Answers
Answer:
[tex]\frac{3}{16} x^{3}-\frac{9}{4}x+6 = y[/tex]
Step-by-step explanation:
Lets start with the easiest part of this question - simply plugging in to get easier equations:
[tex]-8a+4b-2c+d=9\\[/tex]
[tex]8a+4b+2c+d=3[/tex]
Something that now immedietly pops out is that many of the terms would cancel if we added them together. We get the following results by adding the two equations together:
[tex]8b+2d = 12[/tex]
Now lets look at the other bit of inromation the question gives you -- that the two points are horizontal tangents. Taking the derivative of the standard form of a cubic, we get:
[tex]y' = 3ax^2+2bx+c[/tex]
Since the points are both horizontal tangents, y' will be equal to 0 at the points. Thus, plugging in we get:
[tex]y'(-2) = 0 = 12a-4b+c[/tex]
[tex]y'(2) = 0 = 12a+4b+c[/tex]
We again see a simple subtracting opportunity that will cancel out two terms:
[tex]-8b = 0[/tex]
[tex]b = 0[/tex]
Now going back to the equation we got by adding the two equations that we got from simply plugging our points in:
[tex]d = 6[/tex]
Now that we have b and d, we can now plug them back into our step one and derivative equations in order to get a simple system:
[tex]-8a - 2c=3[/tex]
[tex]12a+c=0[/tex]
Solving for a and c, we get:
[tex]a = \frac{3}{16}[/tex]
[tex]c = \frac{-9}{4}[/tex]
Thus, finally, our answer is:
[tex]\frac{3}{16} x^{3}-\frac{9}{4}x+6 = y[/tex]
Attached is desmos, which you can use to check.
Related Questions
please help!
find the value of x in the isosceles triangle shown below.
4
6
Answers
Answer:
B
Step-by-step explanation:
Pythagorean theorem:
6^2 + (4/2)^2 = x^2
36 + 4 = x^2
40 = x^2
x = [tex]\sqrt{40}[/tex]= [tex]2\sqrt{10}[/tex]
Answer is B
Write a real life scenarlo that can be represented by the integer -55
Answers
Answer:
I deposit $500 in my bank from my check this week. I have to withdraw $550 from my bank to pay my medical bills. I am short -55/55 dollars so I wait to pay my medical bills.
I owe $60 to my school for damage on a school laptop. I only have $5 so I am 55 dollars short.
I withdraw $2,000 from my bank to deposit $1950 a week later. I want to deposit the same amount of money I put last week. I am short 55 dollars.
Step-by-step explanation:
I put different scenarios because I didn't know if any of them were good enough.
pls help me with this ! thank you :)
Answers
Answer:
2 is the correct answer
hope this will help you
What is
5
6
−
3
8
?
A.
1
3
B.
9
16
C.
1
12
D.
11
24
Answers
5/6 - 3/8
Rewrite the fractions to have a common denominator:
5/6 x 4 = 20/24
3/8 x 3 = 9/24
Now you have 20/24 - 9/24 = 11/24
The answer is D. 11/24
Answer:
D. 11/24
Step by Step Explanation:
Just use cymath.
Please solve quickly 11-14
Answers
Answer:
Step-by-step explanation:
11). 6x + 3y = 9
3(2x + y) = 9
2x + y = 3
y = -2x + 3
Since variables are of single degree therefore, it's a linear function
12). 3y - 2x = -2x - 12
3y - 2x + 2x = -2x - 12 + 2x
3y = -12
y = -4
Since variable y is of single degree therefore its a linear function.
13). 11y + 4x = -8 + 11y
11y + 4x - 11y = -8 + 11y - 11y
4x = -8
x = -2
Linear function.
14). 4x - 3 + 2y = 8x - 9
4x + 2y - 3 - 4x = 8x - 4x - 9
2y - 3 = 4x - 9
2y = 4x - 9 + 3
2y = 4x - 6
y = 2x - 3
Linear function.
16. A cellphone family plan costs $49 per month plus $.05 per text. Write an equation for the monthly bill b when t texts are sent.
Answers
Is the equation
4. What is the positive solution to the equation 0 =
0=1/3x^2-3
Answers
Answer:
the answer is 9.34 x
Step-by-step explanation:
you do what you have to do it and you will get the answer then my answer was 9.34 great
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(8x-9)°
63°
70°
Answers
Answer:
x= 7
Step-by-step explanation:
Theorem: The sum of the angles of a triangle is 180
Memorize that theorem
8x - 9 + 63 + 70 = 180
8x + 124 = 180
8x = 56
x= 7
46−[38−{27−(15−13−2¯¯¯¯¯¯¯¯¯¯¯¯¯)}]
=
Answers
Answer:
46-38-27-15+13+2
=-17
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Answers
Answer:
Answer is C. 3s + 9
Step-by-step explanation:
The perimeter is the sum of all 3 sides in a triangle
which is s+3 + s+3 + s+3
= 3s + 9
2x+2y=4 and -3x-2y=-7
Answers
Answer: You didnt tell me how to solve it, but I used subsitution. For ubsitution the answer is, (3,-1)
Step-by-step explanation:
Jetpack flyer recently landed in LA (230, 20). He found out his target is in San Francisco (40, 220). His jetpack can go 250 miles without refueling. How far will he have to walk when his jetpack runs out (Rounded to the nearest mile)?
He would have to walk approximately _____ miles when his jetpack runs out (Rounded to the nearest mile). Enter as a number only (units are already in the question).
Answers
Answer:
He has to walk 25.86 miles when his jetpack runs out
Step-by-step explanation:
Distance between LA (230,20) and San Francisco (40,220) is
[tex]\sqrt{(230-40)^2 + (20-220)^2}\\275.86[/tex]miles
He travelled distance of 250 miles without refueling.
He has to walk 25.86 miles when his jetpack runs out
WILL MARK BRAINLIEST TO THE FIRST PERSON!!!!!
Answers
Answer:
3.9
Step-by-step explanation:
3.98371685
Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)6
Answers
Answer: DECAY
Step-by-step explanation:
(.85) is less than 1
math question again plz help
answers are:
6, 8, 5, 11
Answers
If the perimeter is 3(2v-6)
Than
Pull out like factors : 2v - 6 = 2 • (v - 3)
Final result : 6 • (v - 3)
Given the result your answer would be 6.
In Greenville, the library is 8 miles due east of the post office and the zoo is 6 miles due south of the library. What is the distance from the post office to the zoo?
Answers
Answer:
10 miles
Step-by-step explanation:
Simplify.
(-w^2 + 4w - 7)+(2w+3w+6)
Answers
Answer:
-w2 + 9w - 1
..............
what should be added to
11/21 to make it
19/21
Answers
To find what needs to be added subtract the two numbers:
19/21 - 11/21 = 8/21
You need to add 8/21 to 11/21 to get 19/21
2. Use the equation 3x + 4y = 2.
a) Write another equation that will create a linear system
with each number of solutions.
i)
ii) one
üü) infinitely many
none
Verify your answers for part o)
b)
Answers
Answer:
x= −4 /3 y+ 2/ 3
Step-by-step explanation:
The speed of the current in a river 6 mph. A very operator who works top part of the river is looking to buy a new boat for his business. Every day, his route takes him 22.5 miles each way against the current back back to the dock, and he needs to make his trip any tour of nine hours. He has a bow in mind, but he can only test it on a leak where there is no current. How fast must the boat go on the lake in order for it to serve the ferry operators needs?
Answers
Answer:
9 mph
Step-by-step explanation:
Speed of current = 6 mph
Distance to travel one way = 22.5 miles
Let speed of the ferry be [tex]x[/tex] mph
Total time taken for round trip is 9 hours
One way the ferry will be going with the current and in the other way the ferry will be going against the current so
[tex]\dfrac{22.5}{x+6}+\dfrac{22.5}{x-6}=9\\\Rightarrow \dfrac{x-6+x+6}{x^2-36}=\dfrac{9}{22.5}\\\Rightarrow \dfrac{2x}{x^2-36}=0.4\\\Rightarrow \dfrac{2x}{x^2-36}-0.4=0\\\Rightarrow 2x-0.4x^2+14.4=0\\\Rightarrow 0.4x^2-2x-14.4=0\\\Rightarrow 4x^2-20x-144=0\\\Rightarrow x=\dfrac{-\left(-20\right)\pm \sqrt{\left(-20\right)^2-4\times 4\left(-144\right)}}{2\times 4}\\\Rightarrow x=9,-4[/tex]
So, the speed of the boat in still water needs to be 9 mph both ways.
The first terms in the sequence are 1,4, 9, 16 ... what’s the next term in the pattern?
Answers
Answer:
25, 36, 49
Step-by-step explanation:
4 - 1 = 3
9 - 4 = 5
16 - 9 = 7
25 - 16 = 9
36 - 25 = 11
49 - 36 = 13
It goes up by odd numbers
Mr. Walker is looking at the fundraiser totals for the last five years.
A 2-column table with 5 rows. The first column is labeled year with entries 1, 2, 3, 4, 5. The second column is labeled total (in dollars) with entries 896, 925, 880, 963, 914.
How does the mean of the totals compare to the median?
Answers
Answer:
Correct answer is B on EDGE
Step-by-step explanation:
Answer:
ba ba ba B is the answer go go ga ga
Step-by-step explanation:
Can someone please help me k(x) = 4x2 + 1; k(-3)
Answers
Answer:
37
Step-by-step explanation:
k(x) = 4x2 + 1
[tex] = 4( - 3) {}^{2} + 1 \\ 4(9) + 1 \\ 36 + 1 \\ 37[/tex]
Solve for x. (Round to the nearest tenth)
Answers
Answer:
13.7
Step-by-step explanation:
fill the numbers in using pythagorean theory
[tex]a^{2} + b^{2} = c^{2}[/tex]
(the hypotenuse has to be [tex]c^{2}[/tex])
[tex]9.2^{2} + b^{2} = 16.5^{2}[/tex]
[tex]84.64 + b^{2} = 272.25[/tex]
[tex]b^{2} = 187.61[/tex]
(to get [tex]b[/tex] alone you have to find the square root of both sides)
[tex]b = 13.69707[/tex]
round that and you get
[tex]b = 13.7[/tex]!
calculate the amount of money invested at 8.5% per annum when 2,488.80 simple interest was collected after three years. anyone help please
Answers
Answer:
2488.80 divided by 3=838.1
Someone help me please!!!Fully simplify.
Answers
how much is f5+7 if f is 109
Answers
Answer: 552
Step-by-step explanation:
Answer:
the answer is 552
Step-by-step explanation:
5 x 109 + 7 = 552
I need help 911!!! I need thisss
Answers
Slope is (the change in y) / (the change in x).
The formula for slope is:
m = (y2 - y1)/(x2 - x1), with (x1, y1) being one point and (x2, y2) being the second. What you need to do is order the slopes from smallest to largest because slope means the same thing as rate of change.
#17. First, you need to find the slope of function A. To do this, I’m choosing two different points I see on the graph: (1,1) and (2,1). I now plug these into the slope formula:
m = (1-1)/(2-1) = 0/1 = 0.
The slope for function A = 0
To find the slope for function B, you can choose any two points. I’m going to use (3,0) and (6,1)
m = (1-0)/(6-3) = 1/3
The slope for function B is 1/3
For function C, you are already given the slope. That equation is in something called slope-intercept form (y=mx+b), where the x is being multiplied by the slope.
The slope on function C = 1/4
So,, A has the smallest slope, C has the second smallest slope, and B has the largest slope.
#18. The two points in using to find the slope for function A are (0,-3) and (1,0).
m = (0+3)/(1-0) = 3/1 =3
The slope for function A is 3
The two points I’m using for function B are (-2, 10) and (0, 20)
m = (20-10)/(0+2) = 10/2 = 5
The slope for function B is 5
The slope for function C is 1. When the slope is 1, it is not written because any number (other than 0) times 1 equals 1.
Function C has the smallest slope, function B has the second smallest slope, and function C had the largest slope.
It would probably be better for you to try 19 and 20 on your own, and let me or anyone else on Brainly know if you have any questions or something doesn’t make sense.
I hope this has helped!
i have travelled 12 metres on hill during this journey i have risen in height bye 3 metres what is the gradient of this
Answers
Answer:
Step-by-step explanation:
sinθ = 3/12 = 0.25
θ = arcsin(0.25) ≈ 14.5°
If person travelled 12 metres on hill and have risen in height by 3 metres then the gradient of this problem is 14.5°.
What is gradient?Gradient is the degree of inclination or the rate of ascent or descent.It is an inclined surface, grade, ramp.
How to find gradient?The hill and the road through which person travelled forms a right angled triangle. In a right angled triangle sin a is equal to Perpendicular/Hypotenuse where a is angle opposite to perpendicular.
In this we have to apply the above rule:
sin a=3/12
sin a=1/4
sin a=0.25
a= [tex]sin^{-1}[/tex]0.25
a=14.5
Hence the gradient of the problem is 14.5°.
Learn more about gradient at https://brainly.com/question/23016580
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What’s 3% of 4000 and how u find it
Answers
Answer:
First write it as 0.03 × $4,000. Then multiply 3 × $4,000 = $12,000. Lastly put the decimal point where it gives the answer two decimal digits: $120.00.
Step-by-step explanation:
Answer:
3% of 4,000 = 120.
Step-by-step explanation:
To find the answer we have to divide 3 by 100, which equals 0.03. Now multiply 0.03 by 4,000 and we get 120. Therefore, 120 is our answer.