Answers
The limit intercepted by the given function, f'(8) is [tex]\lim_{n \to \8} \frac{\sqrt[3]{(x-8)} -8 }{x-8}[/tex]
What is limit?A limit is a value toward which an expression converges as one or more variables approach certain values, a limit tells us the value of a function when its input closes to a certain value. Limits are used to define continuity, derivatives, and integrals. The limit of a product is equal to the product of the limits. The limit of a quotient is equal to the quotient of the limits. The limit of a constant function is equal to the constant.
Given that a function, f(x) = ∛x
The formula for applying the limit is :-
The first derivative is given by,
f'(x) = limx->c (f(x) - f(c))/(x-c)
Applying limit, we get,
f'(x) = [tex]\lim_{n \to \8} \frac{\sqrt[3]{(x-8)} -8 }{x-8}[/tex]
Hence, The limit intercepted by f'(8) is [tex]\lim_{n \to \8} \frac{\sqrt[3]{(x-8)} -8 }{x-8}[/tex]
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Related Questions
Create an equivalent expression for ( 1.4³ / 1.2⁴)⁻⁶
1.4³/1.2²
1.2²/1.4³
1.4¹⁶/1.2²⁴
1.2²⁴/1.4¹⁶
Answers
The correct answer is: [D]: " [tex]\frac{(1.2)^2^4}{(1.4)^1^8}[/tex] "
Step-by-step explanation:
Given: ( 1.4³ / 1.2⁴)⁻⁶ ;
Note the following properties of exponents:
1) [tex]a^-^b = \frac{1}{a^b}[/tex] ; { [tex]a\neq 0[/tex] } ; and:
2) the 'power of a fraction' rule:
[tex](\frac{a}{b})^c} =\frac{a^c}{b^c}[/tex] ; [tex]b\neq 0[/tex] '
As such:
[tex](\frac{1.4^3}{1.2^4})^{-6}[/tex] ;
= 1 ÷ ( [tex]\frac{1.4^3}{1.2^4})^{6}[/tex] ;
= [tex]\frac{1}{1}[/tex] ÷ ( [tex]\frac{1.4^3}{1.2^4})^{6}[/tex] ;;
= [tex]\frac{1}{1}[/tex] ÷ [tex]\frac{1.4^(^3^*^6^)}{1.2^(^4^*^6^)}[/tex] ;
Note the follow property of exponents:
" [tex](\frac{a}{b})^c = \frac{a^c}{b^c}[/tex] " ; {" b ≠ 0 "}.
⇒ = [tex]\frac{1}{1}[/tex] ÷ [tex]\frac{1.4^(^1^8^)}{1.2^(^2^4^)}[/tex]
Note: Dividing by a fraction or a number; is the same as multiplying by the reciprocal (invert) of that number.
= [tex]\frac{1}{1}[/tex] * [tex]\frac{1.2^(^2^4^)}{{1.4^(^1^8^)}}[/tex] ;
= " [tex]\frac{1.2^(^2^4^)}{{1.4^(^1^8^)}}[/tex] " ;
which corresponds to:
Answer choice: [D]: " [tex]\frac{1.2^(^2^4^)}{{1.4^(^1^8^)}}[/tex] " .
____________
Hope this is helpful! Best of luck!
____________
Oh where do I even start?
Answers
4x-10x=-34-32
-6x=-66
X=11
JL=4x+34=4•11+34=78
JL=78
Brainly pls
Which statement is correct about the product of
3
2
3
and
10
9
?
Because
10
9
is greater than 1, the product of
3
2
3
and
10
9
is greater than
3
2
3
.
Because
10
9
is less than 1, the product of
3
2
3
and
10
9
is greater than
3
2
3
.
Because
10
9
is less than 1, the product of
3
2
3
and
10
9
is less than
3
2
3
.
Because
10
9
is greater than 1, the product of
3
2
3
and
10
9
is less than
3
2
3
.
Answers
option B is correct. 10/9 is greater than 1, the product of [tex]3\frac{2}{3}[/tex] and 10/9 is greater than 3 is the statement,
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
We need to find the product of [tex]3\frac{2}{3}[/tex] and 10/9.
Firstly let us convert the mixed fraction [tex]3\frac{2}{3}[/tex] to the improper fraction.
11/3 is the simplified form of [tex]3\frac{2}{3}[/tex]
11/3×10/9
110/27
4.1
As we observe the 10/9 is greater than 1, the product of [tex]3\frac{2}{3}[/tex] and 10/9 is greater than 3.
Hence, the statement 10/9 is greater than 1, the product of [tex]3\frac{2}{3}[/tex] and 10/9 is greater than 3.
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please have the right answers nothing wrong
Answers
The total distance walked in each case is given below;
15 feet4.5 feet6.75 feet1.5 feet1.5x feetWhat is the total distance?Jada's pet turtle walked 10 feet, and then half that length again
Total distance = 10 + (1/2 of 10)
= 10 + (1/2 × 10)
= 10 + 5
= 15 feet
Jada's pet baby brother walked 3 feet, and then half that length again
Total distance = 3 + (1/2 of 3)
= 3 + (1/2 × 3)
= 3 + 1.5
= 4.5 feet
Jada's pet hamster walked 4.5 feet, and then half that length again
Total distance = 4.5 + (1/2 × 4.5)
= 4.5 + 2.25
= 6.75 feet
Jada's pet robot walked 1 foot, and then half that length again
Total distance = 1 foot + (1/2 × 1)
= 1 + 0.5
= 1.5 feet
A person walked x feet, and then half that length again
Total distance = x + (1/2 × x)
= x + 1/2x
= 1.5x feet
In conclusion, the total distance is calculated by adding the initial distance and additional distance
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Please help I’m not sure how to do this
Answers
The proof that shows that ΔLMN ≅ ΔQPN by either SSS or SAS is explained below.
How to Prove that Two Triangles are Congruent by SAS or SSS?If we can show that two triangles have two pairs of congruent sides and a pair of corresponding congruent included angles, then we can state they are congruent triangles based on the SAS theorem.
On the other hand, if all three corresponding side lengths are congruent to each other, then the triangles are congruent by the SSS theorem.
The proof that can be used to show that the two triangles are congruent by SAS is shown below:
Statement Reasons
1. ∠L ≅ ∠Q, LM ≅ QP, 1. Given
MN ≅PN, NL ≅ NQ
2. ΔLMN ≅ ΔQPN 2. SSS
Based on the given information we are given, another way of writing this proof can be:
Statement Reasons
1. ∠L ≅ ∠Q, LM ≅ QP, 1. Given
MN ≅PN, NL ≅ NQ
2. ΔLMN ≅ ΔQPN 2. SAS
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Pls help me. I’m stuck on this
Answers
The value of t for the given triangle angle will be equal to 1.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given the three angles of the triangle are 111,34, and 35t. The value of t will be calculated as,
35t + 111 + 34 = 180
35t = 180 - 111 - 34
35t = 35
t = 1
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50 POINTS ASAP!!!!!!!!!!!!!!!! 50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!!!!!!!!!!!! 50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!
Answers
Answer:
reflection over the y-axis
Step-by-step explanation:
Answer:
C?
Step-by-step explanation:
The measure of one of the small angles of a right triangle is 6 more than 3 times the measure of the other small angle. Find the measure of both angles.
Input your answers into the following boxes.
The measures of the two angles in the order from the smallest to the greatest are
degrees and
degrees.
Answers
The measures of two angles in the order from the smallest to the greatest are 21° and 69°.
What is a right triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Given the acute angle of a right triangle is 6 more than 3 times the measure of the other small angle.
Assume that the measurement of smaller angle is x.
Then the mathematical expression of 6 more than 3 times of x is 6 + 3x.
The measure of third angle is 90° since it a right triangle.
The sum of all interior angles of a right triangle is 180°.
The equation is
x + (6 + 3x) + 90 =180
x + 6 + 3x + 90 =180
Combine like terms:
(x + 3x) + (6 + 90) = 180
4x + 96 = 180
Subtract 96 from both sides:
4x = 180 - 96
4x = 84
Divide both sides by 4
x = 21
Putting x = 21 in the expression (6 + 3x) :
6 + 3x = 6 + 63 = 69.
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Given the equation cosx = x^2 prove that it has at least one root in the [0, pi] interval. Justify answer by indicating the theorem used.
Answers
1 is the root of the equation cosx = x² in the interval [0, pi]/
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given equation is cosx = x²
cosx-x²=0
y(x)=cosx-x²
y(0)=1
y(π)=-1-π²
y(π)<0<y(0) and y is continuous, there must be a value of x in [0, pi]
where
cosx−x²=0.
Hence, 1 is the root of the equation cosx = x² in the interval [0, pi].
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Consider the functions f(x) = 223 + 922 + 3x + 12 and g(x) = 323 + 10x2 + × + 8.
The graph of their difference, f(x) - g(x), is shown on the coordinate grid.
What is/are the solution(s) to the equation f(x) - g(x) = 4?
List the solutions from least to greatest separated by a coma(s).
Answers
The solutions for the given equation is x=0, x=-4 and x=3.
The given functions are f(x)=2x³+9x²+13x+12 and g(x)=3x³+10x²+x+8.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Now, f(x)-g(x)
= 2x³+9x²+13x+12-(3x³+10x²+x+8)
= 2x³+9x²+13x+12-3x³-10x²-x-8
= -x³-x²+12x+4
Graph the cubic using its end behavior and a few selected points.
Rises to the left and falls to the right
Plot (-2, -16), (-1, -8), (0, 4), (1, 14) and (2, 16)
Given f(x)-g(x)=4
-x³-x²+12x+4=4
⇒ -x³-x²+12x=0
⇒ -x(x²+x-12)=0
⇒ x=0 and x²+x-12=0
⇒ x=0 and x²+4x-3x-12=0
⇒ (x+4)(x-3)=0
⇒ x=0, x=-4 and x=3
Therefore, the solutions for the given equation is x=0, x=-4 and x=3.
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A rectangle with a perimeter of 40 inches has a width that is 3 times the length. What is the length And the width
Answers
The Length is 5 inches and the Breadth is 15 inches
What is Perimeter?
A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter.
Solution:
Perimeter of Rectangle = 2*(Length + Breadth)
According to the question
Breadth = 3*Length
Perimeter = 40
40 = 2*(Length + 3*Length)
20 = 4*Length
Length = 5 inch
Breadth = 15 inch
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The cost of 2 kg of carrots is £7 Work out the cost of 5 kg of carrots.
Answers
Answer:
56
Step-by-step explanation:
The graph of the line with equation Y equals 2/3 X is shown. What is the product of 2/3 and -3
Answers
Answer:
-2
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] * -3
= [tex]\frac{2}{3}[/tex] * [tex]-\frac{3}{1}[/tex]
= [tex]-\frac{6}{3}[/tex]
= [tex]-\frac{2}{1}[/tex]
= -2
which of the following is not a characteristic of a binomial probability distribution?
Multiple choice
Each outcome is mutually exclusive
Each trial is Independent
The probability of sucess remains constant from trail to trail
The number of trails is limited to two
Answers
Answer: The number of trials is limited to two.
In the image below, is a leg of the 45-45-90 triangle.
Answers
Reason:
x and y are the legs.
[tex]5\sqrt{2}[/tex] is the hypotenuse.
The hypotenuse is always opposite the 90 degree angle.
The hypotenuse is always the longest side of any right triangle.
The student made a mistake in solving the equation above. What did the student do wrong?
Answers
In solving the equation, the student did the division wrong, and 29.4/4.2 = 7 which is correct.
What is division?Multiplication is the opposite of division.
If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.
Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
So, the equation is:
4.2p = 29.4
Let's solve as follows:
4.2p = 29.4
p = 29.4/4.2
p = 7
So, the value of p comes to 7.
Where in the image, the value of p is 123.48 which is wrong as the division is not done properly.
Therefore, in solving the equation, the student did the division wrong, and 29.4/4.2 = 7 which is correct.
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A club swimming pool is 34 ft wide and 48 ft long. The club members want an exposed aggregate border in a strip of uniform width around the pool. They have enough material for 344 ft2. How wide can the strip be?
Answers
Answer:
29
he area of the pool is 34 ft * 48 ft = <<34*48=1632>>1632 ft2.
Thus, the total area of the pool and the border strip is 1632 ft2 + 344 ft2 = <<1632+344=1976>>1976 ft2.
Hence, the border strip is 1976 ft2/34 ft = <<1976/34=58>>58 ft long.
Therefore, the border strip can be 58 ft/2 = <<58/2=29>>29 ft wide. Answer: {29}.
Points A(-6,10) and B(2,14) lie on circle O with its center at (2,4) what are the coordinates of point C, which is the midpoint of AB what is the relationship between chord AB and segment OC select the correct answer from drop down menu point C is located at chord Ab is segment OC
Answers
The coordinates of point C is (-2, 12)
The segment OC is perpendicular to the chord AB.
What is midpoint of a line segment?The midpoint of a line segment is given as,
x = (a + c)/2
y = (b + d) / 2
Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.
We have,
Points A(-6,10) and B(2,14) lie on circle O with its center at (2,4).
C is the midpoint of the chord AB.
Now,
The coordinates of C = (x, y).
x = (-6 + 2) / 2 = -4/2 = -2
y = (10 + 14) / 2 = 24/2 = 12
(x, y ) = (-2, 12)
The relationship between chord AB and segment OC.
The segment OC is perpendicular to the chord AB.
Thus,
The coordinates of C is (-2, 12)
The relationship between segment OC and chord AB is that segment OC is perpendicular to chord AB.
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From 2010 to 2012, the average selling price of tablets decreased by 20%. This percent
reduction amounted in a decrease of $140. Find the average selling price of tablets in 2010
and in 2012.
In 2010, the average selling price was $, and in 2012, the average selling price was $[
Answers
Answer:
In 2010, the average selling price was $700, and in 2012, the average selling price was $560.
identify the measure of angle x. i need answer asap
Answers
After solving the angles, the measure of angle x is 145°.
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created.
The vertex of an angle is the location where two points come together.
The Latin word "angulus," which means "corner," is where the term "angle" originates.
The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.
A geometrical shape called an angle is created by connecting two rays at their termini.
In most cases, an angle is expressed in degrees.
(Refer to the image attached below)
We can see that ∠ABC is a straight angle.
∠ABC = ∠ABD + ∠DBC where ∠ABD is x.
Now, solve for x as follows:
∠ABD + ∠DBC = ∠ABC
x + 35 = 180
x = 180 - 35
x = 145°
Therefore, after solving the angles, the measure of angle x is 145°.
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Solve the systems and please show all work using substitution.
Answers
The value of x = -84/17, y= 24/17 and z = 9/17
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
x -2y + z= -6
x- 5z= -12
-x+ 6y + 4z = 3
Put x= -12+ 5z in equation 1 and 3
-12+ 5z - 2y + z= -6
6z - 2y = 6
3z - y= 3............(a)
and, 12 - 5z + 6y + 4z = 3
6y - z = -9.......(b)
Solving a and b we get
6(3z- 3) - z = -9
18z - 18 - z= -9
17z = 9
z= 9/17
and, y= 3(9/17) - 3 = 24/17
and, x = -12 + 120/17= -84/17
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Solve the equation. .35(x+4)=.25(X-6)
Answers
Help would be appreciated
Answers
The correct reason for the similarity of triangles ADC and CBA is given as follows:
SSA.
What are the similarity theorems?The similarity theorems are listed as follows:
SAS: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent by the SAS theorem.ASA: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent by the ASA theorem.SSS: If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are congruent by the SSS theorem.SSA: If two sides and an angle not include between them are respectively equal to two sides and an angle of the other then the two triangles are congruent by the SSA theorem.In this problem, we have that:
Sides AB and DC are equal.Angles BAC and DCA are equal.Sides AC are equal.Two sides and an angle not between them, hence they are congruent by the SSA theorem.
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To simplify 8.3-4 1/5 (6.1+1/2) which operation must be performed first? Which is second and which is third?
Answers
the answer to the expression 8.3-4 1/5 (6.1+1/2)is -19.42
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
The given expression
8.3-4 1/5 (6.1+1/2)
=8.3-4 1/5 (6.6)
=8.3-(6.6*21/5)
=-19.42
Hence the answer is -19.42
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Turn 584/50 in improper fraction 
Answers
584/2
50/2
295/50 div 2
295/25
a summer soccer cam ordered a total of 84 soccer balls and t-shirts for the season. Soccer balls cost $25 each and t-shirts cost $9.50 each. if they paid $1,046 total for the purchase, how many of each item was ordered?
Answers
The Number of Soccer Balls is 16 and the Number of T-Shirts is 68
What is Linear Equation in Two Variables?
A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.
Solution:
Let,
Number of Soccer Balls = x
Number of T-Shirts = y
Equation 1:
x + y = 84 -----------(i)
Equation 2:
25x + 9.5y = 1046 ----------(ii)
Multiplying Equation 1 by 25
25x + 25y = 2100 ---------(iii)
Substracting Equation2 from Equation 1
15.5y = 1054
y = 68
So, x = 16
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A 25-foot-long footbridge has two diagonal supports that meet in the center of the bridge. Each support makes a 65∘ angle with a short vertical support.
What is the length x of a diagonal support, to the nearest tenth of a foot?
x≈_____ feet
Answers
x≈ 13 feet
Cuz I said so
17/6 divided 5/3 what’s the answer
Answers
Answer:
17/6 divided by 5/3 is equal to 17/6 * 3/5, which simplifies to 51/30.
In the data set shown below, what is the value of the quartiles?
{1.3, 1.5, 1.7 2.95, 2, 2.5, 2.7, 2.9, 3, 3.1}
A. Q1 = 1.6; Q2 = 2.5; Q3 = 2.92
B. Q1 = 1.7; Q2 = 2.5; Q3 = 3
C. Q1 = 1.7; Q2 = 2.5; Q3 = 2.9
D. Q1 = 1.6; Q2 = 2.5; Q3 = 2.95
Answers
Answer:
To find the value of the quartiles, we need to first find the median of the data set. The median is the middle value of the data set, or the value that separates the lower half of the data from the upper half. In this data set, the median is 2.5, as it is the middle value when the data is arranged in ascending order.
Once we have the median, we can find the first and third quartiles. The first quartile, also known as Q1, is the median of the lower half of the data set, and the third quartile, also known as Q3, is the median of the upper half of the data set. In this data set, the lower half of the data is {1.3, 1.5, 1.7, 2, 2.5}, and the upper half of the data is {2.7, 2.9, 3, 3.1}. The median of the lower half is 1.7, and the median of the upper half is 2.9.
Therefore, the value of the quartiles is Q1 = 1.7, Q2 = 2.5, and Q3 = 2.9.
Option C, Q1 = 1.7; Q2 = 2.5; Q3 = 2.9, is the correct answer.
Step-by-step explanation:
Answer:
2.95
Step-by-step explanation:
can someone please help
Answers
Step-by-step explanation: When you divide the 2 by 9, you get like 0.222222 (and it repeats forever), then since the 2 is less than 5, you round down, so it would be 0.22 after rounding. I hoped this helped!