Problem 1
Part A
If n is even, then we have a "parabolic" shape going on. I put that in quotes because if n = 2, then we have a true parabola; however, if n is even and larger than 2, then we have a curve that looks like a parabola, but it's not exactly a perfect parabola. All of these curves have in common that the end behavior is the same for the left and right sides.
Consider the example where a = 1 and n = 2. This means
y = a*x^n
turns into
y = 1*x^2
which is the same as
y = x^2
This produces the parent parabola curve. This curve opens upward.
I recommend using Desmos to graph y = a*x^n, where the 'a' and n are parameters set up. Check out the screenshot below.
---------------------
Part B
If n is odd, then we'll get something that looks like a cubic curve. If n = 3, then we get a cubic curve. If n is odd and n > 3, then we get something that looks like a cubic curve, but it's not exactly this perfect cubic.
If we let a = 2 and n = 3, then y = a*x^n becomes y = 2x^3. The graph of which is below.
---------------------
Part C
If a > 0 then the curve is like the previous examples shown earlier.
If a < 0, then we will reflect those given earlier curves over the horizontal x axis. An example is shown below using y = -x^2. This time we have a = -1 and n = 2. In other words, I reflected the example in part A over the x axis.
---------------------
Part D
As 'a' increases, then the graph gets more narrow. It also gets vertically stretched. Consider the example of going from y = 1x^2 to y = 3x^2 as shown below.
As 'a' decreases, then the process is done in reverse: the curve gets more flatter and wider horizontally. We consider the curve to be vertically compressed or squished. So we'd go from y = 3x^2 to y = 1x^2 as an example.
============================================================
Problem 2
Part A
For all of problem 2, we'll only consider negative values of n. We want n to be even, so let's say n = -2. Furthermore, let's say a = 2.
This means y = ax^n becomes y = 2x^(-2) which is the same as y = 2/(x^2)
The curve we get is really two separate pieces. There's a gap or disconnect at x = 0 because of a division by zero error. One piece of the curve is always increasing, while the other piece is always decreasing.
---------------------
Part B
Since we want n to be odd and negative, let's say n = -1. We'll keep a = 2 the same as before.
That means y = ax^n becomes y = 2x^(-1) as shown in the diagram below. What we have is a hyperbola. This is a disconnected set of two curves that collectively entirely define this function in a visual sense. Note the gap when x = 0 due to the division by zero error.
Recall that y = 2x^(-1) is the same as y = 2/x
Again, I'm using Desmos to generate each of these graphs.
Similar to part A, the two pieces are disconnected. This curve is known as hyperbola. It's always increasing if a < 0, and it's always decreasing when a > 0.
---------------------
Part C
If 'a' is positive, then the graph of y = 2/(x^2) is entirely above the x axis (aka everything is positive). On the flip side, if 'a' is negative, then everything swaps to being negative. That will reflect the curve over the x axis to get what you see in the example below. We have a = -2 and n = 2.
---------------------
Part D
As 'a' increases, this means the graph spreads out. If 'a' decreases, then it gets more compressed.
An example is shown below going from y = 1/x to y = 3/x which shows expansion going on (reverse it to get a compression).
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Once again, the screenshots are shown below as examples.
Help thank you………………
Answer:
it is too easy I will answer it soon.
11. The sales tax rate for the state of Washington was 8.4%. What is the final cost of a $5,700 car in Washington,
including tax?
$
Answer:
$5853.60
Step-by-step explanation:
8.4% of $5400 = $453.60
$453.60 + $5400 = $5853.60
Area of the Shaded Region rectangle within reactanlge
Find the area of the shaded region with the following measurements:
Answer:
132
Step-by-step explanation:
First you need to find the area of both regions (shaded and not shaded)
To find the shaded regions area multiply length by width
20 x 8 = 160
Then find the area of the unshaded region
7 x 4 = 28
Finally subtract the unshaded region from the shaded region
160 - 28 = 132
find out the things that can be purchased between rupees 500 to rupees 100 for your house ?
We can buy small vases,Flower pots for our houses.
[tex]\sf\orange{Hope \: it \: helps \: please \: mark \: me \: as \: brainliest!}[/tex]
7 + (-24) / 8 + 4 (-2) =
Answer: 0
Step-by-step explanation:
7+(-24)/8+4(-2 )= 7-24/8+4(-2) = -17/8-8 = -17/0 = 0
ILL GIVE BRAINLIEST
evaluate the expression. 2•7(3^2)/3
Answer:
[tex] \frac{7 \times {3}^{2} }{3} \\ \frac{7 \times 3 \times 3}{3} \\ = 7 \times 3 = 21 \\ thank \: you[/tex]
Write an equivalent expression in standard form for
(5x + 4)(7x+ -12x + 27).
Answer: -25x² + 115x + 108
Concept:
When encountering questions that ask for simplifying polynomial expressions, using the method FOIL would be easier:
First, which means multiplying the first terms together;Outer, which means that we multiply the outermost terms when the binomials are placed side by side;Inner, which means multiply the innermost terms together;Last, which means multiplying the last term in each binomial together;Solve:
Given
(5x + 4) (7x + (-12x) + 27)
Combine like terms in the parentheses
=(5x + 4) (7x - 12x + 27)
=(5x + 4) (-5x + 27)
Expand parentheses and apply the FOIL method
=-25x² + 135x - 20x + 108
Combine like terms
= [tex]\boxed {-25x^2+115x+108}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
[tex]\boxed {\boxed {\sf -25x^2+115x+108}}[/tex]
Step-by-step explanation:
We are asked to find an equivalent expression for (5x + 4)(7x+ -12x + 27). Note that we are multiplying 2 polynomials.
[tex](5x + 4)(7x+ -12x + 27)[/tex]
Notice that the second polynomial has like terms. There are 2 terms with an x (7x and -12x) and we can combine them.
[tex](5x + 4)[(7x+ -12x) + 27][/tex]
[tex](5x + 4)[(-5x) + 27][/tex]
[tex](5x+4)(-5x+27)[/tex]
Now we are multiplying 2 binomials. Therefore, we use the FOIL method. We multiply the First terms, the Outside terms, the Inside terms, and the Last terms.
First: 5x * -5x = -25x²Outside: 5x * 27 = 135x Inside: 4* -5x = -20x Last: 4 * 27=108[tex]-25x^2+135x-20x+108[/tex]
Notice there are 2 terms with an x ( 135x and -20x). They are like terms and can be combined.
[tex]-25x^2+(135x-20x)+108[/tex]
[tex]-25x^2+115x+108[/tex]
The equivalent expression in standard form is -25x²+115x+108
Which set of ordered pairs represents a function?
{(3,6), (3, 1), (9,0), (2, 2)}
{(2,-5), (-3, 6), (-1, -8), (-3,-4)}
{(4, -7), (-2, -1), (-7,4), (9, -1)}
{(3,8), (-2,-9), (1,4), (1,9)}
Answer:
{(4, -7), (-2, -1), (-7,4), (9, -1)}
Step-by-step explanation:
Every other set of ordered pairs has an x-value that has more than one y-value. This is against the rules of a function. Therefore, {(4, -7), (-2, -1), (-7,4), (9, -1)} represents a function.
pleaseeeeee solve this!
Answer:
C
Step-by-step explanation:
One graph line is equal to 10km and there is 2 graph lines between Red Bank and Belleville.
An elevator at a construction site has a maximum capacity of 3325 pounds. If the elevator operator weighs 225 pounds and each cement bag weighs 75 pounds, how many bags of cement can be safely lifted on the elevator in one trip?
The solution to 12x = 36 is x =___. (Only input whole number) Numerical Answers Expected! Answer for Blank 1:
Hi ;-)
12x = 36
x = 36 : 12
x = 3
Hey there! I'm happy to help!
We see that an unknown number x multiplied by 12 is equal to 36. How do we find this number? Well, you can simply go backwards and divide 36 by 12, and this will give us our answer.
36÷12=3
Another way you can think about this is dividing both sides of the equation by 12, which isolates our x.
12x=36
12x÷12=36÷12
x=3
Have a wonderful day and keep on learning! :D
A store advertises a sale on t-shirts. The advertised price is four t-shirts for $48. Write and solve an equation to find the cost of one t-shirt.
a.) $8
b.) $12
c.) $16
d.) $48
22b^9 divided by -2b^5
Answer:
-11 bytes4Step-by-step explanation:
please solve its due
Answer:
2118+3391+4785+6354= 16648
Step-by-step explanation:
Find the value of x
2,8,9,7,6x ; the mean is 6
Answer:
x=2/3
Step-by-step explanation:
The mean is just the average of all the terms. Therefore, you can set up an algebraic expression to solve for x.
[tex]\frac{2+8+9+7+6x}{5} =6[/tex]
[tex]2+8+9+7+6x=30\\26x+6x=30\\6x=4\\x=4/6=2/3\\x=2/3[/tex]
simplify given
[tex] \sin3 \alpha \div \sin \alpha + cos \alpha + cos3 \alpha \div cos \alpha - sin \alpha [/tex]
Step-by-step explanation:
Hey there!
Please see attached picture for your answer.
Hope it helps!
Can you help me please??
Answer:
either a or c sry
Step-by-step explanation:
abhivardhansinghrathore7979
Answer:
hlo
Step-by-step explanation:
which Id I s ths and if u needs we can play t or d join eew-vtej-rxt
Answer:
thanks for the point back
Step-by-step explanation:
thanks
There are □terms in the sequence 1, 3, 9, 27, 81, 243, .... 6561
Answer:
There are(2) terms in sequence1,3,9,27,81,243...6561
Step-by-step explanation:
1,3,9,27,81,243,729,2187,6561
There are 8 terms in the sequence 1, 3, 9, 27, 81, 243, .... 6561.
To determine the number of terms in the given sequence, we can observe that each term is obtained by multiplying the previous term by 3. Starting with the first term, which is 1, we can continue this pattern to find subsequent terms.
1 * 3 = 3
3 * 3 = 9
9 * 3 = 27
27 * 3 = 81
81 * 3 = 243
243 * 3 = 729
729 * 3 = 2187
2187 * 3 = 6561
As we can see, the sequence follows a pattern of multiplying each term by 3. In total, we have gone through 8 terms to reach 6561.
To learn more about sequence click on,
https://brainly.com/question/29153938
#SPJ2
(x3)(x-5)
Fududeey
X=2
Answer:
-18 is the right answer..
Benchmark of 6/10, how do I get this worked out
Answer:
0.60 or 60% is the answer!
Step-by-step explanation:
Hope I helped
100 10 times as much as ___ of
Answer:
1 thousand
Step-by-step explanation:
1 ten = 10 x 1 one (Read, as “1 ten is 10 times as much as 1 one.”) 1 hundred = 10 x 1 ten (Say, “1 hundred is 10 times as much as 1 ten.”) 1 thousand = 10 x 1 hundred (Say, “1 thousand is 10 times as much as 1 hundred.”)i hope im right
compute the absolute value and the conjugate of z = (1 + i) ^ 6
Answer:
z = (1 + i)6 =³√2(cos π4+ isinπ4)´6= 8 µcos3π2+ isin3π2)¶= −8i. Hence |z| = 8 and ¯z = 8i. z = (1 + i)
I think I am not real sure
In polar form, we have
[tex]1+i = \sqrt2 e^{i\pi/4}[/tex]
Then by DeMoivre's theorem,
[tex](1+i)^6 = \left(\sqrt2\right)^6 e^{i\,6\pi/4} = 2^3 e^{i\,3\pi/2} = -8i[/tex]
Then
[tex]|z| = |-8i| = \boxed{8}[/tex]
and
[tex]\bar z = \overline{-8i} = \boxed{8i}[/tex]
Which expression is equivalent to 8(6g)?
Answer:
8(6g) = 48g
I hope I helped you^_^
discoverings of marie curie
Answer:
Marie won the 1911 Nobel Prize in Chemistry for her discovery of the elements polonium and radium, using techniques she invented for isolating radioactive isotopes. Under her direction, the world's first studies were conducted into the treatment of neoplasms by the use of radioactive isotopes.
Basically, she discovered new elements and one of them is radiation which is used world-wide for cancer and other things
Step-by-step explanation:
what's
the answer?????
9514 1404 393
Explanation:
Apparently, you're to show this is an identity.
[tex]\dfrac{\tan^2A}{\tan A-1}+\dfrac{\cot A}{1-\tan A}=1+\sec A\csc A\\\\\dfrac{\tan^2 A-\dfrac{1}{\tan A}}{\tan A-1}=\\\\\dfrac{\tan^3 A-1}{(\tan A)(\tan A-1)}=\\\\\\\dfrac{\tan^2 A+\tan A+1}{\tan A}=\\\\1+\dfrac{\sec^2 A}{\tan A}=\\\\1+\dfrac{1}{\cos A}\cdot\dfrac{1}{\sin A}=1+\sec A\csc A[/tex]
find the length of BE BC=3x+47 DE=10 BD=x+27 CE=x+26
Answer:
B____C____D_____E
BC+ CE = BD + DE
(3x+47) + (x+26) = ( x+27) + (10)
4x + 73 = x + 37
4x – x = 37 – 73
3x = ‐ 36
x = – 36/ 3 —> x = – 12
BC = 3x + 47 = 3(-12) + 47 = - 36 + 47 = 11
BD = x+ 27 = –12+27 = 15
CE = x + 26 = –12+26= 14
So; BE = BD+ DE = 15+ 10= 25Or ;BE= BC + CE = 11+ 14 = 25I hope I helped you^_^
Plz help ASAP need fast plz will mark Brainlyist
Answer:
The correct answer is the third one. CIRCUMFERENCE
What is the correct clases for this drugs
Compazine
heelp me please
Answer:
It is a addiction XD
Step-by-step explanation:
Bsgsgwgwggwgwfeffefecrcr
Convert this rational number
to its decimal form and round
to the nearest thousandth.
1/6
Answer: 0.166
Step-by-step explanation:
Converting to a decimal:
1/6 = 0.1666 (1 divided by 6 - long division)
Rounding:
0.1666 to the nearest thousandth = 0.166