9514 1404 393
Explanation:
1. End behavior is the behavior of the function when the value of the independent variable gets large (or otherwise approaches the end of the domain). There are generally four kinds of end behavior:
the function approaches a constant (horizontal asymptote)the function approaches a function (slant asymptote, for example)the function oscillates between two of the above end behaviorsthe function tends toward +∞ or -∞Of these, behavior 2 will ultimately look like one of the others.
For polynomials, the function will always approach ±∞ as the independent variable approaches ±∞. Whether the signs of the infinities agree or not depends on the even/odd degree of the polynomial, and the sign of its leading coefficient.
For exponential functions, the end behavior is a horizontal asymptote in one direction and a tending toward ±∞ in the other direction.
For trig functions sine and cosine, the end behavior is the same as the "middle" behavior: the function oscillates between two extreme values.
For rational functions (ratios of polynomials), the end behavior will depend on the difference in degree between numerator and denominator. If the degree of the denominator is greater than or equal to that of the numerator, the function will have a horizontal asymptote. If the degree of the numerator is greater, then the end behavior will asymptotically approach the quotient of the two functions—often a "slant asymptote".
__
2. A polynomial inequality written in the form f(x) ≥ 0, or f(x) > 0, will be solved by first identifying the real zeros of the function f(x), including the multiplicity of each. For positive values of x greater than the largest zero, the sign of the function will match the sign of the leading coefficient. The sign will change at each zero that has odd multiplicity, so one can work right to left to identify the sign of the function in each interval between odd-multiplicity zeros.
The value of the function will be zero at each even-multiplicity zero, but will not change sign there. Obviously, the zero at that point will not be included in the solution interval if the inequality is f(x) > 0, but will be if it is f(x) ≥ 0. Once the sign of the function is identified in each interval, the solution to the inequality becomes evident.
As a check on your work, you will notice that the sign of the function for x > max(zeros) will be the same as the sign of the function for x < min(zeros) if the function is of even degree; otherwise, the signs will be different.
The solution to a polynomial inequality is a set of intervals on the real number line. The solution to a polynomial equation is a set of points, which may be in the complex plane.
__
3. A composite function is a function of a function, or a function of a composite function. For example f(g(x)) is a composite function. The composition can be written using either of the equivalent forms ...
[tex](f\circ g)(x)\ \Leftrightarrow\ f(g(x))[/tex]
It can be easy to confuse an improperly written composition operator with a multiplication symbol, so the form f(g(x)) is preferred when the appropriate typography is not available.
When simplifying the form of a composition, the Order of Operations applies. That is, inner parenthetical expressions are evaluated (or simplified) first. As with any function, the argument of the function is substituted wherever the independent variable appears.
For example, in computing the value f(g(2)), first the value of g(2) is determined, then that value is used as the argument of the function f. The same is true of other arguments, whether a single variable, or some complicated expression, or even another composition.
Note that the expression f(g(x)) is written as the composition shown above. The expression g(f(x)) would be written using the composition operator with g on the left of it, and f on the right of it:
[tex](g\circ f)(x)\ \Leftrightarrow\ g(f(x))[/tex]
That is, with respect to the argument of the composition, the functions in a composition expression are right-associative. For example, ...
for h(x)=2x+3, g(x)=x^2, f(x)=x-2 we can evaluate f(g(h(x)) as follows:
f(g(h(x)) = f(g(2x+3) = f((2x+3)^2) = (2x+3)^2 -2
It should be obvious that g(h(f(x)) will have a different result.
g(h(f(x)) = g(h(x-2)) = g(2(x-2)+3) = (2(x-2)+3)^2
look at the image below plz correct answers Surface area of cones 15 points
Answer:
[tex]A\approx 282.7\ m^2[/tex]
Step-by-step explanation:
1. Approach
The easiest method to solve this problem is to use the Pythagorean theorem to find the height of the cone. Then one can substitute the values given and found on the cone into the formula to find the surface area in order to solve for the surface area of the given cone.
2. Height of the cone
Imagine drawing a line from the tip of the cone down to the center of the base. This line will form a right angle with the base, thus, a right triangle is formed between the line, the radius (the distance from the center to the circumference or outer edge on a circle) of the base, and the incline of the cone. The Pythagorean theorem is a formula that relates the sides of a right triangle. This formula is as follows:
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs or the sides adjacent to the right angle of the right triangle, and (c) is the hypotenuse or the side opposite the right angle of the right triangle. Substitute the given values into the formula and solve for the unknown, or rather the height of the cone:
[tex]a^2+b^2=c^2[/tex]
[tex]a^2+5^2=13^2[/tex]
Simplify,
[tex]a^2+5^2=13^2[/tex]
[tex]a^2+25=169[/tex]
Inverse operations,
[tex]a^2+25=169[/tex]
[tex]a^2=144[/tex]
[tex]a=12[/tex]
[tex]h=12[/tex]
3. Find the surface area of the cone.
The following formula can be used to find the surface area of a cone:
[tex]A=\pi r(r+\sqrt{h^2+r^2})[/tex]
Where ([tex]\pi[/tex]) represents the numerical value (3.1415...), (r) represents the radius of the base, and (h) represents the height of the cone. Substitute the given values into the formula and solve for the surface area:
[tex]A=\pi r(r+\sqrt{h^2+r^2})[/tex]
[tex]A=\pi 5(5+\sqrt{12^2+5^2})[/tex]
Simplify,
[tex]A=\pi 5(5+\sqrt{12^2+5^2})[/tex]
[tex]A=\pi 5(5+\sqrt{144+25})[/tex]
[tex]A=\pi 5(5+\sqrt{169})[/tex]
[tex]A=\pi 5(5+13)[/tex]
[tex]A=\pi 5(18)[/tex]
[tex]A=\pi 90[/tex]
[tex]A\approx 282.743[/tex]
this question confuses me so much helpppppp
Answer:
-11°C or 1°C
Step-by-step explanation:
The question said that, by the noon, the temperature changes by 6°C, but it doesn't tell you if it changes for a hotter or colder temperature, so its possible the temperature at the noon to be:
-5 -6 = -11°C
or
-5 +6 = 1°C
To graph the possible temperatures, you have to draw a dot at the numbers -11 and 1
Write true or false.
(I) Two intersecting lines can also be parallel.
(ii) Unlimited number of lines can be drawn through a point.
(iii) through two distinct points we can draw only one straight line.
(i) False. If two lines are parallel, then they never intersect.
(ii) True. We can draw infinitely many different lines through a single point. We can think of rotating a line around a single point to form a circular fan of lines.
(iii) True. Any line is defined uniquely by two distinct points.
Jan needs 1/3 of chocolate chips to make cookies and 3/4 cup to make brownies. How many cups does she need altogether?
Answer:
She needs 1½ cups
Step-by-step explanation:
Number of cups she needs altogether = 1/3 + 3/4 =(4+9)/12 = 13/12 = 1½
pls help! I need the answer fast
Answer:
D
Step-by-step explanation:
area of a rectangle : length × width = 6×3 = 18
area of a circle : pi×r² = pi × (1.5)² = pi × (3/2)² = pi×9/4
the area of the shaded region is simply the area of the rectangle minus the area of the circle.
and so it is
18 - 9×pi/4
Which proportion could be used to determine if the figure ms represent a dilation
Step-by-step explanation:
Three-halves = 4 = 6
HOPE SO IT HELP'S YOU
What is the inverse of the equation y
31 – 2?
Answer:
The inverse is (x+2)/3
Step-by-step explanation:
y = 3x-2
To find the inverse, exchange x and y
x = 3y-2
Solve for y
Add 2 to each side
x+2 = 3y-2+2
x+2 = 3y
Divide by 3
(x+2)/3 = 3y/3
(x+2)/3 = y
The inverse is (x+2)/3
Write an explicit formula for the sequence.
-4,7,-10,13,-16
Step-by-step explanation:
Sequence is
4
,
7
,
10
,
13
,
16
,
.
.
.
a
1
=
4
,
a
2
=
7
,
a
3
=
10
,
.
.
.
If it is Arithmetic sequence,
a
2
−
a
1
=
a
3
−
a
2
=
a
4
−
a
3
& so on
In the given sum,
a
2
−
a
1
=
7
−
4
=
3
a
3
−
a
2
=
10
−
7
=
3
a
4
−
a
3
=
13
−
10
=
3
Since the difference between the successive terms is same and
hence
common difference
d
=
3
9) Given a circle with radius = 6 meters, a central angle of 77 degrees will intercept an arc of what length?
Please show all work
Hey there!
If our central angle is 77, our arc on the outside that it intercepts is going to be 77/360 of the total circumference of the arc. This is because a full circle angle is 360 degrees, so if our central angle was 360, we would just find the circumference of the circle as the arc would be the entire circle.
In our case, we will just find the circumference and then multiply it by 77/360 to find our arc length as we are just looking for a fraction of our total circle.
Circumference is 2πr, so we have 2π(6)≈37.68
Now we multiply this by 77/360.
37.68×77/360≈ 8.06
So now, if you have a radius r and a central angle x, you can use the formula x/360 ×2πr to find the arc length.
Have a wonderful day! :D
What is the value of m in the figure below? If necessary, round your answer to
the nearest tenth of a unit.
A. 18
B. 13.2
C. 12.5
D. 7
First
[tex]\\ \sf\longmapsto BD^2=AD\times DC[/tex]
[tex]\\ \sf\longmapsto BD^2=18^2+7^2[/tex]
[tex]\\ \sf\longmapsto BD^2=324+49[/tex]
[tex]\\ \sf\longmapsto BD^2=363[/tex]
[tex]\\ \sf\longmapsto BD=\sqrt{363}[/tex]
[tex]\\ \sf\longmapsto BD=19.2[/tex]
Now
Using Pythagorean theorem
[tex]\\ \sf\longmapsto BD^2+CD^2=m^2[/tex]
[tex]\\ \sf\longmapsto m^2=7^2+19.2^2[/tex]
[tex]\\ \sf\longmapsto m^2=49+363[/tex]
[tex]\\ \sf\longmapsto m^2=412[/tex]
[tex]\\ \sf\longmapsto m=\sqrt{412}[/tex]
[tex]\\ \sf\longmapsto m=20.3[/tex]
Nearest value in options is 18
Hence option a is correct
A circular pizza has a diameter of 12 inches and is cut into 10 congruent slices. What is the area of each slice, to the nearest tenth?
Group of answer choices
14.4 straight pi inches squared
3.6 straight pi inches squared
2.4 straight pi inches squared
12.4 straight pi inches squared
[tex]\\ \sf\longmapsto Area=2\pi r[/tex]
[tex]\\ \sf\longmapsto Area=2(3.14)\times 6[/tex]
[tex]\\ \sf\longmapsto Area=2(18.84)[/tex]
[tex]\\ \sf\longmapsto Area=37.68in^2[/tex]
Now area of each slice
[tex]\\ \sf\longmapsto \dfrac{37.68}{12}[/tex]
[tex]\\ \sf\longmapsto 3.6in^2[/tex]
The area of each slice of the pizza will be 3.6π square inches. The correct option is B.
What is the area of the sector?The circle is defined as the locus of the point traces around a fixed point called the center and is equidistant from the out trace.
It is given that a circular pizza has a diameter of 12 inches and is cut into 10 congruent slices.
Let r is the radius of the sector and θ be the angle subtends by the sector at the center. Then the area of the sector of the circle will be
Area = (θ/2π) πr²
angle = 2π/10
The area will be calculated as below:-
Area = (2π/10)/2π) πr²
Area = ( π x 6 x 6 ) / 10
Area = 3.6π square inches
Therefore, the area of each slice of the pizza will be 3.6π square inches. The correct option is B.
More about the area of the sector link is given below.
https://brainly.com/question/7512468
#SPJ2
you start at (5,3) you move down 4 units and up 6 units. where do you end?
You end up at the point (5, 5).
Put the steps for deriving the formula for the arc length of a circle in the correct
order.
whats the distance between (-9, -6) and (-2, 2)
Hi! I'm happy to help!
To find the answer we first have to find the distance between the x and y values.
From the first point, we travel from the x point -9, to the x point, -2. This means that we traveled 7 units.
From the first point, we also travel from the first y point, -6, to the second y point, 2. This means we traveled 8 units.
From here we use the Pythagorean Theorem.
The Pythagorean Theorem says that: a²+b²=c²
We can use a and b (the 7 and 8 units we traveled) to find c (the distance between).
Let's insert our values.
7²+8²=49+64=113=c²
To find c, we need to find the square root of c².
√113
This is 10.6301..., if you want to round the the hundredth, or thousandth, your answer would be 10.63, rounding to the nearest tenth, it would be 10.6, and rounding to the nearest whole number would be 11.
I hope this was helpful, keep learning! :D
3/4 + 20 (2/5 x 4/7)
Answer:
i believe the answer is 5.3
Which Expression is equivalent to 3(x + 6)
18x
3x + 2
3x + 18
Answer:
3x+18
Step-by-step explanation:
since 3 is outside the bracket you need to multiply 3 by both x and 6. so 3 multiply x is 3x and 3 multiply 6 is 18, hence 3x+18
Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.
Square root x + 6 - 4 = x
Answer:
-2, (-5 is extraneous)
Step-by-step explanation:
assuming √(x+6) -4 =x
√(x+6) = x+4
square both side
x+6 = (x+4)^2
x+6 = x^2+8x+16
x^2+7x+10=0
(x+2)(x+5) = 0
x = -2, -5
put -5 back into org equation and it is not true
√(-5+6) -4 ≠ -5
find the value of x and y
Answer:
x=50 and y=80
Step-by-step explanation:
ATQ, x+50+y=180 and y+2x=180. x=50 and y=80
ACD = 30, Line segment AC = x + 1, Line segment CD = 2x + 2. What is x equal to? x =
Answer:
AC+ CD = ACD
X+1 + 2X + 2 = 30
3X+3 =30
3X=30–3
3X=27
X= 27/ 3
X= 9
I'm not sure of the solution, but I solved it according to a straight line (Line segment) .
I hope I helped you^_^
The quadrilaterals JKLM and PQRS are similar. Find the length x of SP
Answer:
4.8
Step-by-step explanation:
The scale factor is (3.6)/3=1.2. Hence x/4=1.2, x=4.8
Complete the table for the function
Answer:
C
Step-by-step explanation:
y(x) = x^(1/3)+7
y(-8)=(-8)^(1/3)+7=5
y(-1)=(-1)^(1/3)+7=6
y(1)=(1)^(1/3)+7=8
y(8)=(8)^(1/3)+7=9
which table shows a proportional relationship between x and y?
Answer:
Table C
Step-by-step explanation:
For x and y to be proportional , then the values of
[tex]\frac{y}{x}[/tex] = constant k
Table B
[tex]\frac{y}{x}[/tex] = [tex]\frac{6}{3}[/tex] = 2
[tex]\frac{y}{x}[/tex] = [tex]\frac{24}{6}[/tex] = 4
[tex]\frac{y}{x}[/tex] = [tex]\frac{36}{9}[/tex] = 4
The values are not constant
Table C
[tex]\frac{y}{x}[/tex] = [tex]\frac{2}{3}[/tex]
[tex]\frac{y}{x}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
[tex]\frac{y}{x}[/tex] = [tex]\frac{6}{9}[/tex] = [tex]\frac{2}{3}[/tex]
These values are constant
Then Table C shows a proportional relationship between x and y
If a teacher's guide to a popular SAT workbook is to be printed using a special type of paper, the guide must have at most 400 pages. If the publishing company charges 1 cent per page printed, what is the largest price, in dollars, that can be charged to print 20 copies of the workbook using the special paper?
Answer:
$80
Step-by-step explanation:
To find the largest price, assume that all 20 copies of the workbook will have 400 pages.
Since the company charges 1 cent per page, this means each workbook will cost 400 cents. This is equivalent to 4 dollars.
Find the total cost by multiplying this by 20:
20(4)
= 80
So, the largest price to print 20 copies is $80
Bond A is zero-coupon bond paying $100 one year from now. Bond B is a zero-coupon bond paying $100 two years from now. Bond C is a 10% coupon bond that pays $10 one year from now and $10 plus the $100 principal two years from now. The yield to maturity on bond A is 10%, and the price of bond B is $84.18. Assuming annual compounding, what is the price of Bond A?
Answer:
c
Step-by-step explanation:
What are m and b in the linear equation, using the common meanings of m and b? 2 + 3x + 5 - 2x = y
y=mx+b is the general formula of linear equation
y=-2x+5+3x+2
y=1x+7
m=1
b=7
Linear equation given in the question is,
2 + 3x + 5 - 2x = y
To simplify this equation further,
Add like terms of the equation,(2 + 5) + (3x - 2x) = y
7 + x = y
Now compare this linear equation with the slope-intercept form of the linear equation,
y = mx + b
Here, m = slope of the line'
b = y-intercept
By comparing the equations,
m = 1
b = 7
Learn more,
https://brainly.com/question/15253236
What is an equation of the line that passes through the points (-1, 6) and
(-1, -5)?
Answer:
x = -1
Step-by-step explanation:
Because the line passes through two points that both have the same x value, this means the line is vertical, and the slope is undefined.
So the equation of the line is x = -1.
explain develop spirit of hard work
The productivity of a country is given by f(x, y) = 600x^2/3 y^1/3, where x and y are the amount of labor and capital.
a) Compute the marginal productivities of labor and capital when x = 125 and y = 64.
b) Use part (a) to determine the approximate effect on productivity of increasing capital from 64 to 66 units, while keeping labor fixed at 125 units.
c) What would be the approximate effect of decreasing labor from 125 to 124 units while keeping capital fixed at 64 units?
The area of a rectangle is 44 m^2, and the length of the rectangle is 3 m less than twice the width. Find the dimensions of the rectangle.
length :
width :
Answer:
Length:8
Width:5.5
Step-by-step explanation:
We're given area = 44m^2, and the formula for the area of a rectangle is the length multiplied by the width. So,
A = L * w = 44
We're given that the length is 3m shorter than 2 times the width, which is 2w - 3. "2w" is the same as "2 times the width", and the 3 is subtracted because it says 3m shorter than 2 times the width. So L = 2w - 3, and we can substitute that into our equation above.
(2w - 3)(w) = 44
2w^2 - 3w - 44 = 0
Use the quadratic formula here.
x = {3 ± √(-3)^2 - 4(-44)(2)}/2(2)
= {3 ± √9 + 352}/4
= (3 ± 19)/4
You'll get two answers, but remember, we're measuring the length of the sides of shapes, so it has to be positive. It's impossible to have negative lengths, so we're going to stick with the (3 + 19)/4 answer, which is 22/4, which is 5.5. However, we are not finished yet. This is just the width. Now we need to plug it into the equation for length, which was 2w - 3
2(5.5) - 3 = 11 - 3 = 8
The length is 8m and the width is 5.5m.
Execute the following 18/3+2*8-5.
