Write the cubic term for the Taylor series expansion of f(x) = sin(x) at c = pi/4

I did the work, can you please check for me whether my work is right?

Answer:

Step-by-step explanation:

Insufficient dimensions are given to compute an exact volume of each geometry, so we have to assume that the volume is proportional to the product of base area and height. Then the relative volumes will be ...

  bottle X: (6 in)(2 in)(1 in) = 12 in^3

  bottle Y: (4 in)(3 in)(1.5 in) = 18 in^3

  3rd bottle: (3 in)(6 in^2) = 18 in^3

That is, the relative volumes are ...

  X : Y : 3rd = 12 : 18 : 18 = 1 : 1.5 : 1.5

The corresponding relative prices are ...

  X : Y : 3rd = 9.96 : 14.40 : 13:20 = 1 : 1.446 : 1.325

__

A. Bottle Y has 1.5 times as much lotion as Bottle X.

__

B. Bottle Y is a better buy than Bottle X. (The price relative to X is less than the volume relative to X.)

__

C. The 3rd bottle is the best buy. For the same volume, the price of the 3rd bottle is less than that of Bottle Y.

_____

Note that the relative volume and price ratios are found by dividing all the numbers in the ratio sequence by the first number:

  12 : 18 : 18 = (12/12) : (18/12) : (18/12)

  9.96 : 14.40 : 13.20 = (9.96/9.96) : (14.40/9.96) : (13.20/9.96)

Answer: Center (0, -8) and Radius = 2

The standard equation of a circle is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius.

You can write the equation as (x-0)² + (y-( -8))² = 2². From this, you can conclude that the center is (0,-8) and the radius is 2.

Answer: B

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

3+9=18

Answer: f(120°) = (√3) + 1/2

Step-by-step explanation:

i will solve it with notable relations, because using a calculator is cutting steps.

f(120°) = 2*sin(120°) + cos(120°)

           =2*sin(90° + 30°) + cos(90° + 30°)

here we can use the relations

cos(a + b) = cos(a)*cos(b) - sin(a)*sin(b)

sin(a + b) = cos(a)*sin(b) + cos(b)*sin(a)

then we have

f(120°) = 2*( cos(90°)*sin(30°) + cos(30°)*sin(90°)) +  cos(90°)*cos(30°) - sin(90°)*sin(30°)

and

cos(90°) = 0

sin(90°) = 1

cos(30°) = (√3)/2

sin(30°) = 1/2

We replace those values in the equation and get:

f(120°) = 2*( 0 +  (√3)/2) + 0 +  1/2 = (√3) + 1/2

Answer:

a(n)=89n

Step-by-step explanation:

Given the sequence 89, 178, 267, 356, ...

First Term, a(1)=89

178-89=267-178=89

This is an arithmetic difference with:

Common difference, d=89

The position of any term, n in an arithmetic sequence is derived using the formula:

a(n)=a(1)+(n-1)d

Substituting a(1)=89 and d=89

a(n)=89+89(n-1)

a(n)=89+89n-89

a(n)=89n

The expression that describes the sequence above is: a(n)=89n where n is the position of a term in the sequence.

Answer:

1.89 radians  or 108 degrees.

Step-by-step explanation:

Circumference of the circle = 10 * 3.142

= 31.42.

So 31.42 is equivalent to 2 pi radians, so:

Angle subtended at the center

= (9.42 / 31.42) * 2 pi

=  (9.42 / 31.42) * 2 * 3.142

= 1.89 radians  or 108 degrees..

Answer:

Direction of the police plane = N57.1E

Speed of the police airplane = 255 km/h

Step-by-step explanation:

The diagram of the situation described is presented in the attached image to this question.

Let the distance the police airplane has to travel to intercept the smuggler at 08:30 be x km

The police airplane moves at 06:30 and plans to intercept the smuggler at 08:30; thereby travelling for 2 hours.

By 08:30, the smuggler would have travelled for 2 hours 30 mins, that is, 2.5 hours, travelling at 200 km/h, that is a total distance of 500 km covered.

So, the paths form a triangle.

Using cosine rule, we can obtain the distance, x, that the police airplane has to travel to intercept the smuggler at 08:30.

x² = 150² + 500² - (2×150×500×cos 85°)

x² = 259,426.63858785

x = 509.34 km

We can obtain the direction, Φ, by finding the angle θ using some rule.

[(Sin 85°)/509.34] = [(Sin θ)/500]

Sin θ = (500 × sin 85°)/509.34 = 0.9779 = 77.94°

From the attached image,

Φ + θ = 90° + 45° = 135°

Φ = 135° - θ = 135° - 77.94° = 57.06° = 57.1°

Therefore,

Speed of police airplane = (distance)/(time) = (509.34/2) = 254.67 km/h = 255 km/h

Direction of the police plane = N57.1E

Hope this Helps!!!

Answer:

They have it on Hulu

Step-by-step explanation:

and I heard something about Naruto360.com.

Answer:

I watched it on Utube

Step-by-step explanation:

You can find the episodes free on Utube just type in the episode and you can find it in many languages

Answer:

Integer; - 12

Step-by-step explanation:

If we are considering a situation were there is a drop in temperature, this integer representation would contain a negative;

At the same time the temperature drops by 12 degrees ( ° ) such that this integer is;

Answer; - 12

Answer:

Step-by-step explanation:

In this problem, we have to find the area of an square adjacent to the third side of the right triangle.

To solve this problem, we need to use Pythagorean's Theorem, beacuse it's about a right triangle. Also, this theorem is about square areas, that's the geomtrical meaning of it.

[tex]h^{2} =32 \ u^{2} + 32 \ u^{2} = 64\ u^{2} \\h=\sqrt{64 \ u^{2} } =8u[/tex]

Therefore, the area of a square adjacent to the third side is 64 square units.

Answer:the answer is 8

Step-by-step explanation:

Answer:

128,000

Step-by-step explanation:

I=prt

I=80,000 x 15 x 4

I=128,000

Answer:

$128000

Step-by-step explanation:

Using the given formula :

I = P × R × T

I = 80000 × 15/100 × 4

I = $48000

He saves = 48000 +80000 = $128000

Answer:

See explanation

Step-by-step explanation:

[tex]tan \: A = \frac{2 \sqrt{a} }{a - 1} ...(given) \\ \because \: {sec}^{2} \: A = 1 + {tan}^{2}\: A \\ \therefore\: {sec}^{2} \: A = 1 + \bigg(\frac{2 \sqrt{a} }{a - 1} \bigg)^{2} \\\\ \hspace{38 pt} = 1 + \frac{4a}{ {(a - 1)}^{2} } \\ \\ \hspace{38 pt}= \frac{(a - 1)^{2} + 4a}{ {(a - 1)}^{2} } \\ \\\hspace{38 pt} = \frac{a^{2} - 2a + 1+ 4a}{ {(a - 1)}^{2} } \\ \\ \hspace{38 pt}= \frac{a^{2} + 2a+ 1}{ {(a - 1)}^{2} } \\ \\ \hspace{38 pt}= \frac{(a + 1)^{2}}{ {(a - 1)}^{2} } \\ \\ \therefore {sec}^{2} \: A = \bigg(\frac{a + 1}{ {a - 1}} \bigg) ^{2} \\ \\ \therefore \: {sec} \: A = \pm \bigg(\frac{a + 1}{ {a - 1}} \bigg)\\ \\ [/tex]

In the question It is not mentioned that in which quadrant does angle A lie, so we will assume it to be in first quadrant.

[tex] \therefore \: {sec} \: A = \bigg(\frac{a + 1}{ {a - 1}} \bigg)\\ \\

\red{ \boxed{ \bold{\therefore \: {cos} \: A = \bigg(\frac{a - 1}{ {a + 1}} \bigg)}}} \\ \\ {sin} \: A ={cos} \: A \times {tan} \: A \\ \\ \hspace{25 pt}=\bigg(\frac{a - 1}{ {a + 1}} \bigg) \times \frac{2 \sqrt{a} }{a - 1} \\ \\ \purple {\boxed { \bold{{sin} \: A = \frac{2 \sqrt{a} }{a + 1}}}}[/tex]

Answer:

243.92cm³

Step-by-step explanation:

We have two shapes given in this question. A spherical ornament and a cubic box

Step 1

Find the volume of the Sphere

Volume of the sphere is given as

4/3 πr³

In the question, the radius of the sphere is given as = 4 centimeters.

Therefore,

Volume of the sphere = 4/3 × π × 4³

Volume of the sphere = 268.08cm³

Step 2

We have to find the length of the side or the edge of the cube.

It is important note that: because the spherical ornament is insides the cubic box,

Hence, the diameter of the spherical ornament = length of the side (edge) of the cube.

In the question we are given the radius of the sphere = 4 cm

Diameter = 2 × radius = 2× 4 cm = 8cm

Since,the diameter of the spherical ornament = length of the side (edge) of the cube,

The length of the side of the edge of the cube = 8cm

Step 3

We find the Volume of the cube

Volume of the cube = Length × Width × Height

Where the Length = Width = Height

Therefore, Voulme of the cube = 8cm × 8cm × 8cm

= 512cm³

Step 4

The fourth and final step is to find the space is left in the box to be filled with packing material.

The space left to be filled with packing material = Volume of the cube - Volume of the Spherical ornament

Volume of the cube= 512cm³ Volume of the Spherical ornament =

268.08cm³

Therefore, amount or Volume of space left for the packing material = 512cm³ - 268.08cm³

= 243.92cm³

Therefore, amount of space that is left in the box to be filled with packing material is 243.92cm³

The area of the remaining space for packing the material is 243.9 square cm.

It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.

[tex]\rm V = \dfrac{4}{3} \pi r^3[/tex]

The radius of the sphere = 4 cm

Side of the cube = 8 cm

The volume of the cube = 8×8×8 = 512 square cm

The volume of sphere = (4/3)π(4)³ = 268.082 square cm

Remaining space = 512 - 268.082 = 243.9 square cm

Thus, the area of the remaining space for packing the material is 243.9 square cm.

Learn more about the sphere here:

brainly.com/question/11374994

#SPJ5

Answer: The measures of the angles are 64.6 degrees and 25.4 degrees.

Step-by-step explanation:

Complementary angles add up to 90 degrees.

x can be one angle, and (x-39.2) can be the other

x + (x-39.2) = 90

2x - 39.2 = 90

add 39.2 to both sides

2x = 129.2

divide each side by 2

x = 64.6

find the measure of the other angle

64.6-39.2 = 25.4

The measures of the angles are 64.6 degrees and 25.4 degrees.

Answer:

Step-by-step explanation:

Suppose two complementary angles of measures x And y then

x + y = 90 and y = x - 39.2

if we plug in  x - 39.2 instead of y in the equation x + y = 90 we get :

x + (x - 39.2) = 90

then

2x = 90 + 39.2

then

2x = 129.2

then

x = 129.2/2 = 64.6

therefore

y = 64.6 - 39.2

  = 25.4

______________________________

:)

Answer:

4x+68=180

4x=180-68

4x=112

4. 4

x= 28°

question 2 has been solved that way because 5x+70°=180 because they are on a straight line and angles on a straight line are 180°

Answer:

209 cm^2

Step-by-step explanation:

The area of the parallelogram is

A = bh

A = 19 * 11

A =209

Answer:

c

Step-by-step explanation:

The probability of getting violet first and pink next is [tex]\dfrac{2}{9}[/tex].

Given:

The number of violet balls is 2.

The number of pink balls is 4.

To find:

The probability of getting violet first and pink next, if the first ball drawn is replaced.

Explanation:

We know that,

[tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

Total number of balls is:

[tex]2+4=6[/tex]

The probability of getting violet a ball is [tex]\dfrac{2}{6}[/tex].

The first ball drawn is replaced, then the total number of balls remains the same. Then the probability of getting a pink ball is [tex]\dfrac{4}{6}[/tex].

The probability of getting violet first and pink next, if the first ball drawn is replaced is:

[tex]P=\dfrac{2}{6}\times \dfrac{4}{6}[/tex]

[tex]P=\dfrac{1}{3}\times \dfrac{2}{3}[/tex]

[tex]P=\dfrac{2}{9}[/tex]

Therefore, the probability of getting violet first and pink next is [tex]\dfrac{2}{9}[/tex].

Learn more:

https://brainly.com/question/15620045

Answer: i think 83?"?"?

Answer:

5x-2

Step-by-step explanation:

Answer:

y = 5x + 2

Step-by-step explanation:

“the product of a number and five is two less than the number.” numbers unknown so call them x and y, so you have to find the product of x and 5, which is simply 5x, then you know that 5x is two less than y, so you add 2 to balance the equation, which gives you 5x + 2 = y

edit: the question refers to 2 unknown numbers so 5x - 2 is not the answer as you need an equation not an expression

Answer:

[tex]\frac{10}{10}[/tex]    (10/10)

Step-by-step explanation:

to convert 1.00 into a fraction you have to write 1.00 as numerator and put 1 as the denominator.

then, you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

1.00 = 1.00/1 = 10/10

Answer:

Walkway is 1.5 units²

Step-by-step explanation:

Just subtract the area of the garden from the combined area:

5.5-4=1.5

Also did you mean difference? I don't know what it means by sum.

Answer:

x > 4

Step-by-step explanation:

-3x -24 < -36

Add 24 to each side

-3x -24+24 < -36+24

-3x< -12

Divide each side by -3, remembering to flip the inequality

-3x/-3 >-12/-3

x > 4

Answer:

x > 4

Step-by-step explanation:

Given equation,

→ -3x - 24 < -36

Now the value of x will be,

→ -3x - 24 < -36

→ -3x < -36 + 24

→ -3x < -12

→ x > -12/-3

→ x > 12/3

→ [ x > 4 ]

Hence, the answer is x > 4.

Answer:

The number is 10

Step-by-step explanation:

Of means multiply and is means equals

125% * Number = 12.5

Change to decimal form

1.25 * Number = 12.5

Divide each side by 1.25

1.25 * Number / 1.25 = 12.5/1.25

Number =10

Answer:

D.

Step-by-step explanation:

So find what two numbers multiply to 72 and add up to 17

9 and 8

(z + 9)(z + 8)

Answer:

D. (z + 9)(z + 8)

Step-by-step explanation:

Let's factor z2+17z+72

z2+17z+72

The middle number is 17 and the last number is 72.

Factoring means we want something like

(z+_)(z+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get 17

Multiply together to get 72

Can you think of the two numbers?

Try 8 and 9:

8+9 = 17

8*9 = 72

Fill in the blanks in

(z+_)(z+_)

with 8 and 9 to get...

so (z + 9)(z + 8)

Answer:

  T(t) = 14.5cos(2π(t -206/365)) +63.5

Step-by-step explanation:

The function can be written as ...

  T = A·cos(2π(t -206/365)) +B

where A is half the difference of the high and low temperature values, and B is the average of the high and low temperature values.

  A = (78-49)/2 = 29/2 = 14.5

  B = (78 +49)/2 = 127/2 = 63.5

The value 206/365 is the horizontal right shift of the peak of the function. That makes the peak occur on July 26, as required.

Filling in these values gives us the function ...

  T(t) = 14.5cos(2π(t -206/365)) +63.5

Answer:

Angle BEA

Step-by-step explanation:

They share the same straight line and their degrees add to 180

Answer:C

Step-by-step explanation:

Answer:

it is 8

Step-by-step explanation:

Answer:

The length is 12cm

Step-by-step explanation:

The perimeter is the sum of all the sides

To work out the length of the rectangle you would first need to multiply the width of 4 by 2, this gives you 8. This is because the perimeter of the rectangle is the sum of all the sides, and as the rectangle has two sets of identical parallel lines.

 The next step is to minus 8 from 32, this gives you 24. This is because we are isolating just the set of lengths.

The next step is to divide the value of 24 by 2, this gives you 12. This is because we had previously worked out what double the length is due to it being a set of parallel lines.

1) Multiply 4 by 2.

[tex]4*2=8cm[/tex]

2) Minus 8 from 32.

[tex]32-8=24cm[/tex]

3) Divide 24 by 2.

[tex]24/2=12cm[/tex]

Checking your answer:

To check your answer you would simply add the values of: 12, 12, 4, 4, and if this gives you 32 then the answer is correct.

1) Add 12 and 12 and 4 and 4.

[tex]12+12+4+4=32cm[/tex]

Answer:yes

Step-by-step explanation: 20<_x-8 = 20 <_20 which is correct