Use part 1 of the fundamental theorem of calculus to find the derivative of the function. g(x) = x e5t2 − 4t dt 4 g'(x) =

Answers

Answer 1

The derivative of the given equation is [tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex].

According to the statement

we have given that the statement and we have to find the derivative of that term.

So, We know that the

The given equation is

[tex]g(t) = \int\limits^x_4 {e^{5t^{2} - 4t} } \, dt[/tex]

Now find the derivative of that term

We find the derivative of the given term is with the help of the FTC.

And then

[tex]\frac{dg(x) }{dt} = {e^{5x^{2} - 4x} } \, \frac{dx}{dx}[/tex]

Then the equation become is

[tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex]

So, this is the derivative of the given equation.

So, The derivative of the given equation is [tex]\frac{dg(x) }{dx} = {e^{5x^{2} - 4x} } \,[/tex].

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Related Questions

use the compound interest formulas A=P e^rt to solve the problem given. round answers to the nearest cent.
Find the accumulated value of an investment of $15,000 for 6 years at an interest rate of 5.5% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.

Answers

Answer:

a) $20,771.76

b) $20,817.67

c) $20,484.80

d) $20,864.52

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsed

Part (a): semiannually

Given:

P = $15,000r = 5.5% = 0.055n = 2t = 6 years

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=15000\left(1+\frac{0.055}{2}\right)^{2 \times 6}[/tex]

[tex]\implies \sf A=15000\left(1.0275}{2}\right)^{12}[/tex]

[tex]\implies \sf A=20771.76[/tex]

Part (b): quarterly

Given:

P = $15,000r = 5.5% = 0.055n = 4t = 6 years

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=15000\left(1+\frac{0.055}{4}\right)^{4 \times 6}[/tex]

[tex]\implies \sf A=15000\left(1.01375}\right)^{24}[/tex]

[tex]\implies \sf A=20817.67[/tex]

Part (c): monthly

Given:

P = $15,000r = 5.5% = 0.055n = 12t = 6 years

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=15000\left(1+\frac{0.055}{12}\right)^{12 \times 6}[/tex]

[tex]\implies \sf A=15000\left(1+\frac{0.055}{12}\right)^{72}[/tex]

[tex]\implies \sf A=20484.80[/tex]

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

A = Final amountP = Principal amounte = Euler's number (constant)r = annual interest rate (in decimal form)t = time (in years)

Part (d): continuous

Given:

P = $15,000r = 5.5% = 0.055t = 6 years

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=15000e^{0.055 \times 6}[/tex]

[tex]\implies \sf A=20864.52[/tex]

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. If (5, 7) and (-3, 0) lie on the line ax - by = -20.

i) Find the value of a & b. [IM]
ii) Write the equation of the line in standard form.
iii) Find the coordinate of the point of intersections of the given line with x-axis and y-axis respectively.
iv) Find two more solutions of the given line. ​

Answers

i) The coefficients of the equation of the line are a = 20 / 3 and b = 160 / 21.

ii) The equation of the line in standard form is (20 / 3) · x + (160 / 21) · y = - 20.

iii) The x-intercept and y-intercept of the line are (- 3, 0) and (0, - 21 / 8).

iv) Two alternative solutions of the equation of the line are 20 · x + (160 / 7) · y = - 60 and 140 · x + 160 = 420.

How to derive the equation of a line?

In this problem we know that form of an equation of the line and two points, on which the line pass through. i) We determine the values of the coefficients a and b by solving the following system of linear equations:

5 · a - 7 · b = - 20

- 3 · a = - 20

Whose solution is a = 20 / 3 and b = 160 / 21.

ii) The equation of the line in standard form is (20 / 3) · x + (160 / 21) · y = - 20.

iii) Now we find the coordinates of the intercepts of the line:

x-Intercept

(20 / 3) · x = - 20

x = - 3

y-Intercept

(160 / 21) · y = - 20

y = - 21 / 8

iv) We can find two alternative solutions by using multiples:

20 · x + (160 / 7) · y = - 60

140 · x + 160 = 420

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Which of the following BEST defines an output? please help me, I've been stuck on this one for a while!​

Answers

A statement which best defines an output is: B. an output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.

What is a function?

A function can be defined as a mathematical expression that defines and represents the relationship between two or more variable, which is typically modelled as input (x-values) and output (y-values).

The types of function.

In Mathematics, there are different types of functions and these include the following;

Periodic functionInverse functionModulus functionSignum functionPiece-wise defined function

In this context, we can infer and logically deduce that a statement which best defines an output is that it's the result of a relation or the function rule, which usually are the y-values in a set of ordered pairs, on a table or a graph.

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Complete Question:

Which of the following best defines an output?

A. An output is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph.

B. An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.

C. An output is a special type of relation for which there is a rule that pairs each input with exactly one output.

D. An output is a set of ordered pairs in which no y-value repeats.

16. A rectangle's area is 18 m². Its perimeter is 18
m. One side is
(A)2 m
(B) 6 m
(C) 9 m
(D) 18 m

Answers

Answer is (B) 6
Reason
3 x 6 = 18 (area)
3 + 3 + 6 + 6 = 18 (perimeter)

The answer of your question is option (B)

What is the solution set 5.5x+15.5>32

Answers

Answer:

(3, ∝) or all values of x greater than +3

Step-by-step explanation:

The inequality is [tex]5.5x + 15.5 > 32[/tex]

Subtracting 15.5 from both sides yields

5.5x > 32 - 15.5 or 5.5x > 16.5

Dividing by 5.5 on both sides yields

x > 16.5/5.5 or x > 3

This means the inequality is valid for all values of x > 3

The solution set is the interval (3, ∝ )

Write the equation of the line passing through the point (a, b) and having a slope m.​

Answers

The equation of the line is b = am + c

What are linear equations?

Linear equations are equations that have a constant slope, average rate of change or gradients

How to determine the line equation?

The point is given as

(x, y) = (a, b)

The slope is given as

Slope = m

A linear equation is represented as

y = mx + c

Where me represents the slope

Substitute (x, y) = (a, b)

b = am + c

Hence, the equation of the line is b = am + c

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Which statements describe characteristics of a geometric sequence? check all that apply.

Answers

The Option A is correct that tells us that the There is a common ratio between the terms which represent the Characteristics of the G.P. Series.

According to the statement

we have to explain the characteristics of the Geometric Sequence.

So, For this purpose

We know that the

A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

From its definition it is clear that the

There is a common ratio between the terms.

And this point represent the characteristics of the Geometric Sequence not all other points.

Now, The option A is the correct rather than the other options.

So, The Option A is correct that tells us that the There is a common ratio between the terms which represent the Characteristics of the G.P. Series.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Which statements describe characteristics of a geometric sequence? Check all that apply.

a.There is a common difference between terms

b.Each term is multiplied by the same number to arrive at the next term.

c.The sequence increases or decreases in a linear pattern

d.There is a common ratio between terms

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What is the solution to 3/2b + 5 < 17? Explain how.
(1) b < 8

(2) b > 8

(3) b < 18

(3) b > 18

Answers

Answer:

[tex] \blue{b < 8}[/tex]

Answer 1 is correct

Step-by-step explanation:

[tex] \frac{3}{2} b + 5 < 17[/tex]

Take 5 to the right side.

[tex] \frac{3}{2} b < 17 - 5 [/tex]

[tex]\frac{3b}{2} < 12 [/tex]

Multiply both sides by 2.

[tex]3b <12 \times 2[/tex]

[tex]3b < 24[/tex]

Divide both sides by 3.

[tex]b < 8[/tex]

Find the radius of a circle with
circumference of 23.55 feet.
Use 3.14 for í.
Hint: C = 2πr
radius = [?] feet please explain your answer so I can understand how to do the rest

Answers

Answer:

r = 3.75

Step-by-step explanation:

C = 2(pi)r (write equation)

r = c / 2pi (rearrange for r)

r = 23.55 / 2(3.14) (plug in variables)

r = 23.55 / 6.28 (simplify)

r = 3.75 (solve)

Quick algebra 1 question for 10 points!

Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!

Answers

The answer to this question is 32

Answer:

22

Step-by-step explanation:

| 2^3 - 4*3^2 |  - 4 = | 8 - 36| - 4 =  28-4 = 24

What is the smallest positive integer having eactly 5 different positive integer divisors?

Answers

The smallest positive integer having exactly 5 different positive integer divisors is 60.

What are positive integers?Positive integers are the numbers that we use to count: 1, 2, 3, 4, and so on. A collection of positive integers excludes numbers with a fractional element that is not equal to zero and negative numbers. Positive integers can be used for addition, subtraction, multiplication, and division operations.

To find the smallest positive integer having exactly 5 different positive integer divisors:

Take out the LCM of 1,2,3,4, and 5.The LCM of 1,2,3,4, and 5 is 60.

Therefore, the smallest positive integer having exactly 5 different positive integer divisors is 60.

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Select the graph of the solution. Click until the correct graph appears. 3 x + 1 < 7

Answers

Answer:

Step-by-step explanation:

3x + 1 < 7...subtract 1 from both sides

3x < 7 - 1

3x < 6 ...divide both sides by 3

x < 6/3

x < 2

which means the second answer choice is correct!

Answer: Second Graph

Step-by-step explanation:

Given inequality

3x + 1 < 7

Subtract 1 on both sides

3x + 1 - 1 < 7 - 1

3x < 6

Divide 3 on both sides

3x / 3 < 6 / 3

x < 2

Apply the inequality to the graph

Since it is less than, the circle should be hollow

Since it is less than 2, the line should point to the left

Therefore, it should be the Second Graph

Using Euler's formula, how many
edges does a polyhedron with 9
faces and 14 vertices have?
[?] edges
Euler's Formula: F+ V=E+2

Answers

Answer:

Euler's Formula = F+V=E+2

F=9

V=14

So, 9+14=E+2

23=E+2

23-2=E

21=E

Hence, E (edges) = 21

Step-by-step explanation:

using the order of operations, which operation in the expression 3x2-2³÷4 should be completed first
A.multiply 3 and 2
B.divide 2³ by 4
C.cube 2
D.subtract 2³ from 2

Answers

Answer:

C.  Cube 2.

Step-by-step explanation:

Using PEMDAS  the first operation to be done is E (Exponent)  which is

2³.

A square field was enlarged by adding 5 feet to the length and width of the original field. if the area of the enlarged field is 576 square feet, what was the side length of the original field?

Answers

The side length of the original field is 19 feet.

What is square?

A square is a special kind of rectangle (an equilateral one) and a special kind of parallelogram (an equilateral and equiangular one). A square has four axes of symmetry, and its two finite diagonals (as with any rectangle) are equal. Bisection of a square by a diagonal results in two right triangles.

Suppose the original square is x feet wide. Since its the length and width are the same,

So, length of side of enlarged field = x+5

Area of new enlarged field =  side²  = ( x + 5 )²

So, the enlarged shape would be = ( x + 5 ) ( x + 5)

  Then ,  ( x + 5 ) ( x + 5) = 576

               ( x + 5 )²= 576

                x + 5 = √576

               x + 5  = 24

                 x = 24 - 5 ⇒ 19

Hence, The side length of the original field is 19 feet.

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Solve the given initial-value problem. y'' 4y' 5y = 35e−4x, y(0) = −5, y'(0) = 1

Answers

The solution for the initial value problem is [tex]y_{g} = e^{-2x} (-12cos(x) + 5sin(x)) + 7e^{-4x}[/tex]

Given,

y" + 4y' + 5y = 35[tex]e^{-4x}[/tex]

y(0) = -5

y'(0) = 1

Solve this homogenous equation to get [tex]y_{h}[/tex]

According to differential operator theorem,

[tex]y_{h}[/tex] = [tex]e^{ax}[/tex]( A cos (bx) + B sin (bx)), where A and B are constants.

Therefore,

y" + 4y' + 5y = 0

([tex]D^{2}[/tex] + 4D + 5)y = 0

D = -2± i    

[tex]y_{h} = e^{-2x} ( A cos (x) + B sin (x))[/tex]

Now, solve for [tex]y_{p}[/tex]

A function of the kind [tex]ce^{-4x}[/tex] is the function on the right, we are trying a solution of the form [tex]y_{p} =ce^{-4x}[/tex], here c is a constant.

[tex]y_{p} " + 4y_{p} ' + 5y_{p} = 35e^{-4x} \\=16ce^{-4x} -16ce^{-4x} +5ce^{-4x} = 35e^{-4x} \\= 5ce^{-4x} =35e^{-4x} \\c=\frac{35}{5} =7\\y_{p} =7e^{-4x}[/tex]

Then the general solution will be like:

[tex]y_{g} =y_{h} +y_{p} \\[/tex]

    = [tex]e^{-2x} (Acos(x)+Bsin(x))+7e^{-4x}[/tex]

[tex]y_{g}(0)=-5=A+7=-12\\y_{g} '(0)=e^{-2x} (-Asin(x)+Bcos(x))-2e^{-2x} (Acos(x)+Bsin(x))-28e^{-4x} \\y'_{g} (0)=1=B-2A-28\\[/tex]

       B = 1 - 24 + 28 = 5

Then the solution for the given initial value problem is

[tex]y_{g} =e^{-2x} (-12cos(x)+5sin(x))+7e^{-4x}[/tex]

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please please please

Answers

The amount of water in each mug is 2 / 5 litres

How to find the litres of water in each mug?

The water bottle has 4/5 litres of water.

The litre of water is poured equally in 2 mugs.

Therefore, the amount of water in each mug can be calculated as follows;

amount of water in each mug = 4 / 5 ÷ 2

amount of water in each mug = 4 / 5 × 1 / 2

amount of water in each mug =  4 / 10

amount of water in each mug = 2 / 5 litres

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In first gear, or low gear, an automobile's engine runs about three times as fast as the drive shaft. In second gear, the
engine does not have to run as fast; usually it runs about 1.6 times faster than the drive shaft. Finally, in third, or high
gear, the engine runs at the same speed as the drive shaft.
Engine speed = 2,100 r.p.m.
Transmission in first gear
Drive-shaft speed:

Answers

Engine is currently in first gear as mentioned in question

Speed=2100rpm

Drive shaft speed be x

3x=2100x=700rpm

Answer:

700 rpm

Step-by-step explanation:

A driveshaft is a shaft that transmits mechanical power.

Its speed is measured in rpm (revolutions per minute).

Engine speed

First gear: 3 × drive-shaft speedSecond gear: 1.6 × drive-shaft speedThird gear:  equal to drive-shaft speed

Given engine speed:

2,100 rpm

Therefore, the drive-shaft speeds in the different gears are:

First gear

Drive-shaft speed = 2100 ÷ 3 = 700 rpm

Second gear

Drive-shaft speed = 2100 ÷ 1.6 = 1312.5 rpm

Third gear

Drive-shaft speed = 2100 rpm

which expression shows how the distribuive property can be used to multiply 8x29?

Answers

The expression which shows how the distributive property of the can be used to multiply 8×29 as in the task content is; 8(20 + 9).

Which expression can be used to show how the distributive property can help multiply 8×29?

It follows from the task content that the given product to be multiplied is; 8×29.

Consequently, it follows from convention that the distributive property of multiplication allows that the multiplication in this case can be rewritten as follows;

8×29 = 8 (20 + 9)

Hence, we have; (8×20) + (8×9).

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Plot the axis of symmetry and the point where the maximum value occurs for this function: h(x) = -(x 2)2 8.

Answers

See attachment for the axis of symmetry and maximum point.

What is a function?A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. Originally, functions were the idealization of how a variable quantity depends on another quantity.

To plot the axis of symmetry:

The given function is: [tex]h(x) = -(x+2)^{2} +8[/tex]This function is in the form: [tex]g(x) = a(x-h)^{2} +k[/tex]Where the axis of symmetry is given by, x = h.y comparison, we have -h=2.This implies h=-2Therefore the axis of symmetry is x = -2.

Therefore, the maximum value occurs at the vertex, given by (h,k)=(-2,8).

So, see attachment for the axis of symmetry and maximum point.

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help fast pls!
it doesn't have to be a long explanation i just need the answer and a lil blurb to know ur not lying tysm!!!

Answers

Answer:

c  0.5⁻ˣ

Step-by-step explanation:

The slowest rate is:

0.5⁻ˣ

Ram sold to Shyam an article with 20% profit. Shyam sold same article for Rs. 504 with 5% profit to Ghanashyam. How much did it cost for Ram?
please do this with solutions quickly!!​

Answers

Answer:

Rs 400 is the cost of an article for Ram.....

Step-by-step explanation:

X - cost of an article for Ram

120% = 1.2

1.2*X - Ram’s selling price

5% = 0.05

1.2*X*0.05 - Shyam selling price

1.2*X*0.05 = 504

X = Rs 400 is the cost of an article for Ram

Hope it Helps!!!!

How many 5-letter words can be made using exactly 5 of the letters from
TEXAS and MEXICO? Letters may only be used as many times as they appear. (For
example, XETEX is allowed. However, MATEA is not allowed, since the A appears twice
in MATEA but only once in the given words.)

Answers

The total number of ways by words are formed is 35 ways.

According to the statement

We have given that the 5 letters and we have to make word from them and the letters are repeated as equal to letters in given words.

And we have to find the possible ways.

So, The given words are:

TEXAS and MEXICO

Here X = 2 and E = 2 and all other words are one time used words.

We can find possible ways by use of combination and permutation.

So,

Total number of ways = [tex]3C_{1} ^{5} + 2C_{2} ^{5}[/tex]

here 3 because three letters are not repeatable and 2 letters are repeated for 2 times.

So,

Total number of ways = [tex]3C_{1} ^{5} + 2C_{2} ^{5}[/tex]

Total number of ways = [tex]3(\frac{5!}{1!} ) + 2(\frac{5!}{2!*3!} )[/tex]

Total number of ways = [tex]3(5) + 2(10)[/tex]

Total number of ways = 15 + 20

Total number of ways = 35.

So, The total number of ways by letters are formed is 35 ways.

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Find the co-ordinates of a point which lies on the line joining M(7, -3) and N(-2,-5). If x ordinates of that point is 3.​

Answers

Answer:

(3, -3 8/9)

Step-by-step explanation:

Use a slope calculation or a graph to find the slope of the line.

m = (y-y)/(x-x)

m = (-3- -5)/(7- -2)

m = 2/9

Then write the equation of the line. I used point-slope form. (You could use y=mx+b, slope-intercept form, but you'd have to first calculate b as well)

Point-slope form:

y -Y = m(x-X)

y - -3 = 2/9(x- 7)

y + 3 = 2/9(x - 7)

We know the x-coordinate of the point we're looking for is 3. Fill that in as well and calculate the y that goes with it.

y + 3 = 2/9(3-7)

y+3=2/9(-4)

y = -8/9 - 3

y = -3 8/9

In decimal form this is -3.8888repeating

see image.

The point at x=3 on the line between M(7,-3) and N(-2,-5) is (3, -3 8/9).

A package is oscillating on a spring scale with a period of 5.00 s. at time t = 0.00 s the package has zero speed and is at x = 8.50 cm. at what time after t = 0.00 s will the package first be at x = 4.50 cm?

Answers

Under the assumption of simple harmonic motion, the package will be at x = 4.50 centimeters at a time of 0.805 seconds.

How to analyze an object on simple harmonic motion

Simple harmonic motion is a kind of periodic motion represented by sinusoidal functions. Physically speaking, it is a good approximation for periodic motion due to small perturbations and with absence of frictions and viscous forces on the system.

The position of an object under simple harmonic motion is described by the following equation:

x (t) = A · cos (2π · t / T + Ф)      (1)

Where:

A - Amplitude, in centimetersT - Period, in secondsФ - Angular phase, in radiansx(t) - Position, in centimeters

If we know that T = 5 s, A = 8.50 cm, Ф = 0 rad and x = 4.50 cm, then the time when the package will reach x = 4.50 cm is:

4.50 = 8.50 · cos (2π · t / 5)

9 / 17 = cos (2π · t / 5)

0.322π = 2π · t / 5

t = 0.805 s

Under the assumption of simple harmonic motion, the package will be at x = 4.50 centimeters at a time of 0.805 seconds.

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Examine the ratios to find the one that is not equivalent to the others.

StartFraction 2 Over 5 EndFraction = StartFraction 6 Over 10 EndFraction = StartFraction 8 Over 20 EndFraction = StartFraction 12 Over 30 EndFraction

Which ratio is different from the other three?

Answers

The ratio is different from the other three is StartFraction 6 Over 10 EndFraction; 6/10.

Ratio

A ratio is a number representing a comparison between two named things.

StartFraction 2 Over 5 EndFraction = StartFraction 6 Over 10 EndFraction = StartFraction 8 Over 20 EndFraction = StartFraction 12 Over 30 EndFraction

2/5 = 6/10 = 8/20 = 12/30

2/5 = 0.4

6/10 = 0.6

8/20 = 0.4

12/30 = 0.4

Therefore, the ratio is different from the other three is StartFraction 6 Over 10 EndFraction; 6/10

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Arc CD is Two-thirds of the circumference of a circle. What is the radian measure of the central angle?
StartFraction 2 pi Over 3 EndFraction radians
StartFraction 3 pi Over 4 EndFraction radians
StartFraction 4 pi Over 3 EndFraction radians
StartFraction 3 pi Over 2 EndFraction radians

Answers

Using proportions, it is found that the radian measure of the central angle is given as follows:

[tex]\frac{4\pi}{3}[/tex] radians.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The entire circumference is equivalent to a central angle of [tex]2\pi[/tex] radians. Hence the radian measure of the central angle considering two-thirds of the circumference is given as follows:

[tex]\frac{2}{3} \times 2\pi = \frac{4\pi}{3}[/tex]

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Answer:

Step-by-step explanation:

c edge

Help!!

why might you choose to write a recursive formula rather than an explicit formula to define a sequence

a. you need to know the 54th term in the sequence

b. the sequence is neither arithmetic or geometric

c. you need to know the value of three non-sequential terms in the sequence

d. the sequence is strictly geometric

Answers

We might choose to write a recursive formula rather than an explicit formula to define a sequence because (D) the sequence is strictly geometric.

What is a sequence?A sequence in mathematics is an enumerated collection of items in which repetitions are permitted and order is important. It, like a set, has members (also called elements, or terms). The length of the series is defined as the number of items (which could be infinite). Unlike a set, the same components can appear numerous times in a sequence at different points, and the order does important. Formally, a sequence can be defined as a function from natural numbers (the sequence's places) to the elements at each point. The concept of a sequence can be expanded to include an indexed family, which is defined as a function from an index set that may or may not contain integers to another set of elements.

Recursive formulas are commonly used to compute the nth term of a sequence, where a(n) is the sum of all the preceding values.

Using its position, explicit formulas can compute a(n).

Therefore, we might choose to write a recursive formula rather than an explicit formula to define a sequence because (D) the sequence is strictly geometric.

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Answer: (D)

Step-by-step explanation:

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Given f(x) = 3x - 5 which statement is true? Explain how.
(1) f(0) = 0
(2) f(3) = 4
(3) f(4) = 3
(4) f(5) = 0

Answers

Answer:

(2)

Step-by-step explanation:

by substituting the values of x into f(x) and evaluating

f(0) = 3(0) - 5 = 0 - 5 = - 5 ≠ 0

f(3) = 3(3) - 5 = 9 - 5 = 4 ← True

f(4) = 3(4) - 5 = 12 - 5 = 7 ≠ 3

f(5) = 3(5) - 5 = 15 - 5 = 10 ≠ 0

Hence, statement 2 is true for the equation f(x) = 3x-5

What is equation?

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

Types of Equations:

 Linear Equation: More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1.

  Quadratic Equation: This equation is of second order. At least one of the variables in a quadratic equation needs to be raised to exponent 2.

  Cubic Equation: A third-order equation is this one. At least one of the variables in cubic equations needs to be raised to exponent 3.

  Rational Equation: A fractional equation having a variable in the numerator, denominator, or both is referred to as a rational equation.

Substituting the values of x into f(x) and evaluating

f(x) = 3x - 5

put x = 0

f(0) = 3(0) - 5

= 0 - 5 = - 5

put x = 3

f(3) = 3(3) - 5

= 9 - 5

= 4

put x = 4

f(4) = 3(4) - 5

= 12 - 5

= 7

put x = 5

f(5) = 3(5) - 5

= 15 - 5

= 10

hence statement 2 is true.

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Ask your teacher find the limit. use l'hospital's rule where appropriate. if there is a more elementary method, consider using it. lim x→1 [ln(x5 − 1) − ln(x3 − 1)]

Answers

Answer:

  ln(5/3)

Step-by-step explanation:

The desired limit represents the logarithm of an indeterminate form, so L'Hopital's rule could be applied. However, the logarithm can be simplified to a form that is not indeterminate.

Limit

We can cancel factors of (x-1), which are what make the expression indeterminate at x=1. Then the limit can be evaluated directly by substituting x=1.

  [tex]\diplaystyle \lim\limits_{x\to1}{(\ln(x^5-1)-\ln(x^3-1))}=\lim\limits_{x\to1}\ln{\left(\dfrac{x^5-1}{x^3-1}\right)}\\\\=\lim\limits_{x\to1}\ln\left(\dfrac{x^4+x^3+x^2+x+1}{x^2+x+1}\right)=\ln{\dfrac{5}{3}}[/tex]

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