For the following function y = f(x) = 4x^3 - 5


I worked out this Calculus problem, but I keep getting 1/-432 for part c. Can anyone work out the problem step-by-step so I can understand what I’m doing wrong? It would be greatly appreciated.

The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula [tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex], equivalent to the recurrence formula [tex]a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}[/tex].

A sequence is a set of elements which observes at least a defined rule. In this question we see a sequence which follows this rule:

[tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex]      (1)

Now we prove that given expression contains the pattern:

n = 0

7

n = 1

7 + (- 1)² · 2² = 7 + 4 = 11

n = 2

7 + (- 1)² · 2² + (- 1)³ · 3² = 11 - 9 = 2

n = 3

7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² = 2 + 16 = 18

n = 4

7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² + (- 1)⁵ · 5² = 18 - 25 = - 7

The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula [tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex], equivalent to the recurrence formula [tex]a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}[/tex].

To learn more on patterns: https://brainly.com/question/23136125

#SPJ1

Using linear functions, it is found that the airplane and the helicopter will be at the same altitude after 20 minutes.

A linear function is modeled by:

y = mx + b

In which:

The functions that gives the height of the airplane and the helicopter, after t minutes, is given by:

They will be equal when:

A(t) = H(t).

Hence:

30000 - 1000t = 500t

1500t = 30000

t = 30000/1500

t = 20 minutes.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

By critically observing the given graphs, we can logically deduce that "graph C" returns greatest integer that is less than or equal (≤) to x.

A greatest integer function can be defined as a type of function which returns the greatest integer that is less than or equal (≤) to the number.

Mathematically, the greatest integer that is less than or equal (≤) to a number (x) is represented as follows:

y = [x].

By critically observing the given graphs, we can logically deduce that y in "graph C" returns greatest integer that is less than or equal (≤) to x.

Read more on greatest integer function here: https://brainly.com/question/12165085

#SPJ1

Step-by-step explanation:

Can you attach the questions please? Thanks

answer

Step-by-step explanation:

there are only one

painting, sculpture and photograph.

Answer:

0.2   [or 2/10    ;     or 1/5]

Step-by-step explanation:

100x = 1/10×200

100x = 20

÷100     ÷100

x = 0.2

check:

100 × 0.2 = 20

1/10 × 200 = 20

20 = 20

[true statement]

(Or, you know that 100 is half of 200, and to get from 100 to 200 we had to multiply by 2, and that 100 x 2/10 will be equal; this is harder to word though)

The solution of the given quadratic equation is x=-2 or x=-3.

The given quadratic equation is x²+5x+6=0.

The different methods of solving quadratic equations are factoring, completing the square or using the quadratic formula.

By using the splitting middle term method we can solve x²+5x+6=0.

That is, x²+2x+3x+6=0

⇒x(x+2)+3(x+2)=0

⇒(x+2)(x+3)=0

⇒(x+2)=0, (x+3)=0

⇒x=-2 or x=-3.

Therefore, the solution of the given quadratic equation is x=-2 or x=-3.

To learn more about the quadratic equation visit:

https://brainly.com/question/2263981.

#SPJ1

Answer:

60°

Step-by-step explanation:

since angle on straight line is 180° you take the sum of the exterior angle of R and its interior angle then divide both sides by the coefficient of y to find y then things get easier from there

Answer:

Step-by-step explanation:

Plan

7y and 5y are made on the same straight line. Therefore they are supplementary and add to 180 degrees. <s has to be found by finding 3x and 5y first. Find <s by solving 3y + 5y + x = 180 degrees.

Solution

7y + 5y = 180 degrees               Combine the left

12y = 180 degrees                      Divide by 12

12y/12 = 180/12

y = 15

3y + 5y + x = 180                         Combine the left side

8y + x = 180                                  Substitute 15 for y

8*15 + x = 180                               Combine

120 + x = 180                                Subtract 120 from both sides

120 -120 +x =180 - 120                 Combine

x  = 60

Answer

s = 60 degrees

<TRS = 5y = 75

Answer:

12 minutes

Step-by-step explanation:

added in the picture

The length of CD is 7-3=4.

Therefore, if we dilate by a scale factor of 3, the length is 4(3) = 12

Answer:

b) 12

Step-by-step explanation:

the length of the image is 12. i just know. trust me.

[tex]{\huge \underline{{ \fbox \color{red}{A}}{\fbox \color{green}{n}}{\fbox \color{purple}{s}}{\fbox \color{brown}{w}}{\fbox \color{yellow}{e}}{\fbox \color{gray}{r } }}}[/tex]

Answer :- The result is 5cm

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\bf \red {c {}^{2} = a {}^{2} + b {}^{2}} }[/tex]

[tex] \: \: \: \: \: \: \boxed{ \bf \green{c {}^{2} = (3cm) {}^{2} + (4cm) {}^{2}}}[/tex]

[tex] \: \: \: \: \: \: \: \: \boxed{ \bf \gray{c {}^{2} = 9cm {}^{2} + 16cm {}^{2} }}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \blue {c {}^{2} = 25cm {}^{2} }}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \green{\not{\sqrt {c {}^{ \not{2} }}} = \sqrt{25cm {}^{2} }}}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \red{c = 5cm}}[/tex]

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: hypotenuse = 5 \:\:cm [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \textsf{Pythagoras Theorem } [/tex]

[tex]\qquad \tt \rightarrow \: h {}^{2} = p {}^{2} + b {}^{2} [/tex]

[ h = hypotenuse, p = perpendicular and b = base ]

[tex]\qquad \tt \rightarrow \: {h}^{2} = {3}^{2} + {4}^{2} [/tex]

[tex]\qquad \tt \rightarrow \: {h}^{2} = 9 + 16[/tex]

[tex]\qquad \tt \rightarrow \: h {}^{2} = 25[/tex]

[tex]\qquad \tt \rightarrow \: h = \sqrt{25} [/tex]

[tex]\qquad \tt \rightarrow \: h = 5 \: \: cm[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The correct answer is option A which is the pattern {prime, prime, prime, composite, prime, prime} is followed by 1, 5, 7, 9, 11, 13.

Prime numbers:-

The prime number is defined as the number which is divided by 1 and itself.

Composite numbers:-

The number is defined as the composite number when the number is divided by 1 itself and any other numbers also.

From the given options we need to choose the pattern of the series { prime, prime, prime, composite, prime, prime } so we can see that in option A correct pattern is followed.

Pattern { 1, 5, 7, 9, 11, 13 }

1   → prime

5  → prime

7  → prime

9  → composite

11  → prime

13 → prime

Therefore the correct answer is option A which is the pattern {prime, prime, prime, composite, prime, prime} is followed by 1, 5, 7, 9, 11, 13.

To know more about prime and composite numbers follow

https://brainly.com/question/375267

#SPJ1

Step-by-step explanation:

On a polar plane, the shape will be a line that goes through the pi/2- pi quadrant , and 3pi/2- 2pi quadrant

On a Cartesian or rectangular plane, the shape will be a line as well passing through 2nd and 4th quadrant

Because we have an open circle at (1, 2), and then the line continues up, we conclude that the domain is:

D: x > 1.

Here we know that:

"The second line has an open circle at (1, 2)"

This means that the value x = 1 is not on the domain of the second line, and we know that the line "then continues up through (3, 4)"

(notice that these are two points on the line y = x + 1).

So we conclude that x = 1 is the lower bound of the domain of that line (and we can't tell that there is an upper bound).

Then we can just write the domain as:

D: x > 1.

So the last option is the correct one.

If you want to learn more about domains:

https://brainly.com/question/1770447

#SPJ1

Answer:

Step-by-step explanation:

The answer would be "me" as the indirect object

D. 9.5 cm

To find the perimeter you need to add all the sides.

2.1 + 2.1 + 1 + 3.3 + 1 = 9.5

The question was incomplete. Below you will find the missing parts of the question.

The company actually loses money on their first few products as it costs them more to make them, but once they hit  ?   they break even again. The worst case scenerio is that they produce  ?   items, as they will have a profit of  ?   dollars. The first root tells us that the profit will be 0 when  ?   products are sold.

Answer: The company actually loses money on their first few products as it costs them more to make them, but once they hit  150   they break even again. The worst case scenerio is that they produce  75   items, as they will have a profit of  10000   dollars. The first root tells us that the profit will be 0 when  0   products are sold.

Because the roots are x = 0 and 150, the vertex is (75, 10000).

So, the function is y = [tex]-\frac{10000}{5625}(x-75)^{2} +10000[/tex]

When, y = 0,

[tex]0=-\frac{10000}{5625} (x-75)^{2} +10000[/tex]

⇒ [tex]\frac{10000}{5625} (x-75)^{2}=10000[/tex]

⇒ [tex](x-75)^{2} = 10000(\frac{5625}{10000})[/tex]

⇒ [tex](x-75)^{2} = 5625[/tex]

⇒ [tex]x-75=75[/tex]

⇒ x = 150

When y=0, then x =150, their income was in balance.

When x = 75, then y=10000, they will have a profit of 10000 dollars.

The first root tells us that the profit will be 0 when 0 products are sold.

Learn more about profit margin here :

https://brainly.com/question/10218300

#SPJ10

Step-by-step explanation:

The graph of the cube root parent function y = RootIndex 3 StartRoot x EndRoot is translated to form f(x) shown on the graph.

On a coordinate plane, a cube root function goes through (negative 7, 0), has an inflection point at (negative 6, 1), and goes through (2, 3).

Which equation represents f(x)?

f(x) = RootIndex 3 StartRoot x + 6 EndRoot + 1

f(x) = RootIndex 3 StartRoot x minus 6 EndRoot + 1

f(x) = RootIndex 3 StartRoot x + 6 EndRoot minus 1

f(x) = RootIndex 3 StartRoot x minus 6 EndRoot minus 1

Answer:

Step-by-step explanation:

The translation of the parent function is:

g(x) = ∛(x + 6) + 1

How do translations work?

There are two types of translations, these are:

Horizontal translation:

For a function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N)

If N is positive, the translation is to the left.

If N is negative, the translation is to the right.

Vertical translation:

For a function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N

If N is positive the translation is upwards.

If N is negative the translation is downwards.

Here we start with the parent function:

f(x) = ∛x

And we apply two translations such that:

g(x) = ∛(x + a) + b

Such that:

g(-7) = 0

g(2) = 3

Then we have the system of equations:

∛(-7 + a) + b = 0

∛(2 + a) + b = 3

From the options, the only ones that make the first option true are:

g(x) = ∛(x + 6) + 1

Such that when evaluated in x = -7 we get:

g(-7) =  ∛(-7 + 6) + 1 =  ∛(-1) + 1 = 0

When evaluated in x = 2 it gives:

∛(2 + 6) + 1 =  ∛(8) + 1 = 2+ 1 = 3

So the only option that meets these conditions is:

g(x) = ∛(x + 6) + 1

Which is a translation to the left of 6 units and up 1 unit.

If you want to learn more about translations, you can read:

brainly.com/question/17586310

If Sasha wants her account to be worth $1,000 in 5 years, then she must deposit $833.34.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = PRT

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

Sasha's bank account earns 4% simple interest. Therefore, if she wants it to be worth $1,000 in 5 years then the principal amount must be,

Account balance = PRT + P

$1,000 = P[(0.04×5)+1]

$1,000 = 1.2 P

P = $833.34

Hence, if Sasha wants her account to be worth $1,000 in 5 years, then she must deposit $833.34.

Learn more about Simple Interest:

https://brainly.com/question/2793278

#SPJ1

Answer:

Step-by-step explanation:

Given is isosceles right triangle, since its interior angles are 45°, 45° and 90°.

The missing length is therefore same as the length of the other leg:

Note: This is not included in the answer choices.

Answer:

4 units

Step-by-step explanation:

We can use the converse theorem of the isosceles triangle to find the missing leg.

Converse Isosceles triangle theorem: If two angles are congruent in a triangle, then sides opposite to those angles are also congruent.

Therefore,

As there are two 45° angles, the opposite sides to those are also congruent.

∴ s = 4

The question is incomplete. Below you will find the missing content in the figure.

Prove: m/EIF = m/GIH

Step                                                                    Reason

m∠EIF+m∠FIG = 180°

m∠FIG+m∠GIH= 180°

m∠EIF+m∠FIG= m∠FIG+m∠GIH

m∠EIF = m∠GIH

The figure is shown below.

The correct answer is m∠EIF = m∠GIH

Here lines FH and GE intersect each other at the point I.

we have to prove the angle

m∠EIF = m∠GIH

so,

m∠EIF+m∠FIG = 180° as angels ∠EIF and ∠FIG forming a linear pair summing up to 180°. angels ∠EIF and ∠FIG form straight angels on a line EG.

m∠FIG+m∠GIH= 180° as angels ∠FIG and ∠GIH forming a linear pair summing up to 180°. angels ∠FIG and ∠GIH form straight angels on a line FH.

m∠EIF+m∠FIG= m∠FIG+m∠GIH because of the substitution property of equality. we replace 180° by m∠FIG+m∠GIH.

m∠EIF = m∠GIH because of the subtraction property of equality. We can subtract the same elements from both sides by the subtraction property of equality.

Therefore m∠EIF = m∠GIH.

Learn more about property of equality

here: https://brainly.com/question/1601404

#SPJ10

Answer:

The answer is $2.80.

Step-by-step explanation:

The price was reduced to two dollars and you buy 28 cans for the same price in which you got 20 cans at original price. So you need to take 28 cans times 2, which you will receive 56. Take 56 the price divided by 20 the original price cans and you will receive 2.8 or $2.80. To double check your work, take 2.80 times 20 and see if you get 56. #BallersKnowMath

If f(x)=x²+2 and g(x)=x²+5 then the domain of  the (fog) (x) is (-∞,∞).

Given the f(x)=x²+2 and g(x)=x²+5

We have to find the domain of  the (fog) (x)

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

then,(fog) (x)= (x²+5)²+ 2

                    =x⁴+25+10x²+2

                    = x⁴+27+10x²

Now on any real value of x the value of (fog) (x) exists therefore (fog) (x) can take all the values of the real number.

So domain (fog) (x)= (-∞,∞).

Learn more about the domain here: https://brainly.com/question/26098895

#SPJ10

Answer:

y = 5 and y = 1

Step-by-step explanation:

[tex]\textsc {Subtract 7 from each side :}[/tex]

⇒ (3y - 2)² + 7 - 7 = 43 - 7

⇒ (3y - 2)² = 36

[tex]\textsc {take the square root on each side :}[/tex]

⇒ √(3y - 9)² = √36

⇒ 3y - 9 = ±6

[tex]\textsc {When equal to +6, add 9 on each side :}[/tex]

⇒ 3y - 9 + 9 = 6 + 9

⇒ 3y = 15

[tex]\textsc {Divide by 3 on each side :}[/tex]

⇒ 3y/3 = 15/3

⇒ y = 5

[tex]\textsc {When equal to -6, add 9 on each side :}[/tex]

⇒ 3y - 9 + 9 = -6 + 9

⇒ 3y = 3

[tex]\textsc {Divide by 3 on each side :}[/tex]

⇒ 3y/3 = 3/3

⇒ y = 1

Answer:

73,358,400

Step-by-step explanation:

(2465)8 × (465)8

= 19,720 × 3,720

= 73,358,400

The sum of the geometric series will be 1/4. And the sum of the series will be the negative 0.13.

The complete question is attached below.

Let a be the first term and r be the common ratio. Then the sum of the geometric series will be

S = a / (1 – r)     if r < 1

S = a / (r – 1)     if r > 1

The series is given below.

1/16 + 3/64 + 9/256 + 27/1024 ....

Then we have

a = 1/16

r = (3/64) / (1/16) = 3/4

Then the sum of the series will be

S = (1/16) / [1 – (3/4)]

S = (1/16) / (1/4)

S = 1/4

Let [tex]\rm S = (-0.13)^m[/tex], where m = 1

Then the value of S will be

S = (-0.13)¹

S = -0.13

Hence, the sum of the series will be the negative 0.13.

More about the sum of the geometric series link is given below.

https://brainly.com/question/2771750

#SPJ1

Answer:

-4  option (c)

Step-by-step explanation:

Cramer rule : In this method, the values of the variables in the system are to be calculated using the determinants of matrices

if , D :determinant of the coefficient matrix

[tex]{D}_{x}:[/tex]determinant of the matrix with coefficients except x

then,

[tex]x=\frac{{D}_{x}}{D}[/tex]

similarly,

[tex]y=\frac{{D}_{y}}{D}[/tex]

[tex]z=\frac{{D}_{z}}{D}[/tex]

given,

D = -23

[tex]D_{y}[/tex]  =           [tex]det\left[\begin{array}{ccc}5&7&-1\\2&6&-2\\3&-7&2\end{array}\right][/tex]

[tex]D_{y}[/tex] = 92

therefore, y = 92/(-23)

   y = -4 answer

learn more about determinants at

https://brainly.com/question/11841826

#SPJ10