# Solve the literal equation for y3=5x+6y

y=1/2-5x/6

Step-by-step explanation:

y=1/2-5x/6

if this is helpful than good job

## Related Questions

Happy new year!i wish that everyone is able to fulfil their resolution, and have a better time than they did in 2021

Happy new year to you too! and thankyou :)

thank you it means a lot

Using the unit circle, determine the value of sin 450°

1

Step-by-step explanation:

To find the value of sin 450 degrees using the unit circle, represent 450° in the form (1 × 360°) + 90° [∵ 450°>360°] ∵ sine is a periodic function, sin 450° = sin 90°.

Rotate ‘r’ anticlockwise to form a 90° or 450° angle with the positive x-axis.

The sin of 450 degrees equals the y-coordinate(1) of the point of intersection (0, 1) of unit circle and r.

Hence the value of sin 450° = y = 1

To find the value of sin 450 degrees using the unit circle, represent 450° in the form (1 × 360°) + 90° [∵ 450°>360°] ∵ sine is a periodic function, sin 450° = sin 90°.

How do you do these two questions?

(a) ⅛ tan⁻¹(¼)

(b) sec x − ln│csc x + cot x│+ C

Step-by-step explanation:

(a) ∫₀¹ x / (16 + x⁴) dx

∫₀¹ (x/16) / (1 + (x⁴/16)) dx

⅛ ∫₀¹ (x/2) / (1 + (x²/4)²) dx

If tan u = x²/4, then sec²u du = x/2 dx

⅛ ∫ sec²u / (1 + tan²u) du

⅛ ∫ du

⅛ u + C

⅛ tan⁻¹(x²/4) + C

Evaluate from x=0 to x=1.

⅛ tan⁻¹(1²/4) − ⅛ tan⁻¹(0²/4)

⅛ tan⁻¹(¼)

(b) ∫ (sec³x / tan x) dx

Multiply by cos x / cos x.

∫ (sec²x / sin x) dx

Pythagorean identity.

∫ ((tan²x + 1) / sin x) dx

Divide.

∫ (tan x sec x + csc x) dx

Split the integral

∫ tan x sec x dx + ∫ csc x dx

Multiply second integral by (csc x + cot x) / (csc x + cot x).

∫ tan x sec x dx + ∫ csc x (csc x + cot x) / (csc x + cot x) dx

Integrate.

sec x − ln│csc x + cot x│+ C

(a) Solution : 1/8 cot⁻¹(4) or 1/8 tan⁻¹(¼) (either works)

(b) Solution : tan(x)/sin(x) + In | tan(x/2) | + C

Step-by-step explanation:

(a) We have the integral (x/16 + x⁴)dx on the interval [0 to 1].

For the integrand x/6 + x⁴, simply pose u = x², and du = 2xdx, and substitute:

1/2 ∫ (1/u² + 16)du

'Now pose u as 4v, and substitute though integral substitution. First remember that we have to factor 16 from the denominator, to get 1/2 ∫ 1/(16(u²/16 + 1))' :

∫ 1/4(v² + 1)dv

'Use the common integral ∫ (1/v² + 1)dv = arctan(v), and substitute back v = u/4 to get our solution' :

1/4arctan(u/4) + C

=> Solution : 1/8 cot⁻¹(4) or 1/8 tan⁻¹(¼)

(b) We have the integral ∫ sec³(x)/tan(x)dx, which we are asked to evaluate. Let's start by substitution tan(x) as sin(x)/cos(x), if you remember this property. And sec(x) = 1/cos(x) :

∫ (1/cos(x))³/(sin(x)/cos(x))dx

If we cancel out certain parts we receive the simplified expression:

∫ 1/cos²(x)sin(x)dx

Remember that sec(x) = 1/cos(x):

∫ sec²(x)/sin(x)dx

Now let's start out integration. It would be as follows:

Solution: tan(x)/sin(x) + In | tan(x/2) | + C

Sales of Volkswagen's popular Beetle have grown steadily at auto dealerships in Nevada during the past 5 years. The sales manager has predicted in 2004 and 2005 sales would be 410 VW's. Using exponential smoothing with a alpha = 0.30 develop a forecast for 2006 through 2010. What is the forecast value for 2010?Please answer to one decimal place. (Example: 466.1)Formula: Ft = Ft-1 + alpha(At-1 - Ft-1)Actual sales data:2005 = 4502006 = 4952007 = 5182008 = 5632009 = 584

Step-by-step explanation:

Given the data:

Year___Actual sale (At) ___forecast(Ft)

2005__450_____________410

2006__495____________ 422

2007__518____________ 443.9

2008_ 563____________ 466.1

2009_584____________ 495.2

2010__

Using the formula :

Ft = Ft-1 + alpha(At-1 - Ft-1)

Ft-1 = previous year forecast

At-1 = previous year actual

Alpha = 0.3

Forecast:

2006:

410 + 0.3(450 - 410) = 422.0

2007:

422 + 0.3(495 - 422) = 443.9

2008:

443.9 + 0.3(518 - 443.9) = 466.1

2009:

466.1 + 0.3(563 - 466.1) = 495.2

2010:

495.2 + 0.3(584 - 495.2) = 521.8

Forecasted value for 2010 = 521.8

By utilizing the method of exponential smoothing with alpha=0.3 and applying the forecasting formula iteratively, the forecasted sales of Volkswagen Beetles for 2010 in Nevada is 525.7 units.

### Explanation:

The exponential smoothing method is commonly used in business and economics for forecasting future data in situations where historical data is available. The forecast value for 2010 using exponential smoothing with alpha = 0.30 can be obtained by implementing the provided formula in an iterative manner. This formula takes into account the actual data point from the previous year (At-1) and the forecasted data point for that year (Ft-1).

Let us use the forecast value for 2004 and 2005, which was predicted as 410 for each year, as our initial forecast value (F1).

By applying the formula Ft = Ft-1 + alpha * (At-1 - Ft-1) iteratively for each year from 2006 to 2009, we get:

• Forecast for 2006 (F_2006) would be 410 + 0.30*(450-410) = 422.
• Then, the forecast for 2007 (F_2007) is 422 + 0.30*(495-422) = 443.9.
• The forecast for 2008 (F_2008) is 443.9 + 0.30*(518-443.9) = 466.1.
• For 2009 (F_2009), the forecast is 466.1 + 0.30*(563-466.1) = 496.37.
•

Using these forecasted rates, we then forecast for the year 2010. The forecast for 2010 (F_2010) is calculated by 496.37 + 0.30*(584-496.37) giving 525.67 (rounded to one decimal place). Hence the forecast for the year 2010 using exponential smoothing with the alpha as 0.30 is estimated to be 525.7 VolksWagen Beetles.

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Find the surface area of the triangular prism.5 ft
5 ft
13 ft
4 ft
6 ft

234ft²

Step-by-step explanation:

Surface of the triangular prism

= ab+3bh

= (6ft×13ft)+(3×13ft×4ft)

= 78ft²+156ft²

= 234ft²

Hence, the surface area of the given triangular prism is 234ft².

5Type the correct answer in each box.
50°
60°
709
Х
50°
The value of xis
o, and the value of yis

x = 60°

y = 50°

Step-by-step explanation:

✅x = 180° - (50° + 70°) (sum of interior angles of a triangle theorem)

x = 180° - 120°

x = 60°

✅Based on the exterior angle theorem, the sum of the opposite interior angles of a triangle = the exterior angle.

Therefore,

50° + 60° = x + y

Plug in the value of x

50° + 60° = 60° + y

110° = 60° + y

y = 110° - 60°

y = 50°