MATHEMATICS HIGH SCHOOL

Find the vertex of the parabola
y= x^2-2x-1
vertex (?,?)

Answers

Answer 1
Answer: y=ax^2+bx+c\n\nvertex:(x_v;\ y_v)\n\nx_v=(-b)/(2a)\ and\ y_v=f(x_v)


y=x^2-2x-1\n\na=1;\ b=-2;\ c=-1\n\nx_v=(-(-2))/(2\cdot1)=(2)/(2)=1\n\ny_v=1^2-2\cdot1-1=1-2-1=-2\n\nAnswer:(1;-2)
Answer 2
Answer: y=a(x-h)^2+k \Rightarrow \hbox{vertex}=(h,k)\n\n y=x^2-2x-1\n y=x^2-2x+1-2\n y=(x-1)^2-2 \Rightarrow \hbox{vertex}=(1,-2)

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Find the x-coordinates where f '(x) = 0 for f(x) = 2x + sin(2x) in the interval [0, 2π]. so far I found f'(x)=2cos(2x)+2 cos(2x)=-1

Answers

The solutions of the equation f\left( x \right) = 2x + \sin \left( {2x} \right) in the interval \left[ {0,2\pi } \right] are \boxed{\left( {(\pi )/(2),\pi } \right)} and \boxed{\left( {\frac{{3\pi }}{2},3\pi } \right)}.

Further explanation:

Given:

The function is f\left( x \right) = 2x + \sin \left( {2x} \right).

The first derivative is zero.

Explanation:

The given function is f\left( x \right) = 2x + \sin \left( {2x} \right).

Differentiate the function with respect to x.

\begin{aligned}f'\left( x \right) &= 2 + 2\cos \left( {2x} \right)\n&= 2\left( {1 + \cos 2x} \right)\n\end{aligned}

Substitute 0 for f'\left( x \right).

\begin{aligned}2\left( {1 + \cos 2x} \right) &= 0 \n1 + \cos 2x &= 0\n\cos 2x &= - 1\n2x &= {\cos ^( - 1)}\left( { - 1} \right)\n2x &= \frac{{\left( {2n - 1} \right)\pi }}{2} \n\end{aligned}

In the interval \left[ {0,2\pi } \right] the x-coordinates are \boxed{(\pi )/(2)}{\text{ and }}\boxed{\frac{{3\pi }}{2}}.

The solutions of the equation f\left( x \right) = 2x + \sin \left( {2x} \right) in the interval \left[ {0,2\pi } \right] are \boxed{\left( {(\pi )/(2),\pi } \right)} and \boxed{\left( {\frac{{3\pi }}{2},3\pi } \right)}.

Learn more:

  1. Learn more about inverse of the function brainly.com/question/1632445.
  2. Learn more about equation of circle brainly.com/question/1506955.
  3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Application of derivatives

Keywords: derivative, x – coordinates, interval, far, 2x, sin2x, coordinates, 0, 2pi, y-coordinate.
From there, you simply need algebra and a calculator that works in radians.

Take the inverse cos of both sides to get 2x = arccos(-1) 

Then divide both sides by 2 to get x = arccos(-1) / 2 

Put that into a calculator and you get π/2. But because your bounds are 0 to 2π, you have to add π your solution to get the solution on the other side of the unit circle, which would be (3π/2).

Now that you have the x value, put (π/2) and (3π/2) into f(x) to get the y coordinate. 

f(π/2) = 2(π/2) + sin(2(π/2) = π, which means this solution is just (π/2, π)
f(3π/2 = 2(3π/2) + sin(2(3π/2) = 3π, which means this solution is (3π/2, 3π)

If the measure of angle 2 is (5 x + 14) degrees and angle 3 is (7 x minus 14) degrees, what is the measure of angle 1 in degrees?A.88
B.89
C.90
D.91

Answers

Answer:

d

Step-by-step explanation:

Find the range of the following piecewise function. A. [2,16)

B. (2,16]

C. [2,∞)

D. (2,∞)

Answers

Answer:

  None of the Above

Step-by-step explanation:

The range is [2, ∞) excluding (2, 7) and [11, 16). No part of the piecewise function will give f(x) = 5, for example.

a vehicle travels 24km with a constant speed of 65 km/h and another 50 km with a constant speed of 80 km/h what was its average speed

Answers

average speed=totaldistance/totaltime

totaldistance=24+50=74km

total time
65/24=0.3692307 hours

80/50=1.6 hours
total time=0.3692307+1.6=1.9692307

averagespeed=74/1.9692307=37.5781263 km/h

Pythagorean Theorem Determine the length of the missing side?

Answers

The answer should be 12.2
7^2+10^2=c^2
49+100=c^2
149=c^2
12.2=c

Answer:

c= sqrt149; 12.2 rounded

Step-by-step explanation:

Pythagorean Theorem to find c(hypotenuse): a^2+b^2=c^2

7^2+10^2=149

sqrt149= 12.2 rounded

Mark is solving the following system.x+y+z=2 (1)
3x+2y+z=8 (2)
4x-y-7z=16 (3)

Step 1: He multiplies equation (1) by 7 and adds it to equation (3).
Step 2: He multiplies equation (3) by 2 and adds it to equation (2).

Which statement explains Mark’s mistake?
- He added equation (3) instead of equation (2) in step 1.
- He did not multiply equation (3) by the correct value.
- He did not eliminate the same variables in steps 1 and 2.
- He added equation (3) and equation (2) instead of subtracting.

Answers

Solving the system of linear equations Mark tries to apply elementary transformations in order to eliminate one variable.

He makes such steps:

1. He multiplies equation (1) x+y+z=2 by 7 and adds it to equation (3) 4x-y-7z=16. This gives him:

7x+7y+7x+4x-y-7z=14+16,

11x+6y=30.

2. He multiplies equation (3)  4x-y-7z=16 by 2 and adds it to equation (2) 3x+2y+z=8. This step gives him:

8x-2y-14z+3x+2y+z=32+8,

11x-13z=40.

Thus, he did not eliminate the same variables in steps 1 and 2.

Answer: correct choice is C
I think its he didnt eliminate the same variables
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