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Eva8 [605]
2 years ago
14

If the range of the coordinate transformation f(x,y) = (x – 5, y – 3) is (-6,-6) and (2,-3).

Mathematics
1 answer:
lina2011 [118]2 years ago
6 0

Answer:

(-2,1),(-1,2),(-3,5/3)

Step-by-step explanation:

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Find the equation of the lines, that is parallel to the line 9x-8y=1, and tangent to the elipses 9x^2+16y^2=52.
lara31 [8.8K]

Answer:

The equations of the lines that satisfy these conditions are

y = (9/8)x + (13/4)

And

y = (9/8)x - (13/4)

They can be written further as

8y = 9x + 26

and

8y = 9x - 26

Step-by-step explanation:

The line parallel to the line 9x - 8y = 1 has the same slope as 9x - 8y = 1

Writing the equation of the line in the (y = mx + c) form

8y = 9x - 1

y = (9/8)x - 1

So, the line(s) we are looking for has/have slope(s) of (9/8).

Its equation is then

y = (9/8)x + k

This line is then said to be tangent to the ellipses

9x² + 16y² = 52

So, since the line is a tangent to the ellipses, it will have the same coordinates as the ellipses at the point of contact.

9x² + 16y² = 52

y = (9/8)x + k

y² = (81/64)x² + (18k/8)x + k²

y² = (81/64)x² + (9k/4)x + k²

Substituting this into the ellipses equation,

9x² + 16y² = 52

9x² + 16[(81/64)x² + (9k/4)x + k²] = 52

9x² + (81/4)x² + 36kx + 16k² = 52

29.25x² + 36kx + 16k² - 52 = 0

Taking note that the two lines that will be tangent to the ellipses and parallel to the line given, to establish tangency, we make the discriminant of this equation 0. Hence, the roots of that equation will have equal roots.

So, the discriminant, b² - 4ac = 0

29.25x² + 36kx + 16k² - 52 = 0

a = 29.25

b = 36k

c = 16k² - 52

(36k)² - (4)×(29.25)×(16k² - 52) = 0

1296k² - 1872k² + 6084 = 0

576k² = 6084

k = ±(13/4)

So, the equation(s) of the line(s) required is

y = (9/8)x ± (13/4)

So, the equations include

y = (9/8)x + (13/4)

And

y = (9/8)x - (13/4)

Multiplying by 8, we obtain

8y = 9x + 26

8y = 9x - 26

Hope this Helps!!!

6 0
3 years ago
What is square root of 126 + square root of 56 in standard form
Feliz [49]
\sqrt{126}= 3\sqrt{14} \\ \\ \sqrt{56}=2\sqrt{14} \\ \\ \\ \sqrt{126}+ \sqrt{56}= 3\sqrt{14}+2\sqrt{14}= 5\sqrt{14}
6 0
2 years ago
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HELP I do not understand.
zzz [600]

There is no mode

because none of them appear the most

7 0
3 years ago
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A sprinkler mounted on the ground sends out a jet of water at a 30o angle to the horizontal. The water leaves the nozzle at a sp
dsp73

Answer:

12.7m

Step-by-step explanation:

The equation for motion to be used to find how far the water travels is

xf = xi + Vix(t) + 1/2axt^2

xf = 0 + ViCos α(t) + 0

xf = ViCosα(t)

xf = 12 Cos 30°(t)

xf = (6√3)t

To find the total times we will use the vertical displacement equation

yf = yi + Viy(t) + 1/2ayt^2

0 = 0 + ViSinα(t) + (1/2 * (-9.8)t^2)

0 = 12Sin30°(t) - 4.9t^2

4.9t^2 = 12Sin30°(t)

4.9t^2 = 6t

Divide through by t

4.9t = 6

t = 6/4.9

t = 1.22secs

Put t = 1.22 into (6√3)t

xf = 6√3 * 1.22

xf = 12.7m

5 0
2 years ago
- Round each number to four decimal places: a. 5.16 b. 5.27​
DochEvi [55]

Answer:

wym by 4 decimal places

Step-by-step explanation:

5 0
2 years ago
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