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3 years ago

Solve for x and y: (x + yi) -(2-1) = 12 +7i

Mathematics

1 answer:

kumpel [21]3 years ago

8 0

Answer:

These are the answers.

Step-by-step explanation:

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A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh

aleksklad [387]

The spider's movement is an illustration of a parabola.

The equation of a parabola is: $\mathbf{y = -\frac{1}{160}(x - 40) + 10}$
The focus of a parabola is: (40,-30)
The axis of symmetry is: $\mathbf{x = 40}$
The directrix is: $\mathbf{y = 50}$

(a) The equation

The spider passes through the origin.

So, we have:

$\mathbf{(x,y) = (0,0)}$

The spider jumps to a maximum height of 10mm, midway 80mm.

So, the vertex is:

$\mathbf{(h,k) = (40,10)}$

The equation of a parabola is:

$\mathbf{y = a(x - h)^2 + k}$

So, we have:

$\mathbf{0 = a(0 - 40)^2 + 10}$

Subtract 10 from both sides

$\mathbf{a(0 - 40)^2 =- 10}$

$\mathbf{1600a =- 10}$

Solve for a

$\mathbf{a =- \frac{1}{160}}$

Substitute $\mathbf{a =- \frac{1}{160}}$ and $\mathbf{(h,k) = (40,10)}$ in $\mathbf{(h,k) = (40,10)}$

$\mathbf{y = -\frac{1}{160}(x - 40) + 10}$

(b) The focus, directrix and the axis of symmetry

The focus of a parabola is:

$\mathbf{Focus= (h, k + p)}$

Where:

$\mathbf{p = \frac{1}{4a}}$

So, we have:

$\mathbf{p = \frac{1}{4 \times -1/160}}$

$\mathbf{p = -\frac{160}{4}}$

$\mathbf{p = -40}$

So, we have:

$\mathbf{Focus = (40,10-40)}$

$\mathbf{Focus = (40,-30)}$

The axis of symmetry is:

$\mathbf{x = h}$

So, we have:

$\mathbf{x = 40}$

The directrix is:

$\mathbf{y = k - p}$

$\mathbf{y = 10 + 40}$

$\mathbf{y = 50}$

Read more about parabolas at:

brainly.com/question/25237745

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2 years ago

Which linear function has the greatest y-intercept?

Zolol [24]

Put these all in slope intercept form: y=mx+b

m=slope
b=y intercept

Working out option A)
x+6y=36
6y=-x+36
y=-1/6x+6

Option B)
y=15x+5

Option C)
Is there a typo? Regardless of how I attmpeted to fix it, it had an intercept of either 3 or 4

Option D)
y=4x+7

The answer is D with the greatest y-intercept of 7.

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3 years ago

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y = -2.

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Inga, Kai, and Jason volunteer in the school library. They want to find the average number of pages of a library book. It would

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Answer:

Kai did bc it is from the libraries entire catalog so it could be any genre so it would produce an unbiased sample :)

Step-by-step explanation:

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