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Svet_ta [14]
3 years ago
5

Determine the direction that this parabola opens y=x^2-6x

Mathematics
1 answer:
nalin [4]3 years ago
8 0

Answer:

the graph of the parabola opens upwards.

Step-by-step explanation:

For any quadratic equation of the form

ax ^ 2 + bx + c is true that:

if the main coefficient "a" is negative then the graph of the parabola opens downwards.

If the main coefficient "a" is positive, the parabola opens upwards

In this case the parabola is y=x^2-6x

Note that a=1 and a>0 therefore the graph of the parabola opens upwards.

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Answer:

Thats pretty neat

Step-by-step explanation:

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3 years ago
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Why is the addition or subtraction of k to the output of a function considered a translation?
Nataliya [291]

Answer:

k translates a function up or down

Step-by-step explanation:

hope this helped :)

7 0
3 years ago
Y=x(sin(x)), 0 ≤ x ≤ 2π?
Lemur [1.5K]
Careful; (dy/dx)^2 = x^2 cos^2(x) + 2x sin x cos x + sin^2(x).

<span>So, the arc length equals </span>
<span>∫(x = 0 to 2π) √[1 + (x^2 cos^2(x) + 2x sin x cos x + sin^2(x))] dx </span>
<span>= ∫(x = 0 to 2π) √[1 + x^2 cos^2(x) + x sin(2x) + sin^2(x)] dx, via double angle identity. </span>

<span>Let Δx = (2π - 0)/10 = π/5. </span>
<span>Using Simpson's Rule with n = 10, this integral approximately equals </span>
<span>((π/5)/3) * [f(0) + 4 f(π/5) + 2 f(2π/5) + 4 f(3π/5) + 2 f(4π/5) + 4 f(π) + 2 f(6π/5) + 4 f(7π/5) + 2 f(8π/5) + 4 f(9π/5) + f(2π)], </span>

<span>where f(x) = √[1 + x^2 cos^2(x) + x sin(2x) + sin^2(x)]. </span>
<span>------- </span>
<span>I hope this helps!</span>
4 0
4 years ago
Aaliyah's Tea Shop has caffeinated tea and decaffeinated tea. The tea shop served 50 teas in all, 10 of which were caffeinated.
fenix001 [56]

20% we're caffeinated because out of 50 20% of 50 is 10

8 0
3 years ago
3. y=37x+11y=37x+11 -3x + 7y = 13 Part A: Convert the second equation to slope-intercept form. Show your work! Part B: Determine
melamori03 [73]

We are given first equation y=\frac{3}{7}x+11.

Second equation is -3x + 7y = 13.

Part A: We need to convert that second equation in slope-intercept form y=mx+b.

In order to convert it in slope-intercept form, we need to isolate it for y.

-3x + 7y = 13

Adding 3x on both sides, we get

-3x+3x + 7y = 3x+13

7y = 3x +13.

Dividing both sides by 7, we get

7y/7 = 3x/7 +13/7.

<h3>y= 3/7 x + 13/7.</h3>

Slope for first equation y=3/7 x +11 is 3/7 and slope of second equation y= 3/7 x + 13/7 is also 3/7.

Slopes are same for both equations.

<h3>Part B: Therefore, lines are parallel due to equal slopes.</h3>
7 0
3 years ago
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