Can you PLEASE help me with this?!

Answer:

Start with equation,

         y''(x) = f(x) = 6y/(10x-x²)               about point x₀ = 5

Then,

       y(x) = a₀ + a₁(x-5) + a₂(x-5)²+ a₃(x-5)³ + a₄(x-5)⁴...….

by inspection,

           y(5) = a₀      and       y'(5) = a₁

then,

y''(5) = 6a₀/(50-25) = 6a₀/25              

y'''(x) = 6y'/(10x-x2) - 6y(10-2x)/(10x-x2)2

then,                      

                              y'''(5) = 6a₁/25 - 0 = 6a₁/25                

y''''(x) = 6y''/(10x-x2) -12y'(10-2x)/(10x-x2)² + 12y/(10x-x2)² + 12y(10-2x)2/(10x-x2)³

then,

    y''''(5) = (6/25)(6a₀/25) + 0 + 12a₀/625 + 0

              = 48a₀/625

So,

y(x) = f(x) = f(5) + f'(5)(x-5) + f''(5)(x-5)2/2! + f'''(5)(x-5)3/3! + f''''(5)(x-5)4/4! …

                                                       or

y(x) = f(x) = a₀ + a₁(x-5) + (6ao/25)(x-5)2/2! + (6a1/25)(x-5)3/3! + (48a₀/625)(x-5)4/4!...

                                                         or

y(x) = f(x) = a₀ + a₁(x-5) + (3a₀/25)(x-5)²+ (a₁/25)(x-5)³+ (2a₀/625)(x-5)⁴.....

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Answer:

44

Step-by-step explanation:

if this is the question from edge then trust me

To solve the triangle with the given information, we can use the Law of Sines. The Law of Sines states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In the given triangle, we have the following information:

Angle A = 38.5°

Side a = 182.5

Side b = 243.6

To find the length of side B, we can use the Law of Sines:

\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)}\)

Substituting the known values into the equation:

\(\frac{182.5}{\sin(38.5°)} = \frac{243.6}{\sin(B)}\)

We can solve this equation to find the value of sin(B):

\(\sin(B) = \frac{243.6 \cdot \sin(38.5°)}{182.5}\)

Next, we can use the inverse sine function to find the measure of angle B:

\(B = \sin^{-1}\left(\frac{243.6 \cdot \sin(38.5°)}{182.5}\right)\)

Now that we have the measure of angle B, we can use the Law of Sines again to find the length of side C:

\(\frac{c}{\sin(C)} = \frac{a}{\sin(A)}\)

Substituting the known values into the equation:

\(\frac{c}{\sin(C)} = \frac{182.5}{\sin(38.5°)}\)

Solving for c, we get:

\(c = \frac{182.5 \cdot \sin(C)}{\sin(38.5°)}\)

Finally, we can find the measure of angle C using the fact that the angles in a triangle sum to 180°:

\(C = 180° - A - B\)

Substituting the known values into the equation:

\(C = 180° - 38.5° - B\)

Now we have found the lengths of side B and side C, as well as the measure of angle C, completing the solution for the triangle.

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The Law of Sines states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant. the lengths of side B and side C, as well as the measure of angle C, completing the solution for the triang

In the given triangle, we have the following information:

Angle A = 38.5°

Side a = 182.5

Side b = 243.6

To find the length of side B, we can use the Law of Sines:

\(\frac{a}{\sin(A)} = \frac{b}{\sin(B)}\)

Substituting the known values into the equation:

\(\frac{182.5}{\sin(38.5°)} = \frac{243.6}{\sin(B)}\)

We can solve this equation to find the value of sin(B):

\(\sin(B) = \frac{243.6 \cdot \sin(38.5°)}{182.5}\)

Next, we can use the inverse sine function to find the measure of angle B:

\(B = \sin^{-1}\left(\frac{243.6 \cdot \sin(38.5°)}{182.5}\right)\)

Now that we have the measure of angle B, we can use the Law of Sines again to find the length of side C:

\(\frac{c}{\sin(C)} = \frac{a}{\sin(A)}\)

Substituting the known values into the equation:

\(\frac{c}{\sin(C)} = \frac{182.5}{\sin(38.5°)}\)

Solving for c, we get:

\(c = \frac{182.5 \cdot \sin(C)}{\sin(38.5°)}\)

Finally, we can find the measure of angle C using the fact that the angles in a triangle sum to 180°:

\(C = 180° - A - B\)

Substituting the known values into the equation:

\(C = 180° - 38.5° - B\)

Now we have found the lengths of side B and side C, as well as the measure of angle C, completing the solution for the triangle.

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Answer:

Step-by-step explanation:

Explicit formula of a G.P. is given by,

\(a_n=a(r)^{n-1}\)

Here, \(a_n\) = nth term

a = First term

n = number of term

r = common ratio

Given sequence is 3, 6, 12, .......

a = 3

r = \(\frac{6}{3}\) = 2

Therefore, explicit formula will be,

\(a_n=3(2)^{n-1}\)

Option (3) is the answer.

Parent function → f(x) = 3ˣ

Transformed function → g(x) = \(3^{x+5}\)

Since, g(x) = f(x + 5)

Therefore, function 'f' has been shifted 5 units left.

Option (1) is the answer.

If the incident light changes from a wavelength of 630 nm to 420 nm, the fringe spacing will decrease, resulting in fringes that are closer together.

In a double-slit experiment, when light passes through two narrow slits and hits a viewing screen, interference patterns are observed. The fringe spacing, also known as the separation between adjacent bright fringes, is determined by the wavelength of the incident light. The formula for calculating fringe spacing is given by:

Fringe Spacing = (wavelength * distance from slits to screen) / distance between the slits

Given that the fringe spacing is initially 1.8 mm when the incident light has a wavelength of 630 nm, we can use the formula to calculate the new fringe spacing when the light wavelength changes to 420 nm. Since the distance from the slits to the screen and the distance between the slits remain constant, the only variable that changes is the wavelength. As the wavelength decreases, the fringe spacing will also decrease. Therefore, the fringe spacing will be smaller when the light wavelength is 420 nm compared to when it is 630 nm.

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Answer:

22

Step-by-step explanation:

Use a proportion.

30/15 = 44/x

30x = 15 × 44

2x = 44

x = 22

Answer:

22

Step-by-step explanation:

30 miles/ 15 sessions of tract practice

Per practice Jack is running a total of 2 miles.

So 44 miles/2 miles

22 sessions of track practice

Answer:

98

Step-by-step explanation:

7 : 11 :: x : 154

Also,

\( \frac{7}{11} = \frac{x}{154} \)

\( = > \frac{x}{154} = \frac{7}{11} \)

\( = > x = \frac{7 \times 154}{11} \)

=> x = 7 × 14

=> x = 98 (Ans)

Answer:

21a-14b

15b-20a

Step-by-step explanation:

Answer: a + 3b

Step-by-step explanation:

Okay, so...

7(3a - 2b) = 7(3a) - 7(2b) ... distributive property

21a - 14b

5(3b - 4a) = 5(3b) - 5(4a) ... distributive property

15b - 20a

(21a - 14b) + (15b - 20a) = 21a -12b + 15b - 20a =

a + 3b

Answer: 18 feet

Step-by-step explanation:

Well, first we need to find the circumference because that is the outside of the pipe.

Circumference = 2 x Pi x Radius

Radius is half of diameter.

So we plug in all the values in to the formula.

2 x Pi x 6 inches = Circumference

12Pi = 37.69911184 inches

37 inches to feet = about 3 feet.

3 x 6 = 18 feet.

Answer:

9 people liked neither rugby or football or cricket.

Answer:

14

Step-by-step explanation:

√196

Calculate the square root of 196 and get 14.

14

The surface area of the cone is 578.1 square feet.

We know that for a cone of radius R and slant height H the surface area is given by the formula:

S = pi*R^2 + pi*R*(H)

with pi = 3.14

On the diagram we can see that H = 19.3ft, and the diameter of the base is 14 ft, then the radius is:

R = 14ft/2 = 7ft

REplacing these values in the formula above we will get:

S = 3.14*(7ft)^2 + 3.14*7ft*(19.3ft) = 578.1 ft²

So the correct option is the second one.

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6 weeks from now, you will have $215 in your bank account

The given parameters are:

b = 60 + (20+6)w

When the account balance is $215, we have

60 + (20+6)w = 215

Subtract 60 from both sides

(20+6)w = 155

This gives

26w = 155

Divide both sides by 26

w = 5.96

Approximate

w = 6

Hence, 6 weeks from now, you will have $215 in your bank account

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The average number of miles he would have to ride each day to meet his goal is 6.4 miles

From the question, we are to determine the average number of miles Feng would have to ride each day to meet his goal

Let x represent the average number of miles he would have to ride each day to meet his goal

From, the given information,

"Feng wants to ride his bicycle 45.6 miles this week"

and

"He has already ridden 20 miles"

Then,

The equation that represents the average number of miles he would to ride for 4 more days is

x = (45.6 - 20)/4

x = 25.6/4

x = 6.4 miles

Hence, the average number of miles he would have to ride each day to meet his goal is 6.4 miles

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Answer:

The new location of point C, after a dilation centered at the origin with a scale factor of 1/5, is (2,6). This means that the point has been moved closer to the origin by a factor of 1/5.

Straight-line graphs are commonly referred to as "linear graphs" or "linear equations."

We have,

A straight line graph, often referred to as a linear graph or linear equation, represents a relationship between two variables that can be expressed by a linear equation in the form y = mx + b.

In this equation, 'x' and 'y' are the variables, 'm' is the slope of the line, and 'b' is the y-intercept (the point where the line crosses the y-axis).

The slope 'm' determines the steepness or incline of the line.

A positive slope indicates the line rises as 'x' increases, while a negative slope indicates the line descends as 'x' increases.

The y-intercept 'b' represents the value of 'y' when 'x' is zero, determining where the line crosses the y-axis.

Thus,

Straight line graphs are commonly referred to as "linear graphs" or "linear equations.

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Answer:

yes

Step-by-step explanation:

The internal forces to the right of point D are:

- Shear Force (SF) at D = 70 kN (upward)

- Bending Moment (BM) at D = -40 kNm

When the observable qualities, such as colour, temperature, pressure, concentration, etc. do not vary, the process is said to be in equilibrium.

To determine the internal forces to the right of point D, we need to analyze the equilibrium of forces and moments acting on the beam.

Given:

- Point C is located 2 meters to the left of point D.

- There is a concentrated load of 60 kN applied at point C.

- There is a distributed load of 25 kN/m between points C and D.

- Point D is located 1 meter to the left of point E.

To begin, let's calculate the reaction forces at point D.

1. Vertical Equilibrium:

The sum of vertical forces at point D must be zero.

RDy - 60 = 0

RDy = 60 kN

2. Horizontal Equilibrium:

The sum of horizontal forces at point D must be zero.

RDx = 0 (assuming no horizontal external forces)

Next, let's calculate the internal forces at point D.

3. Moment Equilibrium:

The sum of moments about point D must be zero.

-60(2) + (25 * 2²)/2 + RDy(1) = 0

-120 + 50 + RDy = 0

RDy = 70 kN

4. Shear Force (SF) Diagram:

To determine the shear force at point D, we'll consider the loading to the left of point D.

SF at D = RDy = 70 kN (upward)

5. Bending Moment (BM) Diagram:

To determine the bending moment at point D, we'll integrate the loading from the left end.

BM at D = -60(2) + (25 * 2²)/2 = -40 kNm

Therefore, the internal forces to the right of point D are:

- Shear Force (SF) at D = 70 kN (upward)

- Bending Moment (BM) at D = -40 kNm

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Answer:

0.035°

Step-by-step explanation:

We need to find the value of  \(\theta\) for the given expression. So,

\(\tan\theta=\dfrac{5\sqrt{20}}{11}\)

or

\(\theta=\tan^{-1}\tan\left(\frac{5\sqrt{20}}{11}\right)\\\\=-2.0083\ radian\)

Or we can write as :

\(\theta=0.035^{\circ}\)

So, the value of \(\theta\) is equal to 0.035°.

Answer:

6 · 10⁻³

Step-by-Step Explanation:

The number 6 time 10 to the power -3 is 6 · 10⁻³ in standard form.

Answer:

\(2.28*10^7\)

Step-by-step explanation:

\((2.4*10^3)(9.5*10^3)=(2.4*9.5)(10^3*10^3)=22.8*10^6=2.28*10^7\)

Answer:

228,000

Step-by-step explanation:

(2.4x10^3) x (9.5x10^3)

(2.4x100) x (9.5x100)

240x950

228,000

The nearest year, for the value of the account to reach $6,020 is 8

It would take 8 years for the value of the account to reach $6,020, assuming no deposits or withdrawals are made. This is calculated by finding the present value of the $6,020 ($5,300), then dividing it by the interest rate (2.1%) and then multiplying it by the number of years (8) to get the future value ($6,020).

\(PV = FV / (1+r)^n\)

\(6,020 = 5,300 / (1 + 0.021)^n\)

\(8 = n\)

It would take 8 years for the value of the account to reach $6,020

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The equation representing the relationship will be a = 5,184p.

What is representing the relationship of equations?

Yes, there is a relationship between the screen size and the number of pixels.

The equation representing the relationship will be a = 5,184p.

The equation representing the relationship will be:

= Number of pixels / Screen size

= 31.104 / 6

= 5.184

Therefore, the equation representing the relationship will be a = 5,184p.

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Answer:

\((a+b)(a^2-ab+b^2)=(a^3+b^3)\)

Step-by-step explanation:

Given

The explanation of the question is given with all the steps.

Explanation

In the fourth step,

The equation is given

And inverse is used,

Answer

To find the value of theta, we have to take the inverse of the trigonometric function sin.

Otherwise , we cannot calculate the value of theta.

The distance between Earth and the moon is 3.8 x 10^3 Kilometers. The time taken to travel this distance was 2.1 x 10^3 Minutes.

The formula to calculate speed is Speed = distance/time.

So, the speed of Luna I was 3.6 x 10^3 / 2.1 x 10^3 Kilometers/Mintues.

Hidden sample answer

The requried, 140% is equivalent to 7/5 as a fraction, 1 2/5 as a mixed number, and 2 as a whole number.

To write 140% as a fraction, we first recognize that "percent" means "per hundred," so 140% can be written as the fraction 140/100. We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 20:

140/100 = 7/5

To write 7/5 as a mixed number, we divide the numerator by the denominator and express the result as a whole number plus a fraction. In this case:

7 ÷ 5 = 1 with a remainder of 2

So 7/5 can be written as the mixed number 1 2/5.

To write 7/5 as a whole number, we can round it to the nearest whole number. Since 7/5 is greater than 1.5 and less than 2.5, it rounds to 2.

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A scatter diagram is a preliminary or initial step in exploring a relationship between two variables.

A scatter diagram is a graphical tool used to investigate the relationship between two variables. The first step in exploring a relationship between two variables is to create a scatter diagram.

This diagram shows the relationship between two variables as a set of ordered pairs of data points, where one variable is plotted on the horizontal axis and the other variable is plotted on the vertical axis.

The pattern or trend in the plotted points on the scatter diagram can provide useful information about the relationship between the variables. For example, if the points form a roughly linear pattern, it suggests a positive or negative correlation between the variables, while a scatterplot with no clear pattern suggests no correlation.

Therefore, creating a scatter diagram is an essential first step in exploring a relationship between two variables.

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Answer:

A candy bar costs $0.80

A bag of chips costs $6.20

Step-by-step explanation:

Let's call candy bars x, and bags of chips y.

Ruben ought 2x and 4y for $24

Lucis bought 2x and 2y for $14

This means that 2x+4y = 24 and 2x+2y = 14

Now we have a system of equations that we can solve.

2x + 2y = 14

2(x + y) = 14

x + y = 7

y = 7 - x

Plug this into the next equation to get:

2x + 4y = 24

2x + 4(7 - x) = 24

2x + 28 - 7x = 24

28 - 5x = 24

-5x = -4

x = -4/-5

x = 4/5 = 0.8

plug that x value into y = 7 - x to find y

y = 7 - x

y = 7 - (4/5)

y = 245/35 - 28/35

y = 217/35 = 6.2

now we can check our work:

2(x + y) = 14

2(6.2 + 0.8) = 14

2(7) = 14

14 = 14

^ this means our values are correct

Answer:

A candy bar costs $0.80

A bag of chips costs $6.20