Given:
The equation is
[tex]y=5x^3-6x^2-4x+8[/tex]
To find:
The coordinates of the turning point.
Solution:
We have,
[tex]y=5x^3-6x^2-4x+8[/tex]
Differentiate with respect to x.
[tex]\dfrac{dy}{dx}=5(3x^2)-6(2x)-4(1)+(0)[/tex]
[tex]\dfrac{dy}{dx}=15x^2-12x-4[/tex]
For the turning points [tex]\dfrac{dy}{dx}=0[/tex].
[tex]15x^2-12x-4=0[/tex]
Using quadratic formula:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{-(-12)\pm \sqrt{(-12)^2-4(15)(-4)}}{2(15)}[/tex]
[tex]x=\dfrac{12\pm \sqrt{144+240}}{30}[/tex]
[tex]x=\dfrac{12\pm \sqrt{384}}{30}[/tex]
Now,
[tex]x=\dfrac{12+\sqrt{384}}{30}\text{ and }x=\dfrac{12-\sqrt{384}}{30}[/tex]
[tex]x\approx 1.053\text{ and }x\approx-0.253[/tex]
Putting x=1.053 in the given equation, we get
[tex]y=5(1.053)^3-6(1.053)^2-4(1.053)+8[/tex]
[tex]y\approx 2.973[/tex]
Putting x=−0.253 in the given equation, we get
[tex]y=5(-0.253)^3-6(-0.253)^2-4(-0.253)+8[/tex]
[tex]y\approx 8.547[/tex]
Therefore, the turning points are (1.053,2.973) and (-0.253, 8.547).
If the blue radius below is perpendicular to the chord , which is 14 units long, what is the length of the segment ?
Answer:
The answer is 7 bc 7 is half of 14
Step-by-step explanation:
45 is 3% of what number?
quick I need an answer!
hurry pls!
Answer:
stop rushing brat
Step-by-step explanation:
Step-by-step explanation:
Steps to solve "45 is 3 percent of what number?"
We have, 3% × x = 45
or,
3
100
× x = 45
Multiplying both sides by 100 and dividing both sides by 3,
we have x = 45 ×
100
3
x = 1500
If you are using a calculator, simply enter 45×100÷3, which will give you the answer.
The graph shows your elevation during a run. Which statement is true about your run?
A- You were running uphill for the first 15 minutes.
B- You were running uphill between 10 and 20 minutes into the run.
C- You were running downhill for the last 10 minutea.
D- You were running downhill the first 15 minutes.
Answer:
Its D. You were running downhill the first 15 minutes.
Can someone help me with this problem? 3[x(-6)]
Answer:
-18x
Step-by-step explanation:
First step: remove the parentheses.
So, you'll have -3x*6.
multiply the numbers (3 x 6 = 18)
and you'll get -18x.
hope this helps!
HCF of 10,100,1000.
Answer:
So the greatest common factor 10 and 1000 is 10.
plz mark me as brainliest
HELPPPPPP PLEASEEEEE BRAINLIEST IF CORRECT!!!
Answer:
1<7
Step-by-step explanation:
Hey there!
1.) adjacent
2.) vertical
3.) corresponding
4.) none of these
5.) 1 and 7, 3 and 5, 2 and 8, 4 and 6
6.) 2 and 7, 6 and 3
Have a terrifcly amazing day!
A dairy facility has a bulk milk tank that is shaped like a right circular cylinder. The
tank has a height of 12 feet and a diameter of 216 inches.
If the milk tank was cut to be modeled by a truncated cylinder to of its height,
find the volume, in cubic feet, of the milk tank to the nearest hundredth.
Answer:
800
Step-by-step explanation:
Answer the photo below thanks
Answer:
6x60=360
Step-by-step explanation:
60
please help! how do you do this question?
9514 1404 393
Answer:
(0.75, -1)
Step-by-step explanation:
The center of the circle is at the midpoint of any diameter segment. The midpoint formula can be used.
C = (A +B)/2
C = ((-1, 1) +(2.5, -3))/2 . . . . fill in A and B
C = (-1+2.5, 1-3)/2 . . . . . . . add the coordinates
C = (1.5, -2)/2 . . . . . . finish the addition; next, divide by 2
C = (0.75, -1) . . . . . . the center of the circle
Can someone help me with a full math assignment about slope rate of change and stuff? i will give them brainliest answer too
Answer:
yes of course .
I will help you .
The area of a rectangular room is 240 square feet. The width is 12 feet. What is the length?
Answer:
20 ft
A=wl
l=A/W=240/12=20ft
Grace and her brother Sid want to raise money to go to band camp. Their parents have agreed to help them up to $400 by paying them $25 when one of them mows the lawn and $10 for each hour that one of them babysits their younger brother. They will have to do a combination of both chores in order to earn the money.
Select the equation that represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.
Answer:
I think it would be 25m + 10b = 400
helppppppppppppppppp
Answer:
16.
Step-by-step explanation:
What does 75% Off mean? It means 75% of the price is subtracted. So find 75% of 64.
Here is our equation: 75/100 x 64 = 48.
So 48 dollars is going to be subtracted from 64, which gives us 64-48=16.
So the price of the wedding cake during the sale is 16.
Salma, joe, and alan sent a total of 106 text messages during the weekend, salma sent 9 fewer messages than alan. Joe sent 3 times as many messages as alan. How many messages did they each send?
Answer:
Salma, joe, and alan sent 14, 69, and 23 text messages respectively
Step-by-step explanation:
Given that Salma, joe, and alan sent a total of 106 text messages during the weekend, it means that
s + j + a = 106 where s, j, and a are the number of messages sent by Salma, joe, and alan respectively
Given salma sent 9 fewer messages than alan
s = a - 9
Joe sent 3 times as many messages as alan
j = 3a
hence
a - 9 + 3a + a = 106
5a - 9 = 106
5a = 106 + 9
5a = 115
Divide both sides by 5
a = 115/5
= 23
s = 23 - 9
= 14
j = 3* 23
= 69
Algebraic Expression
x + y + 2
Constants | Variable/s/term/s Degree of term
Constants : 1 (the only constant term is 2)
Variables : 2 (x and y)
Terms : 3 ( x, y and 2)
Degree of term : 1
-8-8(6x+1) i can’t solve this
Answer:
Step-by-step explanation:
Answer: -48x-16
Step-by-step explanation:
-8-8(6x+1)
So we are going to let the first -8 stand still for a moment and focus on the "-8(6x+1) part. We will solve this using distributive property.
-8 x 6x = -48x
and
-8 x 1 = -8
This is our new problem -8 -48x -8 .
Lets do like terms. Our like terms are (-8) and (-8). And we know -8 -8 = -16.
Now we'll add that to our (-48x) . I hope you can understand this!
plz help asap!!
which statement is not true about the data shown by the box plot below ?
Answer:
B
Step-by-step explanation:
the range is about 45
SOMEONE PLEASE HELP
and please explain it so I won't get confused further on
Dado los puntos p1 (-7/2-9/2) y p2 (5/2, 3/2) calcular la representación gráfica, d p1 p2, pto medio de p1 p2, la pendiente (m) de la recta que pasa por medio de ellos. Porfavor ayúdenme la tarea es para el viernes y no entendió
Answer:
Ce clasă ești sa văd daca te pot ajuta
Is 7/8 equivalent to -7/-8
Answer:
No
Step-by-step explanation:
I don't think those are equivalent because 7/8 is positive while -7/-8 is negative.
11. Select from below the best estimate for the decimal that is equivalent to 100.5%
A. 0
B. 1
C. 100
D. 1000
Answer:
c
Step-by-step explanation:
in all honesty because if you round thats what you would get
1. f(x) = x3 - 3x2 - 8x - 60
Answer:
x = -2
Step-by-step explanation:
hope that helps :)
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
So is 0.147 a rational number?
Answer:
Yes because it is a terminating decimal.
Step-by-step explanation:
what is the appropriate unit of measure for the mass of a steel cabinet?
On a team, 4 girls and 2 boys scored a total of 28 points. The difference between the number of points scored by the 4 girls and the number of points scored by the 2 boys is 12. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and each boy Each girl scored points.
Answer:
Each girl earned 2 points
Each boy earned 5 points
Step-by-step explanation:
Let x represent the number of points one girl earned
Let y represent the number of points one boy earned
4x + 2y = 28
4x - 2y = 12
8y = 40
y = 5 points
4x + (2)(5) = 28
4x + 20 = 28
4x = 8
x = 2 points
Each girl earned 2 points
Each boy earned 5 points
What is the value of x?
Answer:
X=14
Step-by-step explanation:
We know that both sides are congruent
so if the other angle is 7- then divide 70 by 5
Hope this helps ^-^
Step-by-step explanation:
step 1. a quadrilateral has 4 sides and 360° internally.
step 2. 70 + 5x + 110(2) = 360.
step 3. 5x = 70
step 4. x = 14.
The Value of (441)2 – (440)2 is :
(i) 841 (ii) 1 (iii) 881 (iv) 0
Which polynomial function has a leading coefficient of 1, roots -2 and 7 with multiplicity 1, and root 5 with multiplicity 2?
Answer:
(D)
Step-by-step explanation:
If it has a leading coefficient of 1, then it can not (A) or (B) because they have a two in front of it. Next, we can check the roots -2 and 7. -2 goes with (x+2), while 7 goes with (x-7). Therefore, you can already see that the answer is (D). To make sure. let us check the root 5 with multiplicity of 2. 5 goes with (x-5), implying that there must be 2 (x-5)'s. Only (D) satifies that as well, so the answer must be (D).
Answer:
D on edge
Step-by-step explanation:
Despite a wide variety of workplaces for those working in Human Services, all workplaces include
comfortable areas for interactions amongst people.
a variety of medical testing equipment.
desks where clients can sit across from the worker.
toys and exercise equipment for children.
Answer:
a variety of medical testing equipment.
Step-by-step explanation:
Answer:
c hope this helps if wrong please tell me
Step-by-step explanation:
Solve and graph the inequality.
7n - 1 > 76
Answer:
n>11
Step-by-step explanation:
I don't know how to graph this answer, sorry!
The solution of the inequality 7n - 1 > 76 gives n < 11 along with the graph.
Given Inequality:
7n - 1 > 76
To solve the inequality add 1 on both side of inequality as
7n - 1 + 1 > 76 + 1
7n > 77
Now, divide the inequality by 7 as
7n/ 7 > 77/ 7
n > 11.
Therefore, the solution is n > 11.
Learn more about Inequality here:
https://brainly.com/question/28823603
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