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lana [24]
3 years ago
8

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). f(x) = 6 cos

x ; g(x) = cos x Vertical stretch by a factor of 6 Horizontal shrink by a factor of one-sixth Horizontal stretch by a factor of 6 Vertical shrink by a factor of one-sixth
Mathematics
1 answer:
meriva3 years ago
7 0

Answer:

  Vertical stretch by a factor of 6

Step-by-step explanation:

Multiplying the function value by a constant moves its y-coordinate farther away from the x-axis by that factor. It causes a vertical stretch. Here, ...

  the vertical stretch factor is 6

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4th one is positive

Step-by-step explanation:

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Here is a triangular pyramid and its net.
galben [10]

Answer:

a) Area of the base of the pyramid = 15.6\ mm^{2}

b) Area of one lateral face = 24\ mm^{2}

c) Lateral Surface Area = 72\ mm^{2}

d) Total Surface Area = 87.6\ mm^{2}

Step-by-step explanation:

We are given the following dimensions of the triangular pyramid:

Side of triangular base = 6mm

Height of triangular base = 5.2mm

Base of lateral face (triangular) = 6mm

Height of lateral face (triangular) = 8mm

a) To find Area of base of pyramid:

We know that it is a triangular pyramid and the base is a equilateral triangle. \text{Area of triangle = } \dfrac{1}{2} \times \text{Base} \times \text{Height} ..... (1)\\

{\Rightarrow \text{Area of pyramid's base = }\dfrac{1}{2} \times 6 \times 5.2\\\Rightarrow 15.6\ mm^{2}

b) To find area of one lateral surface:

Base = 6mm

Height = 8mm

Using equation (1) to find the area:

\Rightarrow \dfrac{1}{2} \times 8 \times 6\\\Rightarrow 24\ mm^{2}

c) To find the lateral surface area:

We know that there are 3 lateral surfaces with equal height and equal base.

Hence, their areas will also be same. So,

\text{Lateral Surface Area = }3 \times \text{ Area of one lateral surface}\\\Rightarrow 3 \times 24 = 72 mm^{2}

d) To find total surface area:

Total Surface area of the given triangular pyramid will be equal to <em>Lateral Surface Area + Area of base</em>

\Rightarrow 72 + 15.6 \\\Rightarrow 87.6\  mm^{2}

Hence,

a) Area of the base of the pyramid = 15.6\ mm^{2}

b) Area of one lateral face = 24\ mm^{2}

c) Lateral Surface Area = 72\ mm^{2}

d) Total Surface Area = 87.6\ mm^{2}

8 0
2 years ago
!
Darina [25.2K]

The graph of the equations was plotted using geogebra graphing and attached.

Let x represent the hours weightlifting and y represent the hours doing cardio exercises.

Since he spend a maximum of 20 hours, hence:

x + y ≤ 20   (1)

Also, he spends at least 8 of those hours weightlifting, hence:

x ≥ 8          (2)

He wants to spend no more than 15 hours doing cardio exercises, this is:

y ≤ 15     (3)

The graph of the equations was plotted using geogebra graphing and attached.

Find out more at: brainly.com/question/17178834

3 0
3 years ago
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