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4 years ago

An equation of the line tangent to y=sin x + 2cosx at (pi/2, 1) is?

Mathematics

1 answer:

Lina20 [59]4 years ago

6 0

Answer:

B. 2x + y = pi + 1.

Step-by-step explanation:

y = sin x + 2 cos x

The slope of a line tangent is the derivative, so:

y' = cos x - 2 sin x

At (pi/2, 1) , substituting for x:-

cos pi/2 - 2 sin pi/2

= 0 - 2 * 1 = -2.

So the slope is - 2 and an equation can be found by using the point-slope formula:

y - y1 = m(x - x1) so:

y - 1 = -2(x - pi/2)

y = -2x + pi + 1

2x + y = pi + 1.

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The following scatter plot shows the number of page views for a popular website and how many people signed up to receive emails

My name is Ann [436]

Answer:

See Explanation.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtract Property of Equality

Algebra I

Slope Formula: $\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

Slope-Intercept Form: y = mx + b

m - slope
b - y-intercept

Linear Regression

Step-by-step explanation:

We can draw any best line of fit, as long as it is reasonable around the points that are given.

We can just take 2 points and use slope formula and Slope-Intercept Form to find the equation for the best line of fit.

Using Linear Regression, we can determine the true best line of fit using graphing utilities.

Finding the best line of fit

Define 2 points

Point (21600, 205)

Point (27000, 290)

Find slope m

Substitute in point [SF]: $\displaystyle m=\frac{290-205}{27000-21600}$
[Fraction] Subtract: $\displaystyle m=\frac{85}{5400}$
[Fraction] Simplify: $\displaystyle m=\frac{17}{1080}$

Find equation

Define equation [SIF]: $\displaystyle y = \frac{17}{1080}x + b$
Substitute in point: $\displaystyle 290 = \frac{17}{1080}(27000) + b$
Multiply: $\displaystyle 290 = 425 + b$
Isolate y-intercept b: $\displaystyle -135 = b$
Rewrite: $\displaystyle b = -135$
Redefine equation: $\displaystyle y = \frac{17}{1080}x - 135$

Slope-Intercept Form tells us that our slope m = $\displaystyle \frac{17}{1080}$ and our y-intercept $\displaystyle b = -135$ .

Setting this as function f(x), we can see from the graph that it is extremely accurate (Blue line).

Using Linear Regression

Depending on the graphing calc you have, the steps may be different.

Using a graphing calc, we can use statistics and determine the best best line of fit.

When we determine the values, we should see that our equation would be g(x) (Green Line).

Credit to Lauren for collabing w/ me in graphing.

6 0

3 years ago

Whats 2x (3x-9x) if you answer this you get 10 points

Masteriza [31]

Answer:

2x(3x-9x)

=2x(-6x)

=-12x^2

7 0

3 years ago

Read 2 more answers

Which is the same as moving the decimal point 3 places to the left in a decimal

Ludmilka [50]

Multiplying the number by 1,000

5 0

3 years ago

Kelsey wants to split 19.2 feet of ribbon equally

timama [110]

Answer:

The answer is 115.2.

Step-by-step explanation:

7 0

3 years ago

C an you simplify 5^-8 x 5^4

EastWind [94]

Answer:

1/625

Step-by-step explanation:

Exponent Rule: $(b^m)(b^n) = b^{m+n}$

Exponent Rule: $b^{-m}=\frac{1}{b^m}$

5⁻⁸ · 5⁴ = -8 + 4 = -4

5⁻⁴

1/5⁴

1/625

6 0

4 years ago