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2 years ago

Let f(x)=25x2−2 .

Mathematics

2 answers:

avanturin [10]2 years ago

8 0

We are given function f(x) = 25x^2 -2.

g(x) is a vertical stretch of f(x) by a factor of 2.

We know, the transformation rule

y= k f(x), vertical stretch by a factor k. For k>0.

Because function f(x) is being vertical stretched by a factor of 2. So, we need to multiply f(x) function by 2.

Therefore, g(x) = 2 f(x) = 2*(25x^2-2).

Therefore, g(x) = 2*(25x^2-2) or g(x) = 50x^2-4.

melamori03 [73]2 years ago

3 0

Answer:

The Given function is

f(x)= 25 x² -2

Now, a function g(x) is obtained when the function f(x) is stretched by a factor of 2.

Consider point (x,y) on f(x).When function is stretched vertically by a factor of 2 ,it means, the coordinate changes from (x,y) to (x,2 y).

Since we have to stretch the function as whole, we will multiply original function by 2.

So, g(x)= 2× [25 x² - 2] =50 x² -4

g(x)=50 x²- 4

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A certain semiconductor device requires a tunneling probability of T = 10-5 for an electron tunneling through a rectangular barr

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2 years ago

Read 2 more answers

Karma is building a rectangular table with an area of 18,000 cm?. He wants to put wood trim around the four edges. What is the s

jok3333 [9.3K]

The shortest length is given by the function for the perimeter of the

rectangular table.

The shortest length of trim he could use is 536.66 cm

<h3>Method used for finding the shortest length of trim</h3>

The given parameter;

Area of the rectangular table Karma is building, A = 18,000 cm²

Required:

The shortest length of trim he could use which he wants to put around the four edges.

Solution:

Let l represent the length of the table, and let w represent the width, therefore;

Perimeter of the table, P = 2·l + 2·w

Area, A = l × w

Which gives;

18,000 = l × w

$l = \dfrac{18,000}{w}$

Which gives;

$P = 2 \cdot \dfrac{18,000}{w} + 2 \cdot w$

At the minimum point, we have;

$\dfrac{d}{dw} P = \dfrac{d}{dw} \left(2 \cdot \dfrac{18,000}{w} + 2 \cdot w\right)= \mathbf{\dfrac{2 \cdot w^2 - 36,000}{w^2} }= 0$

Which gives;

2·w² - 36,000 = w² × 0 = 0

2·w² = 36,000

$w^2 = \dfrac{36,000}{2} = 18,000$

The width of the rectangular table, w = √(18,000)

$Length \ of \ the \ table\ l = \dfrac{18,000}{\sqrt{18,000} } = \sqrt{18,000}$

Therefore;

The perimeter of the table, P ≈ 2 × √(18,000) + 2 × √(18,000) ≈ 536.656

The length of trim required = The perimeter of the rectangular table, P

Therefore;

The shortest length of the trim he could use, given to the nearest hundredth is 536.66 cm

Learn more about area and perimeter of a figure here:

brainly.com/question/9135929

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