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3 years ago

What is the maximum vertical distance between the line y = x 30 and the parabola y = x2 for −5 ≤ x ≤ 6?

1 answer:

7 0

Set y1=x+30 and y2=x^2, plugged those into the distance formula assuming x=a,

d=rad((y2−y1)^2)
d(x)=x^2−x−30

All you have to do is to maximize the given quadratic function. I hope that this is the answer that you were looking for and it has helped you.

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Determine if the pairs of vectors below are "parallel", "orthogonal", or "neither".

Irina18 [472]

Answer:

1.Orthogonal

2.Parallel

3.Neither

Step-by-step explanation:

We have to find pair of vectors are parallel , orthogonal or neither.

1.a=(-3,3,-5) and b=(-6,6,36/5)

We know that when vectors are parallel then,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

When vectors are orthogonal then,

$a_1a_2+b_1b_2+c_1c_2=0$

$\frac{a_1}{a_2}=\frac{-3}{-6}=\frac{1}{2}$

$\frac{b_1}{b_2}=\frac{3}{6}=\frac{1}{2}$

$\frac{c_1}{c_2}=\frac{-5\times 5}{36}=-\frac{25}{36}$

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}$

Hence, the vectors are not parallel.

$a_1a_2+b_1b_2+c_1c_2=-3(-6)+3(6)+(-5)(\frac{36}{5})=18+18-36=0$

Hence, the vectors are orthogonal.

b.a=(-3,3,-5), b=(-6,6,-10)

$\frac{a_1}{a_2}=\frac{-3}{-6}=\frac{1}{2}$

$\frac{b_1}{b_2}=\frac{3}{6}=\frac{1}{2}$

$\frac{c_1}{c_2}=\frac{-5}{-10}=\frac{1}{2}$

$\frac{a_1}{a_2}=\frac{b_1}{b_2}= \frac{c_1}{c_2}$

Hence, the vectors are parallel.

3.a=(-3,3,-5) and b=(12,-12,19)

$a_1a_2+b_1b_2+c_1c_2=-3(12)+3(-12)+(-5)(19)=-36-36-95\neq 0$

Hence, the vectors are not orthogonal.

$\frac{a_1}{a_2}=\frac{-3}{12}=-\frac{1}{4}$

$\frac{b_1}{b_2}=-\frac{3}{12}=-\frac{1}{4}$

$\frac{c_1}{c_2}=\frac{-5}{19}$

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}$

Hence, the vectors are not parallel.

8 0

3 years ago

1 2.2.5 Quiz: Solving Problems by Dividing Fractions

melamori03 [73]

Answer:

the fractions need to be divided into 1

if not then add all the fractions up to make the bird house and its over 1 then the difference is one is the answer as she may need more than 1 day.

Step-by-step explanation:

5 0

3 years ago

(3x^3-2x^2+4)-(2x^2+14)

LenKa [72]

$(3 {x}^{3} - 2 {x}^{2} + 4) - (2 {x}^{2} + 14) \\ 3 {x}^{3} - 2 {x}^{2} + 4 - 2 {x}^{2} - 14 \\ 3 {x}^{3} - 10$

5 0

3 years ago

Describe the key features of the graph of the quadratic function f(x) = x2 + 2x - 1 A. Does the parabola open up or down? B. Is

myrzilka [38]

A.) it opens up because it is positive. B. The vertex is a minimum, because it opens up C/ The axis of symmetry is X=-1, the Vertex is (-1,-2). The Y interecept is y= -1

7 0

4 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=solve%20for%20%22m%22%20t%3D%5Cfrac%7Bms%7D%7Bm%2Bn%7D" id="TexFormula1" title="solve for &quo

dalvyx [7]

Answer:

$\boxed{\sf \ \ \ m = -\dfrac{tn}{t-s} \ \ \ }$