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3 years ago

For the function f(x)=x^2, what effect will multiplying f(x) by 1/2 have on the graph?

1 answer:

5 0

For the function f ( x ) = x² we have the new function f 1 ( x ) = 1/2 x².
f ( x ) = a · x²
- If |a| < 1 the graph is compressed vertically by a factor of a.
- If |a| > 1 the graph is stretched vertically by a factor of a.
Here: a = 1/2 < 1
Answer:
C. The graph will be compressed vertically.

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A farmer has 520 feet of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one s

Setler [38]

Answer:

$310\text{ feet and }210\text{ feet}$

Step-by-step explanation:

GIVEN: A farmer has $520 \text{ feet}$ of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is $310 \text{ feet}$ .

TO FIND: Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions.

SOLUTION:

Let the length of rectangle be $x$ and $y$

perimeter of rectangular pen $=2(x+y)=520\text{ feet}$

$x+y=260$

$y=260-x$

area of rectangular pen $=\text{length}\times\text{width}$

$=xy$

putting value of $y$

$=x(260-x)$

$=260x-x^2$

to maximize $\frac{d \text{(area)}}{dx}=0$

$260-2x=0$

$x=130\text{ feet}$

$y=390\text{ feet}$

but the dimensions must be lesser or equal to than that of barn.

therefore maximum length rectangular pen $=310\text{ feet}$

width of rectangular pen $=210\text{ feet}$

Maximum area of rectangular pen $=310\times210=65100\text{ feet}^2$

Hence maximum area of rectangular pen is $65100\text{ feet}^2$ and dimensions are $310\text{ feet and }210\text{ feet}$

5 0

3 years ago

A ladder is leaning against a building as shown in the

JulsSmile [24]

The length of ladder is 30 ft.

<h3>How can the feet that made up the side of the building is the top of the ladder be known ?</h3>

The formula below can be used in solving the problem

Tan (∅)= $\frac{opposite}{adajacent}$

∅=70°

opposite = BC

Adjacent = 12 ft

70°= opposite/ 12

opposite= 32.96 ft

Therefore, The length of ladder is 30 ft.

NOTE; Since the actual diagram can not be found i solved another on on the same topic

Learn more about Trigonometry on:

brainly.com/question/7380655

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CHECK COMPLETE QUESTION BELOW:

Consider the diagram shown where a ladder is leaning against the side of a building. the base of the ladder is 12ft from the building. how long is the ladder? (to the nearest ft)

a. 25ft

b. 30ft

c. 35ft

d. 40ft