Please find the general limit of the following function:
[tex]\lim_{x \to 9}(x^2 + 2^7 + (9.1 \times 10))[/tex]
Answers
Answer:
The general limit exists at x = 9 and is equal to 300.
Step-by-step explanation:
We want to find the general limit of the function:
[tex]\displaystyle \lim_{x \to 9}(x^2+2^7+(9.1\times 10))[/tex]
By definition, a general limit exists at a point if the two one-sided limits exist and are equivalent to each other.
So, let's find each one-sided limit: the left-hand side and the right-hand side.
The left-hand limit is given by:
[tex]\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))[/tex]Since the given function is a polynomial, we can use direct substitution. This yields:
[tex]=(9)^2+2^7+(9.1\times 10)[/tex]
Evaluate:
[tex]300[/tex]
Therefore:
[tex]\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))=300[/tex]
The right-hand limit is given by:
[tex]\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))[/tex]
Again, since the function is a polynomial, we can use direct substitution. This yields:
[tex]=(9)^2+2^7+(9.1\times 10)[/tex]
Evaluate:
[tex]=300[/tex]
Therefore:
[tex]\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300[/tex]
Thus, we can see that:
[tex]\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1\times 10))=\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300[/tex]
Since the two-sided limits exist and are equivalent, the general limit of the function does exist at x = 9 and is equal to 300.
Step-by-step explanation:
Hey there!
Please look your required answer in picture.
Note: In left hand limit always take a smaller near number of the approaching number. For example as in the solution I took the 8.99,8.999 as it is smaller than 9 but very near to it.
And in right hand limit always take a smaller and just greater near number than the approaching number. For example, I took 9.01,9.001 which a just greater but very near to 9.
Hope it helps!
![Please Find The General Limit Of The Following Function:[tex]\lim_{x \to 9}(x^2 + 2^7 + (9.1 \times 10))[/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/VXEkDv7kz8vh9qpxMdJg0pkGvnX4gJ0D.jpeg)
Related Questions
The area of a square rug is 64 ft.² what is the perimeter of the rug?
Answers
Answer:
[tex]32[/tex][tex] {ft}^{2} [/tex]
Step-by-step explanation:
The area of a square rug = 64 ft²
First we will find the side of square rug = [tex] {64}^{2} = {s}^{2} [/tex]
[tex] {s}^{2} = 8 [/tex]
Perimeter of the rug = [tex]4 \times 8 [/tex][tex] = 32[/tex]ft²
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The answer choices are
A. 4
B. 5
C. 6
D. 7
E. 8
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Find the
surface area of the
prism.
Answers
Answer:
D. 972 ft^2
Step-by-step explanation:
SA = 2B + PH
where SA = total surface area of the prism,
B = area of a base
P = perimeter of the base
H = height of the prism
SA = 2 * bh/2 + (15 ft + 12 ft + 9 ft)(24 ft)
SA = (9 ft)(12 ft) + (15 ft + 12 ft + 9 ft)(24 ft)
SA = 972 ft^2
The triangle below is isosceles. Find the length of side x in simplest radical form with
a rational denominator.
х
4
Answers
Answer:
x = 2√2
Step-by-step explanation:
Since the triangle is isosceles, it means 2 of the angles are equal and 2 of the sides are also equal.
Now, since we see that it is also a right angled triangle, it means one angle is 90°.
Let the equal angles be a.
Thus;
a + a + 90 = 180 (since sum of angles in a triangle is 180)
2a + 90 = 180
2a = 180 - 90
2a = 90
a = 90/2
a = 45°
Now, using sine rule, we can find x. Thus;
x/sin 45 = 4/sin 90
sin 90 = 1
sin 45 = 1/√2
Thus;
x = (4 × 1/√2)/1
x = 4/√2
Let's rationalize the denominator to get;
x = (4/√2) × √2/√2
x = (4√2)/2
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Please write out the steps in explanation on how to solve these
1836-1347 and 4865-3956
Answers
-1347
———-
490
Subtract the number starting from the right to the left. ANSWER: 490
The sum of the numbers x, y, and z is 50. The ratio of x to y is 1 : 4, and the ratio of y to z is 4 : 5. What is the value of y?
A. 4
B. 8
C. 10
D. 20
Answers
Answer:
x：y：z
1：4
4：5
-------------
1：4：5
-------------
let a:b:c＝k:4k:5k
k+4k+5k=50
10k=50
k=5
y=4(5)
=20(D)
Answer:
D. 20
Step-by-step explanation:
x:y:z
1:4:5
1+4+5=10
50÷10=5
1=5
4=?
4=4×5
=20
The average weight of a particular box of crackers is 37.0 ounces with a standard deviation of 0.5 ounce. The weights of the boxes are normally distributed.
What percent of the boxes weigh more than 36.0 ounces?
What percent of the boxes weigh less than 36.5 ounces?
Answers
Please help it's for my test.
The area of a parallelogram is 108 square inches. What is the length of the parallelogram if the height is 6 inches?
Answers
Answer:
18 inches
Step-by-step explanation:
just FYI this is using base and height this is not trigonometry or diagonals but whenever you want to find the area of a parallelogram you have the base times the height and so you have the formula A= B * H but here you want to find the base so we divide the area by the height since those are your givens
A/H=B
108/6=18
The mean of a distribution is 276, while the median is 318. Which of these
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A It is negatively skewed,
B. It is symmetric
C. It is the same throughout
D. It is positively skewed
Answers
Answer:
A.
Step-by-step explanation:
The mean is less than the median so it is skewed to the left or negatively skewed.
7 more than 3 multiplied by x algebraic expression
Answers
Answer:
3x + 7
Step-by-step explanation:
O TRIGONOMETRIC FUNCTIONS
Arc length and central angle measure
Na
A circular arc has measure 18 in and is intercepted
a central angle of
radians. Find the radius r of the circle.
Do not round any intermediate computations, and round your answer to the nearest tenth.
?
Answers
Answer:
r = 22.9 in.
Step-by-step explanation:
Central angle in radians, ∅ = π/4
Length of arc, S = 18 in.
radius (r) = ?
Length of arc, C = r∅
Plug in the values and find r
18 = r*π/4
18 = (πr)/4
Multiply both sides by 4
4*18 = πr
72 = πr
Divide both sides by π
72/π = r
r = 22.9183118
r = 22.9 in. (Nearest tenth)
29 members in math club, treasury has $364 to spend, shirts are $11 caps are $14. How many caps and shirts can he buy to exhaust the funds available?
Answers
Answer:
14 shirts, 15 caps
Step-by-step explanation:
15 x 14 = 210$
14 × = 154$
210+154 = 364$
The perimeter of a rectangle is 54 cm. Find its length and width if the length is represented
by 3x + 2 and the width is represented by 2x – 5.
HELP FAST!!
Answers
Answer:
length = 20
width = 7
Step-by-step explanation:
Perimeter of a rectangle is
P = 2(l+w)
54 = 2( 3x+2 + 2x-5)
Combine like terms
54 = 2( 5x -3)
Divide each side by 2
54/2 = 5x-3
27 = 5x-3
Add 3 to each side
27+3 = 5x-3+3
30 = 5x
Divide by 5
30/5 = 5x/5
6 =x
3x+2 = 3(6)+2 = 18+2 = 20
2x-5 = 2(6)-2 =12-5 =7
Answer:
Length = 20 cm
Width = 7 cm
Step-by-step explanation:
Given that :-
The perimeter of a rectangle is 54 cm. Its length and width if the length is represented by 3x + 2 and the width is represented by 2x – 5.To find :-
Find the measures of length and width
Solution :-
To calculate the measures of length and width of rectangle . we gave given in question that perimeter of rectangle is 54 cm and length is represented by 3x + 2 and width is represented by 2x-5.Using Formula :-
Perimeter of rectangle = 2 ( l + b )
Where,
l is the length and w is the width of rectangle.Perimeter = 54 cmSubstitute the values
54 cm = 2 ( 3x + 2 + 2x - 5 )
Combine like terms
54 cm = 2 ( 3 x + 2 x + 2 - 5)
54 cm = 2 ( 5 x -3)
Simplify both sides of the equation.
54 = 2( 5x− 3 )
54 = (2)(5x) + (2)(−3). .. ( Distribute )
54 = 10x +−6
54 = 10x −6
Flip the equation.
10x −6 = 54
Add 6 to both sides.
10x −6 + 6 = 54 + 6
10x = 60
Divide both sides by 10.
10x / 10 = 60 / 10
x = 6
Therefore ,
Length = 3x + 2 =3 ×6 + 2 = 18 + 2 = 20 cm
Width = 2x- 5 = 2 × 6 - 5 = 12 - 5 = 7 cm
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A) if the y-coordinate is positive, the cosine will equal a positive charge.
B) if the x-coordinate are negative, the cosine will equal a negative value.
C) if the x-coordinate is in Quadrant l, the cosine will equal a negative value.
D) if the x- and y-coordinates are negative, the cosine will equal a positive value.
Answers
9514 1404 393
Answer:
B) if the x-coordinate is negative, the cosine will equal a negative value
Step-by-step explanation:
The cosine of the angle is the x-coordinate of the point where the terminal ray intersects the unit circle. Its sign will match the sign of the coordinates of point A on the terminal ray.
if the x-coordinate is negative, the cosine will be negative
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Answers
[tex] {36}^{2x + 5} = {216}^{x - 1} [/tex]
[tex] {6}^{2(2x + 5)} = {6}^{3(x - 1)} [/tex]
[tex] {6}^{(4x + 10)} = {6}^{(3x - 3)} [/tex]
Since bases i.e 6 are same exponents are equal
4x+10= 3x-3
4x-3x = -3-10
x= -13
Answer:
x = -13
Step-by-step explanation:
36 = 6^2
216 = 6^3
36^(2x + 5) = 6^(2)^(2x + 5)
When taking an exponent to an exponet: multiply the exponents
36^(2x + 5) = 6^(4x + 10)
216^(x - 1) = 6^(3)^(x - 1)
When taking an exponent to an exponet: multiply the exponents
216^(x - 1) = 6^(3x - 3)
-----------------------------
Therefor
6^(4x + 10) = 6^(3x - 3)
Since the bases are the same the exponents are equal
4x + 10 = 3x - 3
Subtract 3x from both sides
x + 10 = -3
subtract 10 from both sides
x = -13
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compounded monthly, how much will it be worth in 4 years?
Answers
Answer: $678.83
Step-by-step explanation:
A = P(1 + r/n)nt
A = 600.00(1 + 0.0309/12)(12)(4)
A = 600.00(1 + 0.002575)(48)
A = $678.83
Draw the next five shapes in this pattern.
Answers
Answer:
what next five shapes in the pattern
Answer:
I can make one up for you
Square , Circle , Square , Prism , Sphere , Cone , Semi-Circle , Square , Circle,
What are the next 5 shapes ?
Step-by-step explanation:
1/4 es mayor o menor que 3/16
Answers
Answer:
1/4
Step-by-step explanation:
Have a nice day :)
ten un buen dia :)
Answer: 3/16 es menor than 1/4.
The base of a solid right pyramid is a square with an
edge length of n units. The height of the pyramid is n
1 units
Which expression represents the volume of the
pyramid?
VA
on(n-1) units
on(n-1)2 units
or’n - 1) units
on*(n − 1) units
(n-1)
n
Answers
Answer:
C
Step-by-step explanation:
Base area = n^2
V = (base area * height)/3 = (n^2 *(n-1)/3 = 1/3n^2(n-1)
The expression for the volume of pyramid is V = ( 1/3 )n² ( n - 1 ) units³
What is the volume of a pyramid?The volume of a pyramid, is the product of the area of its base with the height of the pyramid, and divide by 3. We express this product with the formula V = ( 1/3) ×B×h, where B is the area of the base of the pyramid, and h is its height.
Volume of Pyramid = ( 1/3 )a²H
Given data ,
Let the base edge length of the solid pyramid be = n units
So , the base area of the pyramid = n² units²
Let the height of the pyramid be = ( n - 1 ) units
And , Volume of Pyramid = ( 1/3 )a²H
On simplifying , we get
V = ( 1/3 ) n² ( n - 1 ) units³
Hence , the expression is V = ( 1/3 ) n² ( n - 1 ) units³
To learn more about volume of pyramid click :
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[tex]what is the inverse of f(x)=2x+3[/tex]
Answers
Find the exact value of tan A in simplest radical form
Answers
Answer:
tan A = 4 / 7
Step-by-step explanation:
tan A = opp side / adjacent side
tan A = 4 / 7
Steven earns extra money babysitting. He charges $35.00 for 4 hours and $70.00 for 8
hours.
Enter an equation to represent the relationship. Let x represent the number of hours
Steven babysits and y represent the amount he charges.
The equation is y =
Answers
Answer:
Step-by-step explanation:
35/4 = 8.75
70/8 = 8.75
x= 1 (hour) y = 8.75$
Answer:
y= 35x/4
Step-by-step explanation:
We can solve this by plotting a graph of these values of (4,35) and (8,70). We find that this graph is a straight line. Meaning we can solve it in the form Y = mx, where m is the gradient. there is no y intercept as our range is greater than x =0. So the gradient will be 70-35/8-4, which is 35/4. Simply substitute it into the formula to obtain y= 35x/4!
A professor of statistics at NCSU refutes the claim that the average student spends 3 hours studying for the midterm exam. Which hypothesis is used to test the claim?
A. H_0: μ < = 3 vs. H_1: μ > 3
B. H_0: μ = 3 vs. H_1: μ ≠ 3
C. H_0: μ ≠ 3 vs. H_1: μ = 3
D. H_0: μ > = 3 vs. H_1: μ < 3
Answers
Answer:
D. H_0: μ > = 3 vs. H_1: μ < 3
Step-by-step explanation:
A professor of statistics at NCSU refutes the claim that the average student spends 3 hours studying for the midterm exam.
The claim is that the average student spends 3 hours studying, so the null hypothesis is that the mean is at least 3, that is:
[tex]H_0: \mu \geq 3[/tex]
At the alternative hypothesis, we test if the mean is less than 3, so:
[tex]H_1: \mu < 3[/tex]
This means that the correct answer is given by option D.
PLEASE ANSWER!! Find EF using Pythagorean theorem. Express answer to one decimal place.
Answers
Answer:
115.5 cm
Step-by-step explanation:
A^2 + B^2 = C^2
41^2 + 108^2 = C^2
C^2 = 13345
C = 115.5 cm
helpppp y’all sososososo
Answers
Answer:
3/4
Step-by-step explanation:
Answer:
I think the answer is 4/8 ✨
5.- Si en un gallinero contamos los picos, las crestas y las patas obtenemos 144, ¿Cuántas gallinas hay? Utiliza una
expresión algebraica.
Answers
Answer:
En total hay 36 gallinas en el gallinero.
Step-by-step explanation:
Dado que si en un gallinero contamos los picos, las crestas y las patas obtenemos 144, para determinar cuántas gallinas hay sabiendo que cada gallina tiene un pico, una cresta y dos patas, se debe realizar el siguiente cálculo:
X + X + 2X = 144
4X = 144
X = 144 / 4
X = 36
Por lo tanto, en total hay 36 gallinas en el gallinero.
After Noam transformed the graph of the function f (x)= |x|, the graph's vertex became (0,48), Which sequences of transformations could he had used - Need for a test, I see it was answered but there is no answer or how to get the answer. Please respond QUICK.....
Answers
Answer:
f(x) = |x|+48 would make the vertex be (0,48)
Step-by-step explanation:
Since the y-coordinate changed, this means that only vertical shift could have occured. Therefore, 48 must've been added to |x|.
Geri runs a total of3.1 miles, how many feet is this
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Based on geometric properties, which statements are correct?
A) The formula V = lwh can be used to model the shape of a cake.
B) The formula V = 1/2bhl can be used to model the shape of a tent
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Answers
Answer:
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Step-by-step explanation: I just did it on USATestPrep
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Answers
=========================================================
Explanation:
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