Answer:
Point A does not lie on the curve y = x²
Step-by-step explanation:
Given points:
[tex]\sf A: \left(\dfrac{3}{2}, \dfrac{9}{2}\right)[/tex]
[tex]\sf B: \left(-1,1 \right)[/tex]
[tex]\sf C: \left(4,16 \right)[/tex]
[tex]\sf D: \left(\dfrac{1}{2}, \dfrac{1}{4}\right)[/tex]
To determine if the given points lie on the curve y = x², simply substitute the x-value of each point into the equation and compare y-values.
Point A
[tex]\boxed{\begin{aligned}x=\dfrac{3}{2} \implies y&=\left(\dfrac{3}{2} \right)^2\\\\y&=\dfrac{3^2}{2^2}\\\\y&=\dfrac{9}{4}\end{aligned}}[/tex]
As 9/4 ≠ 9/2, point A does not lie on the curve.
Point B
[tex]\boxed{\begin{aligned}x= -1\implies y&=\left(-1 \right)^2\\y&=1\end{aligned}}[/tex]
As 1 = 1, point B does lie on the curve.
Point C
[tex]\boxed{\begin{aligned}x=4 \implies y&=\left( 4\right)^2\\y&=16\end{aligned}}[/tex]
As 16 = 16, point C does lie on the curve.
Point D
[tex]\boxed{\begin{aligned}x=\dfrac{1}{2} \implies y&=\left(\dfrac{1}{2} \right)^2\\\\y&=\dfrac{1^2}{2^2}\\\\y&=\dfrac{1}{4}\end{aligned}}[/tex]
As 1/4 = 1/4, point D does lie on the curve.
Calculate the difference and enter below. 5-(-5)
Answer: 10
Step-by-step explanation: As I said in your previous question, we can make this an addition problem, to make it easy, and make more sense. S0, it would be 5+5, which is our answer; 10. I hoped this helped
3. RETIREMENT Mr. Ram has $410,000 in a
retirement account that earns 3.85%
simple interest each year.
Find the amount
of interest earned after 5 years.
Lets turn 3.85% into a decimal first. Multiply 0.0385 with 410,000 which gives you 15785. Add that to 410,000 which gives you 425785. Multiply 3.85 by 425785. Repeat that process 5 times until you get the amount of interest earned after 5 years.
A sample of 60 account balances of a credit company showed an average balance of $1151. The sample standard deviation was $112. You want to determine if the mean of all account balances is significantly different from $1120. Use a 0.01 level of significance. Choose the t-statistic and the appropriate conclusion.
Group of answer choices
t = 2.144 ; fail to reject the null hypothesis
t = 2.019 ; fail to reject the null hypothesis
t = 2.019 ; reject the null hypothesis
t = 2.144 ; reject the null hypothesis
Find the p value also and explain how to get it.
The t-statistic for this hypothesis test is 2.019 and the appropriate conclusion is that we fail to reject the null hypothesis.
To find the p-value, we can use the t-distribution calculator and enter in the degrees of freedom (df = 59), the t-statistic (t = 2.019), and the significance level (alpha = 0.01). The resulting p-value is 0.055, which is greater than the significance level of 0.01. Therefore, we are unable to reject the null hypothesis.
The formula for the t-statistic can be used to calculate the t-statistic for this hypothesis test:
t = (1151 - 1120) / (112 / √60)
t = 2.019
Therefore, the t-statistic for this hypothesis test is 2.019 and the appropriate conclusion is that we fail to reject the null hypothesis.
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Algebra
A line has a slope of 0 and passes through the point (13, 2). What is its equation in
slope-intercept form?
Answer:
y = 2 (This equation is in slope intercept form.)
Step-by-step explanation:
y = 0x + b
2 = 0(13) + b
2 = 0 + b
b = 2
y = 2
out of 139 7th graders, 86 voted math as their favorite subject. what percent is this?
Answer:
61.9%
Step-by-step explanation:
percent = part/whole × 100%
part = 86
whole = 139
percent = 86/139 × 100%
percent = 61.9%
Answer:
The percent is:
61.87%
Step-by-step explanation:
86 / 139 = 0.6187
0.6187 * 100 = 61.87%
0=-16r^2-50
algebra question
[tex]r=\frac{5i\sqrt{2} }{4}, -\frac{5i\sqrt{2} }{4}[/tex] or simply just say ± [tex]\frac{5i\sqrt{2} }{4}[/tex].
Hope this helps!
Answer:
[tex]r=\dfrac{5\sqrt{2}}{4}}\:i\:,\quad \;\;r=-\dfrac{5\sqrt{2}}{4}}\:i[/tex]
Step-by-step explanation:
To solve the given equation, rearrange the equation to isolate r.
Given equation:
[tex]0=-16r^2-50[/tex]
Add 16r² to both sides of the equation:
[tex]0+16r^2=-16r^2-50+16r^2[/tex]
[tex]16r^2=-50[/tex]
Divide both sides of the equation by 16:
[tex]\dfrac{16r^2}{16}=\dfrac{-50}{16}[/tex]
[tex]r^2=-\dfrac{25}{8}[/tex]
[tex]\textsf{For\;\:}x^2=f\left(a\right)\textsf{\:the\:solutions\:are\:\:}x=\pm\sqrt{f\left(a\right)}[/tex]
[tex]r=\pm\sqrt{-\dfrac{25}{8}}[/tex]
[tex]\textsf{Apply\;the\:radical\:rule:}\;\:\sqrt{-a}=\sqrt{a}\sqrt{-1}[/tex]
[tex]r=\pm\sqrt{\dfrac{25}{8}}\sqrt{ -1}[/tex]
[tex]\textsf{Apply\;the\:imaginary\:number\:rule:}\;\:\sqrt{-1}=i[/tex]
[tex]r=\pm\sqrt{\dfrac{25}{8}}\:i[/tex]
[tex]\textsf{Apply\;the\:radical\:rule:}\:\:\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}},\:\quad \:a\ge 0,\:b\ge 0[/tex]
[tex]r=\pm\dfrac{\sqrt{25}}{\sqrt{8}}\:i[/tex]
Simplify the numerator and denominator of the fraction:
[tex]r=\pm\dfrac{5}{2\sqrt{2}}\:i[/tex]
Rationalise the denominator by multiply the numerator and denominator by √2:
[tex]r=\pm\dfrac{5\cdot\sqrt{2}}{2\sqrt{2}\cdot \sqrt{2}}\:i[/tex]
[tex]r=\pm\dfrac{5\sqrt{2}}{4}}\:i[/tex]
Therefore, the solutions to the given equation are:
[tex]r=\dfrac{5\sqrt{2}}{4}}\:i\:,\quad \;\;r=-\dfrac{5\sqrt{2}}{4}}\:i[/tex]
Anthony the anteater requires 1800 calories each day. He gets 1 calorie from every
50 ants that he eats. If he sticks his tongue out 150 times per minute and averages 2
ants per lick, how many hours will it take for him to get 1800 calories?
Answer: 5 hours
Step-by-step explanation:
1800cal/day
a= ants
50a= 1 cal
150 licks per minute, 2 ants per lick--- 2*150 = 300 ants per minute
6*50a= 1 cal*6
-- 300a = 6cal
The anteater can get a avg of 6 calories per minute.
6*60 = 360
We can make a equation:
x =calories
360x = 1800
360/360x = 1800/360
x = 5
It would take the anteater a total of 5 hours to withdraw 1800 calories from ants. This is 300*60*5 ants!
To check:
360(5)=1800
1800=1800
can someone pleaseee help me with this math question
Answer:
(a) To find the range of the function f(x), we need to consider all possible values of x in the range -7 ≤ x ≤ 7 and x ≠ -5. For each value of x, we can evaluate the function to find the corresponding value of f(x). Then, we can find the minimum and maximum values of f(x) in this range to determine the range of the function.
For example, if x = -7, then the function will return a value of 2 - 12/(-7) + 5 = 2 + 2 + 5 = 9. If x = 7, then the function will return a value of 2 - 12/7 + 5 = 2 - 1 + 5 = 6.
We can see that the minimum value of the function is 6, which is achieved when x = 7, and the maximum value of the function is 9, which is achieved when x = -7. Therefore, the range of the function is {6, 9}.
(b) To find the inverse of the function f(x), we need to switch the x and y values in the function definition to obtain a new function g(y) such that g(f(x)) = x for all values of x in the domain of the original function.
In this case, the inverse of the function f(x) is given by g(y) = (2 - y + 5)/(-12). This inverse function is defined for all values of y in the range {6, 9}, which is the range of the original function.
To find the value of f^-1(0), we can plug in 0 for y in the inverse function g(y) to obtain g(0) = (2 - 0 + 5)/(-12) = -1/12. Therefore, f^-1(0) = -1/12.
Identify the slope and y-intercept of each linear function's equation.
x-3=y
-x + 3 = y
y=1-3x
y=3x-1
Intro
slope = 3, y-intercept at -1
slope =-3, y-intercept at 1
slope = 1 y-intercept at -3
slope-1-y-intercept at 3
Done
A. y = 3x-1; slope is 3 and y-intercept is -1
B. -x+3 = y; slope is -1 and y-intercept is 3
C. x-3 = y; slope is 1 and y-intercept is -3
D. y = 1-3x; slope is -3 and y-intercept is 1
What is slope-intercept form?In math, slope interceptor form is the method of writing an equation for a line in the form y = mx + b.
Slope-Intercept form
The slope - intercept form equation with slope m and y intercept c is given by, y = mx+c
Option A:
y = 3x-1
slope m = 3
y-intercept c = -1
Option B:
-x+3 = y
slope m = -1
y-intercept c = 3
Option C:
x-3 = y
slope m = 1
y-intercept c = -3
Option D:
y = 1-3x
slope m = -3
y-intercept c = 1
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HELP ME PLEASE ASAP!!!
Maya has 360 meters of fencing and wishes to form three sides of a rectangular field. The fourth side borders a river and will not need fencing. As shown below, one of the sides has length x (in meters).
Answer:
a) [tex]A(x)=360x-2x^2[/tex]
b) [tex]90m[/tex]
c) [tex]16200m^2[/tex]
Step-by-step explanation:
This is related to a differential topic called optimisation.
We here have two sides of the field that are equal to [tex]x[/tex], and another unknown (that we will call [tex]y[/tex]). Maya has 360m of fencing, so we will say that [tex]2x+y=360[/tex], and this means that [tex]y=360-2x[/tex].
Our first task is to find a function for the area of the field. We know that the area of a field is length × width. We know we have a length of [tex]y[/tex] which is [tex]360-2x[/tex] and a width of [tex]x[/tex], therefore:
[tex]A(x)=x(360-2x)=360x-2x^2[/tex]
To find the maximum value of [tex]x[/tex], we must first differentiate the function:
[tex]A'(x)=360-4x[/tex]
We must then set the equation equal to 0 and solve for [tex]x[/tex], where the line/curve would be stationary.
[tex]360-4x=0[/tex]
[tex]4x=360[/tex]
[tex]x=90[/tex]
Finally, to find the maximum area, we would substitute this value of [tex]x[/tex] back into the original equation:
[tex]A(x)=360x-2x^2\\\\A(90)=360(90)-2(90)^2\\\\A(90)=16200[/tex]
For the following:
(a) The area is A(x) = x × (180 - x)(b) The side length x that gives the maximum area is 90 meters.(c) Maximum area that the field can have is 8100 square meters.How to find area and length?(a) To find a function A(x) that gives the area of the field in terms of x, use the information given about the fencing and the shape of the field.
Let the length of the other two sides (perpendicular to the side with length x) be y (in meters).
The perimeter of the rectangle is given by the sum of all four sides:
Perimeter = 2x + 2y
According to the problem, the perimeter is 360 meters, set up an equation:
2x + 2y = 360
Now, solve this equation for y in terms of x:
2y = 360 - 2x
y = (360 - 2x) / 2
y = 180 - x
The area A(x) of the rectangle is given by the product of its length (x) and width (y):
A(x) = x × y
A(x) = x × (180 - x)
(b) To find the side length x that gives the maximum area for the field, maximize the function A(x) from part (a). To do that, take the derivative of A(x) with respect to x, set it equal to zero, and solve for x:
A(x) = x × (180 - x)
dA/dx = (180 - x) - x
dA/dx = 180 - 2x
Now, set dA/dx = 0 and solve for x:
180 - 2x = 0
2x = 180
x = 90
So, the side length x that gives the maximum area is 90 meters.
(c) Now there is the value of x, find the maximum area by substituting x = 90 into the area function A(x) from part (a):
A(x) = x × (180 - x)
A(90) = 90 × (180 - 90)
A(90) = 90 × 90
A(90) = 8100
The maximum area that the field can have is 8100 square meters.
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PLS HELP I’m struggling with this question and could use some help to answer it.
The required inverse function of the given function is given as f⁻¹(x) = [9 - 8y] / [1 + y], the domain of the inverse function is all real numbers except -1, and the range of the inverse function is all real numbers.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
f(x) = -x + 9 / [8 + 9x]
Now,
y = f(x)
y = -x + 9 / [8 + 9x]
x = 9 - 8y / [1 + y]
Now,
x ⇄ y
y = 9 - 8x / 1 + x
Now y = f⁻¹[x]
f⁻¹(x) = [9 - 8y] / [1 + y],
Thus, the required inverse function is f⁻¹(x) = [9 - 8y] / [1 + y], the domain of the inverse function is all real numbers except -1, and its range is all real numbers.
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Help quick!! What is the sum of the interior angles of a regular polygon with 5 sides? I think it’s D but I’m still confused.
Answer:
D) 540
Step-by-step explanation:
he sum of the interior angles of a polygon can be found using the formula (n - 2) * 180 degrees, where n is the number of sides in the polygon. In this case, we are given that the polygon has 5 sides, so we can plug this into the formula to find the sum of its interior angles:
(5 - 2) * 180 degrees = 3 * 180 degrees = 540 degrees
Therefore, the sum of the interior angles of a regular polygon with 5 sides is 540 degrees.
ASAP PLEASEEE!!!
Suppose that the function g is defined, for all real numbers, as follows. Find g(-2), g(1), and g(2).
Answer:
for g(-2)
we wil take -1/4 x -1
so g(-2) = - 1/2
for g(1)
we will take (x+1)²
so g(1) = (1+1)² = 4
for g(2)
we will take (x+1)²
so g(2)= ,(2+1)² = 9
The library has 65400 art books and 9600 science books. What part of all the books are science books.
Answer: it should be 12.8 percent
Step-by-step explanation:
A bus is going 44 miles an hour from one town to another. The bus arrives 7 minutes late. How many miles apart are the two towns?
Answer:
Step-by-step explanation:
let the distance be x miles
the difference in time taken between two towns = 7 minutes
44 - x = 49
x = 49 - 44
x = 5 miles
Therefore , the distance between two towns is 5 miles .
You wish to buy a home for $315,000. You have a 30 year mortgage at 3.75% annual interest rate. If you put 10% down, what will be the monthly payment you make to the bank?
0.9(315 000) * 30(0.0375)
= 283 500 * 1.125
= 318 937.5 (total amount of 30 year mortgage)
= 318 937.5 / 360
= $885.94 (monthly payment)
CHECKING:315 00 * 0.1 = 31 500 (amount of down)
315 000 - 31 500 = 283 500 (balance without interest)
283 500 * 30(0.0375) = 318 937.5 (balance with interest)
318 937.5 / 30(12) = 885.94
Therefore, the monthly payment will be $885.94
CREDITS:heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-
WILL MAKE BRAINLIEST!!!!!!
PLEASE ANSWER FAST
If your velocity is 20 m/s south and you traveled for 10 MINUTES, how far have you gone?
ryland is creating an article about commonly used compression algorithms for an online educational site. he's debating whether to express each algorithm in natural language, flow charts, pseudocode, or c , a general-purpose programming language. which of these is a good argument for expressing the algorithm in pseudocode? choose 1 answer:
Pseudocode doesn't depend on the syntax and subtitles of a particular programming language, so his readers will be able to understand it as long as they know at least one language.
In computer science, pseudocode is a undeniable language description of the stairs in an set of rules or any other system. Pseudocode frequently makes use of structural conventions of a regular programming language, however is supposed for human studying as opposed to gadget studying. Pseudocode is known via way of means of the programmers of all types. it allows the programmer to pay attention most effective at the set of rules a part of the code development. It can't be compiled into an executable program.
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Complete question:
Ryland is creating an article about commonly used compression algorithms for an online educational site.
He's debating whether to express each algorithm in natural language, flow charts, pseudocode, or C++, a general-purpose programming language.
Which of these is a good argument for expressing the algorithm in pseudocode?
A group of hikers park their car at a trail head and hike into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, d, from the car on the day of their hike after h hours.
The campers will be 40 miles from their car after 12 hours.
Given :
A group of hikers park their car at a trail head and hike into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, d, from the car on the day of their hike after h hours .
We can pick two points on the line graphed and substitute the coordinates into this formula to find the slope:
slope m = y2 - y1 / x2 - x1
Choosing the points (0,4) and (2,10), we get:
m = 4 - 10 / 0 - 2
= -6 / -2
= 6 / 2
= 3
We can substitute the point (0,4) and the slope into y = mx + b and solve for "b":
4 = 3 * 0 + b
b = 4
Then, the equation of this line is:
y = 3x + 4
Since the distance in miles is represented on the y-axis and the time in hours is represented on the x-axis. we can rewrite the equation as:
d = 3h + 4
if h = 12
d = 3 * 12 + 4
= 36 + 4
= 40 miles
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Full question :
A group of hikers park their car at a trail head and hike into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, d, from the car on the day of their hike after h hours.How many miles will the campers be from their car after 12 hours?
Please help!! Determine the measure of the exterior angle.
Answer:
[tex]92.05^{\circ}[/tex]
Step-by-step explanation:
By the exterior angle theorem, the answer is [tex]m\angle Y+m\angle Z=92.05^{\circ}[/tex].
Answer:
A
Step-by-step explanation:
exterior angle = sum of the other two angles
63.25 + 28.8
92.05°
MATHEMATICAL CONNECTIONS Graph the lines on the same coordinate plane.
Answer:
see attached for a graphcentroid: (0, 2)Step-by-step explanation:
You want the graphs of the given lines, and the centroid of the triangle they form.
y1 = 3x -4y2 = 3/4x +5y3 = -3/2x -4GraphIt works well to start by plotting the y-intercept of each equation, then using the slope to identify the "rise" and "run" to another point on the line. Then the line can be drawn through the points.
y1: y-intercept = (0, -4); additional point 3 up and 1 over: (1, -1).y2: y-intercept = (0, 5); additional point 3 up and 4 over: (4, 8).y3: y-intercept = (0, -4); additional point 3 down and 2 over: (2, -7). This one is more easily plotted in the reverse direction, 3 up and 2 to the left: (-2, -1).VerticesThe graph shows you the points of intersection of the lines are ...
(-4, 2), (4, 8), (0, -4) . . . . . . . . . the last is the y-intercepts of y1 and y3
CentroidThe centroid coordinates are the average of the vertex coordinates, their sum divided by 3.
centroid = ((-4, 2) +(4, 8) +(0, -4))/3 = (-4+4+0, 2+8-4)/3 = (0, 6)/3
centroid = (0, 2)
__
Additional comment
The slope of each line is the x-coefficient in the equation. That slope is the ratio of "rise" (change in y) to "run" (change in x) for the line. It is often convenient to draw a graph by finding points on the line counting the grid squares for rise and run.
I need help please ANYONE???!!!!!
The distance between P and T on the coordinate grid is
units. (Input whole numbers only.)
Image of a coordinate grid with point P located at negative 10, 15 and point T located at 15, 15.
Answer:
25
Step-by-step explanation:
find all values of the scalar k for which the two vectors are orthogonal. (enter your answers as a comma-separated list.) u
Therefore, the value of the scalar k for which the two vectors are orthogonal is k =1/5.
What is vector ?In physics and mathematics, the term "vector" is used to refer, informally, to certain quantities that cannot be described by a single number or to certain constituents of vector spaces.
Here,
When the dot product of two vectors is zero, those two vectors are said to be orthogonal.
Dot product:
Let's assume we have the two vectors a and b.
a = (1,2) (1,2)
b = (2,3) (2,3)
Their dot item is:
a.b = (1,2). (1,2).
(2,3) = 1*2 + 2*3 = 8
Regarding this issue:
u = (2,3) (2,3)
(k + 1, k - 1) = v
So
u.v = (2,3). (2,3).
(k + 1, k - 1) = 2k + 1, 3k - 1, or 2k + 2, 3k - 3, or 5k - 1
The vectors must be orthogonal for the dot product to equal 0.
So:
=> 5k -1 =0
=> 5k =1
=> k =1/5
Therefore , the value of the scalar k for which the two vectors are orthogonal is k =1/5.
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θ =120°
θ =240°
θ =270°
θ =0°
θ =210°
θ =180°
θ =90°
02410.0 points
The charge on an electron is 1.60218 x 10⁻¹⁹C and its mass is 9.10939 x 10⁻³¹ kg.
What is the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1mT ?
Answer in units of eV.
The kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1 mT is 0.07623125 eV.
In the given question, the charge on an electron is 1.60218 x 10^(-19) C and its mass is 9.10939 x 10^(-31) kg.
We have to find the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1 mT.
E = 0.18 kV/m
B = 1.1 mT
mass m = 9.10939*10^(-31) kg
Then force on a moving charge in electric and magnetic field = Lorentz force
F = qE+ q*VB
So,
F = qE+ q*VB = 0
E = V*B
Find V , so
V = E/B
V = 0.18*10^3 /( 1.1*10^-3)
V =163637 m/s
so KE = 1/2*m*v^2
Then put values..
KE = 0.5*9.11*10^(-31)*163637^(2)
KE = 1.2197*10^(-20) J
in eV = 1.2197*10^-20 / ( 1.6*10^-19 )
eV = 0.07623125 eV
Hence, the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1 mT is 0.07623125 eV.
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5. A table of values and the plot of the residuals for the line of best fit are shown.
x
The point that the line estimate best fits is the point x = 6 with a residual of 0.18
How to interpret the residuals of the line of best fit?
We are given a table which displays the point and then their residual values are also added from the graph to get;
The table is as follows:
x y Residual Absolute Residual value
1 10 0.4 0.4
2 8 -1.125 1.125
2.5 9.5 0.625 0.625
4 8 -0.25 0.25
5 8 0.2 0.2
6 7.5 0.18 0.18
7.2 7 0.19 0.19
8.5 6 -0.25 0.25
The residual value is negative if the point on the scatter plot lies below the regression line and it is positive if the point on the scatter plot lies above the regression line.
Formula for the residual value is;
Residual value = Actual y-value(i.e. on scatter plot) - Observed y-value
Now, the residual value is farthest from the line if the absolute value of the residual value is highest.
Hence, the highest absolute residual value is: 1.125
The point that it best fits is the lowest absolute value which is 0.18
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. in addition to limit theorems that deal with sums, there are limit theorems that deal with extreme values such as maxima or minima. here is an example. let u1,..., un be independent uniform random variables on [0, 1], and let u(n) be the maximum. find the cdf of u(n) and a standardized u(n), and show that the cdf of the standardized variable tends to a limiting value.
As per the limit theorem, the CDF of the standardized variable tends to a limiting value.
The term limit theorem states that the average of a large number of id and the random variables converges to the expected value.
Here we have given that let u1,..., un be independent uniform random variables on [0, 1], and let u(n) be the maximum. find the CDF of u(n) and a standardized u(n).
And we need to prove that the the cdf of the standardized variable tends to a limiting value.
Let us consider the density function of a uniform random variable on [0,1] is f(x)=1 and the cdf is F(x)=x for x∈[0,1], so for U(n), the density function is
fₙ(x) = nxⁿ⁻¹
Whereas the CDF is written as,
fₙ(x) = xⁿ
When we equate both then we get
fₙ(x) = nx²ⁿ⁻¹
Therefore, the given statement is proved.
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Find the sum of 6.34 × 1019 and 2.246 × 1017.
8.586 × 1019
6.36246 × 1036
6.36246 × 1019
8.586 × 1036
The correct answer would be C, 6.36246 × 1019
16. 21) Thex- andy-axes are the asymptotes of a hyperbola that passes through the point(2,2). Its equation is a) x2−y2=0
b) xy=4
c) y2−x2=0
d) x2+y2=4
The equation of the hyperbola with given x and y axes will be x² + y² = 4 that is option D is correct.
The hyperbola x² + y² = 4 is a standard form of the equation for a hyperbola centered at the origin, which means that the hyperbola passes through the point (0,0). However, the given information states that the hyperbola passes through the point (2,2). This can be achieved by shifting the hyperbola to the right and up by 2 units, resulting in the equation (x-2)² + (y-2)² = 4.
The asymptotes of a hyperbola are the lines that the hyperbola approaches but never touches as it extends to infinity. The asymptotes of a hyperbola centered at the origin are the x-axis and y-axis. Since this hyperbola has been shifted to the right and up by 2 units, the asymptotes are the x-axis and y-axis shifted by 2 units in the same direction. Therefore, the x- and y-axes are the asymptotes of this hyperbola.
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Select the graph that matches the system of inequalities. 2x – y ≤ 3 x – 2y ≥ –2
Answer:
Step-by-step explanation:
Graph A