help please!!
simplify the following:
[tex] \displaystyle \lim_{n\to \infty } \frac{1 + 2 + 3 + \dots {\dots} +n }{ {n}^{2} } [/tex]
[tex] \text{ note: must provide explanation}[/tex]
Answer:
[tex] \dfrac{1}{2} [/tex]
Step-by-step explanation:
we are given a limit
and we want to simplify it
notice that, the numerator is in a sequence of sum of natural number
recall that,
[tex] \rm \displaystyle \: 1 + 2 + 3 + \dots {\dots }+ n = \frac{n(n + 1)}{2} [/tex]
so substitute:
[tex]\displaystyle \lim_{n\to \infty } \frac{ \dfrac{n(n + 1)}{2} }{ {n}^{2} } [/tex]
now recall L'Hôpital's rule
[tex] \displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)} [/tex]
first simplify the complex fraction:
[tex]\displaystyle \lim_{n\to \infty } \frac{n+ 1}{2n} [/tex]
apply L'Hôpital's rule:
[tex]\displaystyle \lim_{ n\to \infty } \frac{ \dfrac{d}{dn} n+ 1}{ \dfrac{d}{dn} 2n} [/tex]
simplify:
[tex] \dfrac{1}{2} [/tex]
and we are done:
Step-by-step explanation:
solution given:
The given expression takes a form[tex] \frac{ \infty }{ \infty } [/tex]
when n=[tex] \infty [/tex]
so,
[tex] \displaystyle \lim_{n\to \infty } \frac{1 + 2 + 3 + \dots {\dots} +n }{ {n}^{2} } [/tex]
[tex] \displaystyle \lim_{n\to \infty }\frac{n(n+1)}{ 2{n}^{2} }[/tex]
[tex] \displaystyle \lim_{n\to \infty }\frac{n+1}{ 2n}[/tex]
[tex] \frac{1}{2} [/tex]
[tex] \displaystyle \lim_{n\to \infty }[1+\frac{1}{ n}][/tex]
=[tex] \frac{1}{2} [/tex](1+[tex] \frac{1}{ \infty }) [/tex]
=[tex] \frac{1}{2} [/tex] is your answer
write the base and power of each of the following exponent.
(-23/56)^6
Answer:
-191.10
Step-by-step explanation:
When you divide 56/23 you get 2.4, 2.4 is negative.
Multiply 2.4 6 times
&
2.4^6.
You get -191.10.
I am probably wrong but I tried.
Find the absolute extrema of the given function: f(x)=x^4 − 3x^2 + 4, on the interval [−1,1]
Answer:
The absolute maximum is 4, and the absolute minimum is 2.
Step-by-step explanation:
We are given the function:
[tex]f(x)=x^4-3x^2+4[/tex]
And we want to find the absolute extrema of the function on the interval [-1, 1].
So, we will find the smallest and largest y-value within the interval. First, we can evaluate the function at its endpoints. So:
[tex]f(-1)=(-1)^4-3(-1)^2+4=2[/tex]
And:
[tex]f(1)=(1)^4-3(1)^2+4=2[/tex]
Our endpoints are (-1, 2) and (1, 2).
Recall that extrema only occurs at critical points. Critical points are where the derivative of the function equals 0. So, we can find the derivative of the function:
[tex]\displaystyle f'(x)=\frac{d}{dx}\left[x^4-3x^2+4\right][/tex]
Differentiate:
[tex]f'(x)=4x^3-6x[/tex]
Set the function equal to 0:
[tex]0=4x^3-6x[/tex]
Solve for x. Factor:
[tex]2x(2x^2-3)=0[/tex]
Zero Product Property:
[tex]2x=0\text{ or } 2x^2-3=0[/tex]
Solve for each case. Therefore:
[tex]\displaystyle x=0\text{ or } x=\pm\frac{\sqrt6}{2}[/tex]
The second case is outside of our interval. So we can ignore it.
Evaluate the function at x = 0:
[tex]f(0)=(0)^4-3(0)^2+4=4[/tex]
Therefore, for our function on the interval [-1, 1], the absolute maximum is 4, and the absolute minimum is 2.
which point is located on the x-axis
Answer:
Point C
Step-by-step explanation:
X axis is bottom row and Point C is directly on it.
I need help! Im very confused!
Answer:
Surface area of net = 310 cm²
Step-by-step explanation:
Given:
Dimension of two same rectangle = 11 cm by 9 cm
Dimension of single rectangle = 11 cm by 7 cm
Height of two triangle = 5 Cm
Base of two triangle = 7 Cm
Find;
Surface area of net
Computation:
Surface area of net = Surface area of two same rectangle + Surface area of single rectangle + Surface area of two same triangle
Surface area of net = 2[l x b] + [l x b] + 2[(1/2)(b)(h)]
Surface area of net = 2[11 x 9] + [11 x 7] + 2[(1/2)(7)(5)]
Surface area of net = 198 + 77 + 35
Surface area of net = 310 cm²
HELP PLEASE 1O POINTS
Answer: 35
Step-by-step explanation:
I need help on this problem for math, please answer ASAP :)
Answer:
x = 6
Step-by-step explanation:
10x + 11 + 17x + 7 = 180°
combine like terms:
27x + 18 = 180
subtract 17 from both sides of the equation:
27x = 162
divide both sides by 27:
x = 6
Give the value of each trigonometric ratio.
cos m
cos n
sin m
sin n
tan m
tan n
Step-by-step explanation:
Cos m = 35/37 = 0.94
Cos n = 12/37 = 0.32
Sin m = 12/37 = 0.32
Sin n = 35/37 = 0.94
tan m = 12/35 = 0.34
tan n = 35/12 = 2.91
How do I solve this finding the first four of the sequence?
Answer:
Step-by-step explanation:
a(1) = -7 (given)
a(2) = a(1) + 4 = -7 + 4 = -3
a(3) = a(2) + 4 = -3 + 4 = 1
a(4) = a(3) + 4 = 1 + 4 = 5
and so on.
Answer:
Step-by-step explanation:
What is the average of 88 and 72
Answer:
80
Step-by-step explanation:
(●'◡'●)
ILL BRAINLIEST YOU IF YOU GET IT RIGHT
Which diagram shows a pair of angle measure that proves lines c and d are parallel?
Answer:
C
Step-by-step explanation:
At first glance, it seems like all the answers work. But some careful thinking allows us to find the correct answer.
For this question, we will be using the process of elimination.
First, we can eliminate D, because it does not provide any angles on line d, so we cannot prove that line c is parallel to line d.
Second, we can eliminate A. It seems that the 2 angles makes it so that lines c and d must be parallel, however, that is only true if lines a and b are parallel. Since we don't know whether or not lines a and b are parallel, we cannot prove that lines c and d are parallel, so we can eliminate this choice.
Third, we can eliminate B. Like the diagram in A, this diagram can only prove lines c and d are parallel if lines a and b are parallel, and since we don't know whether or not lines a and b are parallel, we cannot prove tat lines c and d are parallel, so we can eliminate this choice.
We are left with C, so the answer must be C.
Of course, just to make sure, we will also check diagram C. Because the 2 angles provided in the diagram are on line a and none are on line b, we do not need line a to be related to line b in any way, as such we can pretend that line b does not exist in this diagram. We can then see that lines c and d must be parallel for this diagram, or else the angles would not work, so C is correct.
Two angles whose sum is 180° are called supplementary angles. The correct option is C.
What are supplementary angles?Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
When two parallel lines are cut by a transverse. The angles formed on the exterior of the parallel lines are known as the Exterior Angle.
Now, For two lines two be parallel in the given diagram the measure of the angle the exterior angle on the same side of the transverse should be supplementary to each other.
The diagram shows a pair of angle measure that proves lines c and d are parallel in option c. This is because lines c and d are parallel and a is transversal to the two lines. And the measure of the exterior angles formed on the same side of the transversal is supplementary.
Hence, the correct option is C.
Learn more about Supplementary angle here:
https://brainly.com/question/2882938
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i need help with this
which of the following points is a solution to the system of inequalities shown graphed below?
1.(-3,1)
2.(-1,4)
3.(3,-2)
4.(-2,-4)
The following are the last 10 run scores Colin got in cricket: 21, 14, 23, 23, 20, 8, 23, 34, 10, 22 a) Work out Colin's mean score. b) Colin plays cricket again on Sunday. He gets 22 runs. What is his new mean score? Give your answers as decimals. Please answer ASAP.
Answer:
19.8,41.8
Step-by-step explanation:
wish you all the best hope you understand.
What is the area? Plz show me step by step. :)
Answer:
124
Step-by-step explanation:
A triangle is BH/2
6.2 is the height and 5 is the base
one triangle is 15.5 so multiply it by 8 since its an octagon
Solve the system by substitution.
y = 8x – 6
y = 2x
Answer:
x = 1
y = 2
Step-by-step explanation:
y =8x - 6 ---------------------------------(I)
y = 2x -------------------------------------(II)
substitute y = 2x in equation (I)
2x = 8x - 6
Add 6 to both sides
2x + 6 = 8x
Subtract 2x from both sides
6 = 8x - 2x
6 = 6x
Divide both sides by 6
6/6 = x
x = 1
Substitute x = 1 in equation (II)
y = 2*1
y = 2
what is the equation of the line
(0,1) (4,-1)
hope it helps this to you figthing sheeeeeeeeeeeeeeeeeeeeeeeesh!!!
How many faces, vertices, and edges are in the figure below?
Answer:
faces = 7, vertices = 7, edges = 12
Step-by-step explanation:
i took the test just now :D (brainlest always acceptable! :D)
The number of faces, vertices, and edges are 8, 18 and 12.
We are given that;
The figure of hexagonal prism
Now,
A hexagonal prism is a 3D shape with
8 faces, 18 edges, and 12 vertices12.
The faces are 2 hexagons and 6 rectangles.
The figure below shows the faces, edges and vertices of a hexagonal prism.
Therefore, by the prism answer will be 8 faces, 18 edges, and 12 vertices12.
Learn more about rectangular prism;
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Help please
The lines on a coordinate plane are perpendicular.
Perpendicular lines form what type of angles?
Answer:
B. Right angles
Step-by-step explanation:
When perpendicular lines intersect, they create 90° angles (aka right angles)
i need help on thissssssssss
Answer:
s2Wzwxr tcyvybubububyxrz
The ____________ organs produce hormones called estrogen and testosterone. *
A soccer dome shaped like a hemisphere has a volume of 450,000 m^3. What is the area of its field? Use 3.14 for pi
Answer:
Step-by-step explanation:
450,000=2/3(3.14)r
450,000 times 3/2=2/3(3.14)r times 3/2
675,000=3.14r
675,000/3.14=3.14r/3.14
about 214968.15287=r
So now we know r. We can use it to find the area of the circle
Pi times r squared
3.14 times 214968.15287 squared
area equals about 15573.44815
The area of the hemisphere is 45065.41
How to determine the area?The given parameters are:
Shape = Hemisphere
Volume = 450000
The volume is calculated as:
Volume = 2/3pi r^3
This gives
450,000=2/3 * 3.14 * r^3
Solve for r^3
r^3 = 450000 * 3/(2 * 3.14)
This gives
r^3 = 214968.152
Take the cube roots
r = 59.9
The area is then calculated as;
Area = 4pi r^2
This gives
Area = 4 * 3.14 * 59.9^2
Evaluate
Area = 45065.41
Hence, the area of the hemisphere is 45065.41
Read more about areas at:
https://brainly.com/question/24487155
HELP ASAPPPP DUDE PLS PLS PLSSSSSS NOOO LINKS
Answer:
Step-by-step explanation:
use 25,000*(1-0.15)^8 = $ 6812.26
An olive press produces 6 2/3 gallons of oil in 32 minutes. At this rate, how many gallons of olive oil will be produced in 1 hour?
A. 3.6 gallons
B. 12.5 gallons
C. 8.8 gallons
D. 6.2 gallons
PLEASE HELP ITS A TEST!!!!
identify the center and radius of the circle. Then write the equation of the circle.
Answer:
Radius = 2
Step-by-step explanation:
x² + y² - 10x + 8y + 37 = 0
Regroup terms
(x² - 10x) + (y² + 8y) = -37
Complete the square
(x² - 10x + 5²) + (y² + 8y + 4²) = -37 + 5² + 4²
(x² - 5)² + (y² + 4)² = 2²
Center (5,-4)
Bananas cost 0.59 per pound. Create an equation that could be used to find the total cost of y of x bananas
Answer:
y = 0.59x
Step-by-step explanation:
Cost per pound of banana = $0.59
If Number of banana's = x
Total Cost of an item = price per item * number of items
Therefore,
Total cost, y = price per pound of banana * number of bananas
y = 0.59 * x
y = 0.59x
Explain why a 75% discount followed by an additional 25% discount is not the
same as a 100% discount.
Answer:
Because you first take 75% off of the first price then 25% off the discounted price
Example:
Lets say you have a item that cost $50 and you use a 75% discount card that will make the item $37.5. The you add an additional 25% off which will equal $9.38.
9. Lines A and B are parallel lines. Find the measures of angles 1, 2 and 3.
Answer:
<1 = 33
<2 = 90
<3 = 57
Step-by-step explanation:
<3 = 57 because of alternate interior angles
<2 + <3 + 33 = 180
<2 + 57 + 33 = 180
<2 + 90 = 180
<2 = 90
<1 + <2 + 57 = 180
<1 + 90 + 57 = 180
<1 + 147 = 180
<1 = 33
True or False? When an exponential function decreases, it is called exponential growth.
Answer:
When we know the initial population
, the next thing we need to solve the growth constant
to derive the exponential growth function.
If the problem gives the time it takes for the population to double or the doubling time
τ
. We can find the growth constant by substituting the doubling constant into the equation and solving for t.
This means that the statement is TRUE because the term for initial population cancels out when solving for k and the doubling time is given.
Step-by-step explanation:
can i have brainliest
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
Answer and Step-by-step explanation:
To find the sequence, we must plug in values for n and solve, starting with 0.
f(0) = ⁻13 - 2(0) = ⁻13
f(1) = ⁻13 - 2(1) = ⁻13 - 2 = ⁻15
f(1) = ⁻13 - 2(2) = ⁻13 - 4 = ⁻17
f(1) = ⁻13 - 2(3) = ⁻13 - 6 = ⁻19
When seeing this, we can see that the answer to the questions is A.
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