F(x)= -2x^2 +8x -12 in vertex form
Answers
y = -2x² + 8x - 12
+ 12 + 12
y + 12 = -2x² + 8x
y + 12 - 8 = -2x² + 8x - 8
y - 4 = -2(x²) - 2(-4x) - 2(4)
y - 4 = -2(x² - 4x + 4)
y - 4 = -2(x² - 2x - 2x + 4)
y - 4 = -2[x(x) - x(2) - 2(x) - 2(-2)]
y - 4 = -2[x(x - 2) - 2(x - 2)]
y - 4 = -2(x - 2)(x - 2)
y - 4 = -2(x - 2)²
+ 4 + 4
y = -2(x - 2)² + 4
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How do you rename each additive inverse without parentheses -(2x+7)
Answers
2
sin
x
at the point (π/6,1)
π
6
1
.
The equation of this tangent line can be written in the form y=mx+b
y
m
x
b
where
Answers
Final answer:
To find the equation of the tangent line to the curve y=2sinx at the point (π/6,1), we take the derivative to find the slope and then use the point-slope form of the line equation. The result is y = √3x + 1 - √3π/6.
Explanation:
The subject of this question is calculus and focuses specifically on finding the equation of the tangent line to the curve y=2sinx at a given point. To do this, we use the formula y=mx+b.
Firstly, the slope of the tangent line is obtained by taking the derivative of the function at the point of tangency. The derivative of y=2sinx is y'=2cosx. For the given point (π/6,1), the slope (m) would be 2cos(π/6) = √3.
Secondly, we use the point-slope form of the line equation to find b. Inserting the values of the slope (m) and the given point into the equation, we get 1 = √3(π/6) + b. Solving for b gives b = 1 - √3π/6.
Finally, the equation of the tangent line is y = √3x + 1 - √3π/6.
Learn more about Tangent Line here:
#SPJ2
f(x) = 2sin(x)
f(π/6) = 1
f'(x) 2cos(x)
f'(π/6) = 2×co(π/6) = 2 × root(3)×0.5 =root(3)
The equation of this tangent line is : y= root(3)(x-π/6)+1
y = root(3)x+1 - π/6(root(x)) in the form y=mx+b
m = root(3) and b = 1 - π/6(root(x))
Answers
5x + 3(x – 5) = 6x + 2x – 15
Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points)
Part B: Name one property you used to solve this equation. (4 points)
Answers
Hi there
5x+3(x-5)=6x+2x-15
Simplify both sides of the equation
5x+3(x-5)=6x+2x-15
Distribute
5x+3x-15=6x+2x-15
Combine like terms
(5x+3x)-15= (6x+2x)-15
8x-15=8x-15
Subtract 8x from both sides
8x-15-8x=8x-15-8x
-15=-15
Add 15 to both sides
-15+15=-15+15
0=0
All real numbers are solutions
To solve this equation I used " The distributive property"
I hope that's help !
Good night !
Answers
(5,2)
5=x
y=2
5-3=2
hope that helps
y = x - 3. (x, y)
Answers
Rectangle:
Length = 2 units
Width = 3 units
Area = Length x Width = 3 x 2 = 6 units²
Triangle:
Base = 2
Height = 2
Area = 1/2BH = 1/2(2)(2) = 2 units²
Total Area:
2 u² + 6 u² = 8 units²
Hope this helps! :)