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GrogVix [38]
3 years ago
12

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}

<u>(a) The equation</u>

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}

<u>(b) The focus, directrix and the axis of symmetry</u>

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

4 0
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.
5 0
3 years ago
Read 2 more answers
Find the midline for f(x)=−2+4cosx.
diamong [38]
The mid-line for f(x) = 4cos x is y = 0. In the given equation, the term -2 is described as the y-shift. Therefore the mid-line for f(x) = -2 + 4cos x is:
y = -2.
7 0
3 years ago
Inga, Kai, and Jason volunteer in the school library. They want to find the average number of pages of a library book. It would
Arisa [49]

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:

7 0
3 years ago
Read 2 more answers
During the first 50 minutes of flight, the Concorde climbs from ground level to an altitude of about 52,000 ft. What is the conc
horsena [70]

Let

x--------> the time in minutes

y-------> an altitude in feet

we know that

For x=0 min  y=0 ft

For x=50 min y=52,000 ft

so

the rate of change is equal to calculate the slope of the linear equation

\frac{52,000-0}{50-0}=\frac{52,000}{50}=1,040\frac{ft}{min}

Round to the nearest hundred-------->1,000\frac{ft}{min}

therefore

<u>the answer is</u>

1,000\frac{ft}{min}


7 0
3 years ago
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