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3 years ago

Write the equation of a line PARALLEL to y = 2x + 3 that passes through the point (3, 1).

Mathematics

1 answer:

White raven [17]3 years ago

8 0

Answer:

Step-by-step explanation:

y - 1 = 2(x - 3)

y - 1 = 2x - 6

y = 2x - 5

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Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 41 and 6

Lapatulllka [165]

Answer:

(a). The sinusoidal function is

-14×cos((π/12)×(t-2))+55

(b). The temperature of 48 ° first occurs at 6.00 a.m.

Step-by-step explanation:

To solve the question, we note that an example of a sinusoidal function is a cosine function

a×cos×(2π/k)t+b = Temperature

For a 24 hour period, the sinusoidal function becomes

2π/k =24 or k = π/12 and

a = (69 - 41)/2 = 14 also b = 69 -14 = 55

Therefore the sinusoidal function becomes

14×cos((π/12)×t)+55 = Temperature at a particular time of day

checking we have

at 6 a.m. 14×cos(π/2) +55 = 55 ° okay

However the average temperature supposed to occur at 8 a.m.

Therefore we have time adjustment by 2 hours hence

Our equation becomes

-14×cos((π/12)×(t-2))+55 = Temperature

Therefore at 8 a.m. we have

-14×cos((π/12)×(8-2))+55 = 55 ° = average temperature

And

(b) For 48 °, we have

-14×cos((π/12)×(t-2))+55 = 48

or t = 6 a.m.

7 0

4 years ago

Write the equation of the trigonometric graph.

prisoha [69]

Answer:

$f(x)= \sin(6x)+3$

Step-by-step explanation:

The parent function of this graph is: y = sin(x)

The sine function is periodic, meaning it repeats forever.

Standard form of a sine function:

$f(x) = \sf A \sin (B(x + C)) + D$

A = amplitude (height from the mid-line to the peak)
2π/B = period (horizontal distance between consecutive peaks)
C = phase shift (horizontal shift - positive is to the left)
D = vertical shift

The parent function y = sin(x) has the following:

Amplitude (A) = 1
Period = 2π
Phase shift (C) = 0
Vertical shift (D) = 0
Mid-line: y = 0

From inspection of the given graph:

Amplitude (A) = 1
$\sf Period=\dfrac{\pi}{12}-\dfrac{-\pi}{4}=\dfrac{\pi}{3}$
Phase shift (C) = 0
Vertical shift (D) = +3 (as mid-line is y = 3)

$\sf If\:Period=\dfrac{\pi}{3} \implies \dfrac{2 \pi}{B}=\dfrac{\pi}{3}\implies B=6$

Substituting the values into the standard form:

$\implies f(x) =1 \sin (6(x + 0)) + 3$

$\implies f(x) = \sin (6x) + 3$

Therefore, the equation of the given trigonometric graph is:

$f(x)= \sin(6x)+3$

6 0

2 years ago

{(-5,9),(2, 31), (9, 143), (11, 151),(0, 42),(5, 97)}

wlad13 [49]

The number 7 is the best prediction of the output when the input is 13.

<h3>What is the equation of a line passing through two given points in 2 dimensional plane?</h3>

Suppose the given points are (x_1, y_1) and (x_2, y_2), then the equation of the straight line joining both two points is given by

$(y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)$

The equation of the line is found as;

$\rm y-y_1= \frac{y_2-y_1}{x_2-x_1} \\\\ \rm y-9= \frac{31-9}{2+5} (x+5)\\\\ 7y-63 = \frac{31-9}{2+5} (c+5)\\\\ 7y-63=22x+110\\\\ 7y= 22x+173 \\\\ but ,x=13\\\\ 7y=22 \times 13 +173\\\\ y= \frac{1259}{7} \\\\ y= 179$

Learn more about straight line equation here:

brainly.com/question/380976

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8 0

2 years ago

Kevin is making a picture frame he has a piece of trim that is 5 feet long how many 7 inch long pieces can kevin cut from the tr

pogonyaev

Answer:

8 pieces

Step-by-step explanation:

5 0

3 years ago

A game has a rectangular board with an area of 44in2. There is a square hole near the top of the game board in which you must no

zzz [600]

9/44 chance of tossing it through the hole.

3 0

3 years ago

Read 2 more answers