Its 1
Doubled:-
[tex]\\ \rm\longmapsto 1\times 1=1=1^3[/tex]
Tripled[tex]\\ \rm\longmapsto 1\times 1\times 1=1=1^2[/tex]
lim x-> 0^+ (1+sin7x)^8/x
If you mean
[tex]\displaystyle \lim_{x\to0^+} \frac{(1+\sin(7x))^8}x[/tex]
then the limit doesn't exist, since 1 + sin(7x) approaches 1 while the denominator approaches 0.
However, if instead you mean
[tex]\displaystyle \lim_{x\to0^+}(1+\sin(7x))^{8/x}[/tex]
rewrite the limand as
[tex](1+\sin(7x))^{8/x} = \exp\left(\ln(1+\sin(7x))^{8/x}\right) \\\\ = \exp\left(\dfrac{8\ln(1+\sin(7x))}x\right) \\\\ =\exp\left(\dfrac{\ln(1+\sin(7x))}x\right)^8[/tex]
The exponential function is continuous at 0, so we can pass the limit through it:
[tex]\displaystyle\lim_{x\to0^+}\exp\left(\dfrac{\ln(1+\sin(7x))}x\right)^8 = \exp\left(\lim_{x\to0^+}\dfrac{\ln(1+\sin(7x))}x\right)^8[/tex]
The remaining limit takes the indeterminate form 0/0, since ln(1 + sin(7x)) approaches ln(1) = 0, and so does x in the denominator. Apply L'Hopital's rule:
[tex]\displaystyle\exp\left(\lim_{x\to0^+}\dfrac{7\cos(7x)}{1+\sin(7x)}\right)^8 = \exp\left(7\right)^8 = \left(e^7\right)^8 = \boxed{e^{56}}[/tex]
What is the coordinate of point A?
There are 4 spaces between 34 and 35. This means each line is 1/4
A is located at 34.25
34.25 is the correct answer
what is the y intercept of the quadratic function f(x)=x^2+x-6
Answer:
[tex](0,\, -6)[/tex].
Step-by-step explanation:
On a cartesian plane, the [tex]y[/tex]-intercept of a function is the point where the graph of that function intersects with the [tex]y\![/tex]-axis.
The [tex]y[/tex]-axis of a cartesian plane is the same as the equation [tex]x = 0[/tex] (that is, the collection of all points with an [tex]x[/tex]-coordinate of [tex]0[/tex].)
Construct a system of two equations, with one equation representing [tex]y[/tex]-axis and [tex]y = f(x)[/tex] to represent the graph of this function:
[tex]\begin{aligned}\begin{cases} y = x^{2} + x - 6 & \text{for the quadratic function} \\ x = 0 & \text{for the $y$-axis}\end{cases}\end{aligned}[/tex].
Solve this system for [tex]x[/tex] and for [tex]y[/tex]. If a solution exists, then the [tex]y\![/tex]-axis and the graph of [tex]y = f(x)[/tex] would indeed intersect. The point [tex](x,\, y)[/tex] would be the intersection of the [tex]y\!\![/tex]-axis and the graph of [tex]y = f(x)\![/tex].
Substitute the second equation of the system into the first.
[tex]\begin{aligned}\begin{cases} x = 0 \\ y = -6\end{cases}\end{aligned}[/tex].
Hence, the intersection of the [tex]y[/tex]-axis and the graph of [tex]y = f(x)[/tex] would be [tex](0,\, -6)[/tex]. By definition, this point would be the [tex]y\![/tex]-intercept of [tex]y = f(x)\![/tex].
Answer: (0, -6)
Step-by-step explanation:
got it right on my test
HELPPPP FAST PLEASEEEE
Answer:
135, 9, 15
Step-by-step explanation:
Beads per necklace=(Total beads used)/(Total number of necklace made) = 135/9 = 15
Based on mathemAtical models, the chance of rain today is 60%. Is that theoretical or experimental.
IM GIVING BRAINLIEST!! suppose F is a 10-newton vector direction 60 degrees north of east and g is a 12-newton vector directed 45 degrees north of east. find the magnitude and direction of the resultant vector r = f + g. round the answer to the nearest tenth
Answer: The magnificent of east and g is a round out of the fraction that is in direct to 32 degrees and the other direction of the resultant 10 = 12 + F
45 = 60 + F.
K4.m, if k = 3 and m = 5/6
Replace k with 3 and m with 5/6
3^4 x 5/6
Simplify 3^4 which is 3 x 3 x 3 x 3= 81
Now you have :
81 x 5/6 = 67 and 1/2 ( 67.5 as a decimal)
What is the correct formula for finding the 6th power of a complex number in polar form?
Answer:
Step-by-step explanation:
Let [tex]z=r\cos \theta + i\sin \theta[/tex]
then by the Moivre
[tex]z^6 = r^6 \left( \cos \theta +i\sin \theta)^6= r^6\left(\cos (6\theta) + i\sin(6\theta)\right)[/tex]
bag I contain 3 red and 4 black balls while another bag II contains 5 red and 6 black balls. One ball is drawn at random from one bags and it is to be red. Find the probability that it was drawn from bag II g
Answer:
Step-by-step explanation:
selecting Bag |1/2
p(red from bag ||)=1/2×5/11=5/22
What does this symbol mean ~=
Answer:
It means that it is approximately equal to or about/around.
What’s 2,312 divided by 8 =
Answer:
289
Step-by-step explanation:
bro u could have used the calculator
Answer:
2312/8 =289 is the answer
Two major league players got a total of 226 hits. Washington had 18 more hits than Sanchez. Find the number of hits for each player.
Answer:
Washington had 115 hits and Sanchez had 111 hits.
Step-by-step explanation:
2s + 4 = 226
2s = 222
s = 111
s + 4 = 115
The table shows the times for the 100-meter dash. What is the
difference between the men'stime and the women's time?
Write your answer in both decimal and fraction form.
Times for 100-meter Dash
Men's winner
9.58
2009
Women's winner
10.49
1988
Answer:
0.91 (make sure to include unit of measurement)
Step-by-step explanation:
10.49 - 9.58 = 0.91
What is the slope of the line represented by the equation f(x) = -3x + 7?
Answer:
m=-3
Step-by-step explanation:
If Efx =1050 and mean x =15 find the value of N
Answer:
your answer is 70.
Step-by-step explanation:
mean=Efx/n=1050/15=70
What is the probability of getting tails on two coins only
Answer:
This states that the probability of the occurrence of two mutually exclusive events is the sum of their individual probabilities. As you can see from the picture, the probability of getting one head and one tail on the toss of two coins is 0.5.
Step-by-step explanation:
may this answer is helpful for you
which statement best describes f(x)=-2√x-7+1
it is under mapping and function
f of x is equal to -2 root x-7 plus one
Power Function:
Exercise: Recognize and analyze the graph of the power function as the exponent "n" and the coefficient "a" vary
1. Consider a positive exponent power function
A) Describe the graph of the function when n is even, for this you must attach an image of the graph of the function that meets these conditions.
B) Describe the graph of the function when n is odd, for this you must attach an image of the graph of the function that meets these conditions.
C) Describe what happened when the coefficient a is positive and also when it is negative. Is there any change in the graph?
D) Describe what happened when the coefficient a increases or decreases. What happens to the graph of the function?
2. Consider a negative exponent power function
A) Describe the graph of the function when n is even, for this you must attach an image of the graph of the function that meets these conditions.
B) Describe the graph of the function when n is odd, for this you must attach an image of the graph of the function that meets these conditions.
C) Describe what happened when the coefficient a is positive and also when it is negative. Is there any change in the graph?
D) Describe what happened when the coefficient a increases or decreases. What happens to the graph of the function?
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).
============================================================
Once again, the screenshots are shown below as examples.
The following table gives a partial set of values of a polynomial function.
x | -2 | -1 | 0 | 1 | 2 | 3
g(x) |-14| -2 | 0 |-4| -6| 2
Between which two values would a relative minimum most likely occur?
-2 and 0
-1 and 1
0 and 2
1 and 3
(-2 and 0 is incorrect btw)
Using the concepts of relative minimum and relative maximum, it is found that a relative minimum is most likely to occur between 1 and 3.
--------------------------------------------
A relative minimum occurs when the function is decreasing, then it starts to increase.A relative maximum occurs when the function is increasing, then it starts to decrease.--------------------------------------------
Over the interval -2 and 0, the function is increasing the whole time, which means that a relative minimum is not likely to occur.Over the interval -1 and 1, the function is increasing, then it starts to decrease, which means that a relative maximum is likely to occur.Over the interval 0 and 2, the function is decreasing the whole time, which means that a relative minimum is not likely to occur.Over the interval 1 and 3, the function is decreasing, then it starts to increase, which means that a relative minimum is likely to occur. This is the correct option.A similar problem is given at https://brainly.com/question/9839310
Answer:
x | -2 | -1 | 0 | 1 | 2 | 3
g(x) |-14| -2 | 0 |-4| -6| 2
Between which two values would a relative minimum most likely occur?
-2 and 0
-1 and 1
0 and 2
1 and 3
the correct answer is 1 and 3
Help plz due in 20 min
Answer:
its either the 3rd one or the 5th one
sorry hope this helps a little bit
Step-by-step explanation:
Answer:
49½+5½
Step-by-step explanation:
Because here, we have 7√5, which we can place the two numbers in index form, 7 is equal to√49 which is 49½ and √5 is equal to 5½. So the answer is 49½•5½
Months Days. Hours
12 7 19
Step-by-step explanation:
12 months
7 days
19 hours
PLEASE HELP!!! MATH IS HORRIBLE! URGENT!!
What is the algebraic expression for the word phrase "the quotient of 24 and 6 less than m"?
A. m-6/24
B. 24/m-6
C. 6-m/24
D. 24/6-m
Answer:
A. m-6/24
Step-by-step explanation:
This is the required expression because,
1. Quotient of 24 and 6 less than m.
2. It means quotient of 24 and 6 subtracted from m.
3. Representing it mathematically, m-6/24.
The mathematical expression for "the quotient of 24 and 6 less than m" is m - 6/24 option (A) is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
The expression in the word is: "the quotient of 24 and 6 less than m"
Here m is the number.
The quotient of 24 and 6 is 6/24
Linear expression can be defined as the relation between two variables, if we plot the graph of the linear expression we will get a straight line.
If in the linear expression, one variable is present, then the expression is known as the linear expression in one variable.
The quotient of 24 and 6 is less than m which means 6/24 should be subtracted from m.
= m - 6/24
Thus, the mathematical expression for "the quotient of 24 and 6 less than m" is m - 6/24 option (A) is correct.
Learn more about the expression here:
brainly.com/question/14083225
#SPJ2
Select the conic section that represents the equation.
x² + y²=8
circle
ellipse
parabola
hyperbola
Answer:
hyperbola!!!
Step-by-step explanation:
Another name for plane 2
Answer: https://www.lmtsd.org/cms/lib/PA01000427/Centricity/Domain/187/1.1%20Answer%20Key.pdf
Step-by-step explanation:
that sould work
What is ³√64? Please help!
The answer you are looking for is 4.
To prove your answer, just test it.
Solution/Explanation:
³√64=4.
Does 4³=64?
Yes, it does. So, what does this mean?
It means that the answer is correct.
So, therefore, the final answer is 4.
I hope this helped you find the answer to your question.
So, the answer that you are looking for is 4.
YA'LL ARE SMART!! PLEASE HELP!!
Answer:
Its C
Step-by-step explanation:
Substitute in 3 for x and check. The equation doesn't work.
Substitute 2 in for y. The equation still doesn't work.
So its right.
lol are u using edguenity
rip
4) Write a mathematical statement for:
8 less than 3 times a number.
Plz hurry 5 mind
Answer:
It is 8 < 3n
Step-by-step explanation:
8 < { 3 times a number }
let this number be x :
[tex]» \: 8 < \{3 \times n \} \\ » \: 8 < 3n[/tex]
Gasoline is 3.129 when you stop to fill up your tank this week.
You purchase 15 gallons of fuel.
How much will you have to pay for the fuel?
Answer:
46.935, $46.94
WILL GIVE BRAINLYEST IF YOU HELP ME WITH THIS PLZZ
Answer:
x=7
EF = 5
DF = 16
Step-by-step explanation:
DF = DE + EF
3x-5 = 11 + 2x-9
Combine like terms
3x-5 = 2x+2
Subtract 2x from each side
3x-5 -2x = 2x+2-2x
x-5 = 2
Add 5 to each side
x-5+5 = 2+5
x=7
EF = 2x-7 =2*7-9 = 14-9 = 5
DF = 11 +5 =16
Answer:
x=7
Step-by-step explanation:
11+(2x-9) = 3x-5
2+2x=3x-5
7=x
4743 in ^2 = ___ ft^2
9514 1404 393
Answer:
32 15/16 ft^2
Step-by-step explanation:
There are 144 square inches in a square foot, so the number of square feet is ...
(4743 in²) × (1 ft²)/(144 in²) = (4743/144) ft² = 32 15/16 ft² = 32.9375 ft²