decreasing. As x approaches -4.919 from the right side, the graph will be increasing. Therefore, the behavior of the graph near x ≈ -4.919 is a local minimum.
x ≈ -0.488:
When x is close to -0.488, y is close to zero. Similarly, as x approaches -0.488 from the left side, the graph will be decreasing, and as x approaches -0.488 from the right side, the graph will be increasing. Therefore, the behavior of the graph near x ≈ -0.488 is also a local minimum.
x ≈ 1.752:
When x is close to 1.752, y is close to zero. In this case, as x approaches 1.752 from the left side, the graph will be increasing, and as x approaches 1.752 from the right side, the graph will be decreasing. Therefore, the behavior of the graph near x ≈ 1.752 is a local maximum.
for such more question on graph
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A solid piece of wood shaped as a cylinder with an 8-centimeter diameter is cut as shown.
What is the surface area of the figure? Express the answer in terms of π.
96 + 64π cm2
96 + 80π cm2
96 + 112π cm2
96 + 128π cm2
Answer:
A
Step-by-step explanation:
What is the domain of the function y = l n (x + 2)
A. x < -2
B. x > -2
C. x < 2
D. x > 2
Answer:
Option B.
Step-by-step explanation:
For a function f(x), the domain is the set of all the possible values of x that can be used in the function.
We know that the natural logarithm is only defined for positive real numbers.
So, the function:
Ln(x + 2)
Works always that
x + 2 > 0
So we can just solve this inequality for x, and that will give us the domain of the function.
To isolate x, we just need to subtract 2 in both sides of the inequality.
x + 2 - 2 > 0 - 2
x > - 2
This is the domain of the function.
The correct option is B.
Answer:
b.x>-2
Step-by-step explanation:
edge 2021
Plssss help SUNDAY HOMEWORKKKKKKKKKKKK
Answer:
already did
Step-by-step explanation:
Show the given equation in a graph
x + y = 5
Answer:
you us the equation given and plot points in the graph that are given with the equation.
Find the area and round it to the nearest hundredth if necessary
Answer:
16.28 squared inches
Step-by-step explanation:
Use the formula A = bh.
b = base
h = height
A = (4.4) (3.7)
A = 16.28
What is the vertex of the graph of the function f(x) = x^2 + 8x - 2?
Answer:
(-4,-18)
Step-by-step explanation:
go to math(way).com to find the answer
hello please help i’ll give brainliest:)
Answer:
Its is 85
Step-by-step explanation:
It is 85 because you need to see out of all of those numbers which one is one is in the middle so just mark one number from each side untill you get to the middle number!
Dentro de 15 años la edad de Carlos será el doble de la edad de Ana. Hace 6 años la edad de Carlos era el triple de la de Ana. Calcular la suma de sus edades y dar como respuesta la suma de cifras de este resultado
Answer:
Ana tiene 27 años mientras que Carlos, tiene 69 años
La suma de las edades es: 27+69 = 96
La suma de las cifras de este resultado es 9+6 = 15
Step-by-step explanation:
Vamos a hacer una linea temporal para ubicarnos en tiempo.
AÑO 2021, Ana tiene una edad A mientras que Carlos tiene una edad C
15 años para adelante
AÑO 2036, la edad de Carlos es el doble de la de Ana
C = 2A
Si nos vamos 6 años para atrás
AÑO 2015, la edad de Carlos es el triple de la de Ana
C = 3A
Como de 2015 a 2036 pasan 21 años, podemos plantear que
La edad de Carlos + 21 va a ser 2 veces la edad de Ana, traducido:
C + 21 = 2A, pero en 2015, ya sabemos que la edad de Carlos es el triple de la de Ana, entonces:
3A + 21 = 2A. Si despejamos:
3A - 2A = -21
A = |21| Ésta es la edad de Ana. (Ponemos valor absoluto porque una edad no puede ir negativa.
Si Ana en 2014 tiene 21 años, Carlos tiene 63 (el triple) por lo que sumamos 6 años y llegamos al presente:
En 2021, Ana tiene 27 años (21+6), mientras que Carlos tiene 69 (63+6). Edades actuales.
Nos corremos 15 años al futuro, por lo que llegamos al año 2036.
Carlos pasa a tener 84 años (69+15) y Ana, 42 (27+15) donde verificamos que la edad de Carlos, es el doble que la de Ana, 84/42 = 2.
Finalmente la suma de las edades es: 27+69 = 96
La suma de las cifras de este resultado es 9+6 = 15
A line is parallel to y = 2x + 1 and
intersects the point (3, 2). What is
the equation of this parallel line?
Start by entering this into point-slope form.
y 52 = [?](x-[])
Answer:
y= 2x-4
Step-by-step explanation:
y-2= 2(x-3)
y-2=2x-6
y= 2x-6+2
y= 2x-4
Use a calculator to find the value of these data. Round the value to three
decimal places.
A-0.953
B. -1.909
C. 0.909
D. 0.953
The value of coefficient of correlation coefficient is -0.953 which is a negative correlation between x and y option (A) is correct.
What is correlation?It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
We have given data in the table.
As we know, the formula for the correlation is given by:
[tex]\rm r = \dfrac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{[n\sum x^2- (\sum x)^2]}}\sqrt{[n\sum y^2- (\sum y)^2]}}[/tex]
After plugging the value, we will get the value of r:
r = -0.953
Thus, the value of coefficient of correlation coefficient is -0.953 which is a negative correlation between x and y option (A) is correct.
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A soup recipe calls for cup of cheese, cup of milk, and 4 potatoes. The recipe serves 2 people,
What is the correct amount of cheese, milk, and potatoes needed to serve 5 people using this soup recipe?
Answer:
2 1/2 cup cheese
2 1/2 cup milk
10 potatoes
Step-by-step explanation
take half of each and multiply it by 5
At Edison Middle School, 54.4% of the
72
students chose chicken tacos as their
favorite school lunch, and 36% chose fish
tacos. There are 750 students in the
school. How many did NOT choose a type
of taco?
PLZ HELPP (7th grade math) ASSAAPPP
Answer:
6.912 students did NOT choose a taco type out of the 72 students.
Step-by-step explanation:
I got the number of kids for 54.4% of 72 and 36%, and added them, then subtracted that from 72 to get the total amount
750 - 750 * 0.544 - 750 * 0.36 = 72.
The radius of a circle is 7 ft. Find its area to the nearest tenth
Answer:
153.9 ft²
Step-by-step explanation:
A(Circle) = πr²
⇒ π(7)² ⇒ 49π ≈ 153.9 ft²
Answer:
47.0
Step-by-step explanation:
A=L^2
A=7*7
A=47
47 to the nearest tenth
=47.0
A crayon has a mass of 10.0 g and volume of 5.0 mL. What is the density?
Answer:
2000 g/L
Step-by-step explanation:
(10.0 g) / (0.005 L) = 2000 g/L
hey! i’ll give brainliest please help.
Answer:
shah
:) hope this helps!
will give brainlyist if quick Which of the equations is graphed below?
Answer:
c
Step-by-step explanation:
Find the missing value for the parallelogram
Answer:
y = 85°
z = 35°
x = 60°
Step-by-step explanation:
y) 180 - 120 = 60, therefore:
180 - (35 + 60)
=> y = 85
z)
=> z = 35
x)
180 - (35 + 85)
=> x = 60
Hope this helps!
Answer:
to find y
you find the bottom right angle
which is 180-120 = 60
then you do 60+35 = 95
then 180 -95 because the sum of all angles in a triangle is 180
so the answer is 85 = y
There is a rule where the alternate angles between the parallel lines are identical
if y = 85 that means that the angle next to 35 is 85
same for angle z, if the top right 35, that means that angle z = 35
Now you add 35 + 85 = 120
180 - 120 = 60 = angle x
In summary
x=60
y=85
z=35
Hope that answers your question
Don't hesitate to leave a comment if you are confused about something
Step-by-step explanation:
Simplify √14q times 2√4q
Answer:
[tex]4\sqrt{14} q^{2}[/tex]
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
How many solutions does the equation
-2(x + 3) = 2x - (5 – x) have?
Step-by-step explanation:
-2(x + 3) = 2x - (5 – x)
-2x+6= 2x-5+x
-2x+6=3x-5
-2x-3x=-5-6
-5x=-11
x= 11/5
( 1 solution)
Answer:
Solution given:
-2(x + 3) = 2x - (5 – x)
-2x-6=2x-5+x
-6+5=2x+2x+x
5x=-1
x=[tex] \frac{-1}{5} [/tex]
It has one Solution.
ahhhh someone help pls!!!!
Answer:
I may be wrong but I think it's 90 I may be wrong but hey I tryed.
Step-by-step explanation:
8.6 divided by 1,000 =
find the quotient. divide decimals by power of ten.
Find the area of the circle. Round to the nearest hundredth (3.14 for pie)
Answer:
hn
Step-by-step explanation:
gggggg
Solve for x. Rolind to the nearest hundredth.
Please help me using product rule
Using the product rule, then (A) is the answer.
Help please ;3; ksajnwns
Answer:
yes
no
yes
yes
Step-by-step explanation:
replace every number on y
and check whether it works or not.
A circle has a circumference of 10 feet. What is the
diameter?
Dave rolled a number cube 10 times and recorded the frequency of each result in this table. According to the table, what is the experimental probability in simplest form that the number cube shows 6? A.1/10 B.1/6 C. 3/10 D. 1/2
Answer:
C is infact correct
Step-by-step explanation:
Give guy above brainly
The experimental probability in simplest form that the number cube shows 6 will be 3/10.
What is probability ?Probability is a branch of mathematics that deals with the occurrence of a random event.
According to the question
Dave rolled a number cube 10 times and recorded the frequency of each result in this table.
From the table it can be seen that the frequency of rolling a 6 is 3 and the probability of the event occuring is 1/6
so ,
The experimental probability in simplest form that the number cube shows 6 will be
= Frequency / No. of times the dice is rolled
= 3/10
The experimental probability in simplest form that the number cube shows 6 will be 3/10.
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An experiment consists of spinning the spinners shown and adding the numbers together. Complete the array.
Answer:
[tex]\begin{array}{ccccc}{} & {1} & {2} & {3} & {4} & {1} & {2} & {3} & {4} & {5} & {2} & {3} & {4} & {5} & {6} & {3} & {4} & {5} & {6} & {7} & {4} & {5} & {6} & {6} & {8} \ \end{array}[/tex]
Step-by-step explanation:
Given
[tex]Spinner = \{1,2,3,4\}[/tex]
Array:
[tex]\begin{array}{ccccc}{} & {1} & {2} & {3} & {4} & {1} & {} & { } & { } & {5} & {2} & { } & {} & { } & { } & {3} & {4} & { } & {} & { } & {4} & { } & {6} & { } & {} \ \end{array}[/tex]
Required
Complete the blanks
To do this, we simply add up corresponding row and column elements.
[tex]\begin{array}{ccccc}{} & {1} & {2} & {3} & {4} & {1} & {} & { } & { } & {5} & {2} & { } & {} & { } & { } & {3} & {4} & { } & {} & { } & {4} & { } & {6} & { } & {} \ \end{array}[/tex]
So, we have:
[tex]\begin{array}{ccccc}{} & {1} & {2} & {3} & {4} & {1} & {1+1} & {1+2 } & {1+3 } & {4} & {2} & {2+1 } & {2+2} & {2+3 } & {2+4 } & {3} & {4} & {3+2 } & {3+3} & {3+4 } & {4} & {4+1 } & {6} & {4+3 } & {4+4} \ \end{array}[/tex]
Add
[tex]\begin{array}{ccccc}{} & {1} & {2} & {3} & {4} & {1} & {2} & {3} & {4} & {5} & {2} & {3} & {4} & {5} & {6} & {3} & {4} & {5} & {6} & {7} & {4} & {5} & {6} & {6} & {8} \ \end{array}[/tex]
Sarah kept track of the points she scored during her first five basketball games in the table shown. easy help
Answer:
E
Step-by-step explanation:
If you add 22 onto the sum of all the points and divide by the amount of games (6), you get 12.
Which expression is equivalent to 16x4 – 64? and explain the answer plzz
Answer:
4(4x1-16)
Hope this helps
Have a good day :)
PS I disibuted 4 to 4x1 to get 16 and 4 to -16 to get -64
Step-by-step explanation: