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3 years ago

Which transformations are needed to change the parent some function to the sine function below?

Mathematics

2 answers:

Marrrta [24]3 years ago

5 0

Beginning with the function y = sin x, which would have range from -1 to 1 and period of 2pi:
Vertical compression of 1/2 compresses the range from -1/2 to 1/2
Phase shift of pi/2 to the left
Horizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4pi
Vertical shift of 1 unit up moves the range to 1/2 to 3/2
So the first choice looks like a good answer.

Umnica [9.8K]3 years ago

5 0

The first choice is the answer:
Solution:the function y = sin x, which would have range from -1 to 1 and period of 2pi:
So the answer would be:Vertical compression of 1/2 compresses the range from -1/2 to 1/2Phase shift of pi/2 to the leftHorizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4piVertical shift of 1 unit up moves the range to 1/2 to 3/2

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(x-4)/5=9-(2x-41)/9

jok3333 [9.3K]

For this question, you have to take Least Common Multiplier for which in this case will be "45" as, the denominators can get similar and get multiplied by a same value to form a similar expression. This allows us to cancel out them by common factors. Full process shown below.

$\mathbf{Given \: \: Expression: \: \dfrac{x - 4}{5} = 9 - \dfrac{2x - 41}{9}}$

$\mathbf{\dfrac{x - 4}{5} \times 45 = 9 \times 45 - \dfrac{2x - 41}{9} \times 45}$

$\mathbf{9(x - 4) = 405 - 5 (2x - 41)}$

$\mathbf{9x - 36 = 405 - 10x + 205}$

$\mathbf{9x - 36 = - 10x + 610}$

$\mathbf{9x - 36 + 36 = - 10x + 610 + 36}$

$\mathbf{9x = - 10x + 646}$

$\mathbf{9x + 10x = - 10x + 646 + 10x}$

$\mathbf{19x = 646}$

$\mathbf{\dfrac{19x}{19} = \dfrac{646}{19}}$

$\mathbf{\therefore \quad x = 34}$

$\boxed{\mathbf{\underline{\therefore \quad Final \: \: Answer \: \: is; \: \: x = 34}}}$

Hope it helps.

3 0

2 years ago

From the observation deck of a skyscraper, Harper measures a 45^{\circ} ∘ angle of depression to a ship in the harbor below. If

Evgesh-ka [11]

The horizontal distance between the base of the skyscraper to the ship is 1145 feet.

Data;

Angle = 45 degree
Observation deck (adjacent) = 1145 ft
horizontal distance (opposite) = x

<h3>Trigonometric Ratios</h3>

Using trigonometric ratios, we have the value of adjacent and angle, we can easily use tangent of the angle to find the horizontal distance

$tan\theta = \frac{opposite}{adjacent}$

Substitute the values into the equation and solve

$tan45 = \frac{x}{1145}\\ x = 1145tan45\\x = 1145ft$

The horizontal distance between the base of the skyscraper to the ship is 1145 feet.

Learn more on trigonometric ratio here;

brainly.com/question/4326804

5 0

2 years ago

Maths-please help Factorise 3y+15

djyliett [7]

Answer:

3(y + 5)

Step-by-step explanation:

Factorization is a process which is like the opposite of expansion. It involves factoring out the common factors from the given terms.

Thus to factorize 3y + 15, we have to consider the common factor(s) of the two terms. The common factor is 3 because the two terms (i.e 3y and 15) are both divisible by 3 only.

So that:

3y + 15= 3( $\frac{3y}{3}$ + $\frac{15}{3}$ )

= 3(y + 5)

The outcome of the process is 3(y + 5).

7 0

3 years ago

What is the mean for this data set?

Ann [662]

Mean - 26
Mode- 29,6
Median-29

4 0

3 years ago

Below is a scale drawing of a stage that Syla is designing. A rectangle with length 8 centimeters and width 5 centimeters. Using

serious [3.7K]

Answer:

Step-by-step explanation:

Given the dimension

Length of the rectangle = 8cm

Width = 5cm

Note that when the scale was 1:7, syla multiplied the width by a factor of 7 i.e 5*7 = 35m

If syla changes the the scale to 1 cm : 10 m for the rectangle, then the width of the shorter side will be multiplied by a factor of 10 due to the change in scale i.e;

5 * 10 = 50m

Hence the width of the new stage will be 50 m

6 0

3 years ago