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3 years ago

PLEASE HELP!

Mathematics

1 answer:

Oksana_A [137]3 years ago

6 0

Answer:

c) A rectangle with width of 9 mm and length of 45 cm.

d) A rectangle with width of 10 cm and length of 44 cm.

Step-by-step explanation:

Given:

Length of the rectangle = 32 in.

Width of the rectangle = 8 in.

First we will find the ratio of length by width.

$\frac{length}{width}= \frac{32}{8} = \frac{4}{1} \ \ \ \ equation \ 1$

Now we need to find from the given Option which rectangles are not similar to Carl's Rectangle.

So we will check for each.

a) A rectangle with width of 23 cm and length of 92 cm.

we will find the ratio of length by width.

$\frac{length}{width}= \frac{92}{23} = \frac{4}{1} \ \ \ \ equation \ 2$

By Definition of Similar rectangles which states that;

"When ratio of the dimension of 2 corresponding rectangles are equal then the 2 rectangles are said to be similar."

Now Comparing equation 1 and equation 2 we get;

equation 1 $=$ equation 2

Hence This rectangle is similar to Carl's rectangle.

b) A rectangle with width of 2.5 inch and length of 10 inch.

we will find the ratio of length by width.

$\frac{length}{width}= \frac{10}{2.5} = \frac{4}{1} \ \ \ \ equation \ 2$

By Definition of Similar rectangles which states that;

"When ratio of the dimension of 2 corresponding rectangles are equal then the 2 rectangles are said to be similar."

Now Comparing equation 1 and equation 2 we get;

equation 1 $=$ equation 2

Hence This rectangle is similar to Carl's rectangle.

c) A rectangle with width of 9 mm and length of 45 cm.

we will find the ratio of length by width.

$\frac{length}{width}= \frac{45}{9} = \frac{5}{1} \ \ \ \ equation \ 2$

By Definition of Similar rectangles which states that;

"When ratio of the dimension of corresponding rectangles are equal then the 2 rectangles are said to be similar."

Now Comparing equation 1 and equation 2 we get;

equation 1 $\neq$ equation 2

Hence This rectangle is not similar to Carl's rectangle.

d) A rectangle with width of 10 cm and length of 44 cm.

we will find the ratio of length by width.

$\frac{length}{width}= \frac{44}{10} = \frac{11}{5} \ \ \ \ equation \ 2$

By Definition of Similar rectangles which states that;

"When ratio of the dimension of corresponding rectangles are equal then the 2 rectangles are said to be similar."

Now Comparing equation 1 and equation 2 we get;

equation 1 $\neq$ equation 2

Hence This rectangle is not similar to Carl's rectangle.

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Graph y = 3(x + 2)3 - 3 and describe the end behavior.

-BARSIC- [3]

1) The function is 3(x + 2)³ - 3

2) The end behaviour is the limits when x approaches +/- infinity.

3) Since the polynomial is of odd degree you can predict that the ends head off in opposite direction. The limits confirm that.

4) The limit when x approaches negative infinity is negative infinity, then the left end of the function heads off downward (toward - ∞).

5) The limit when x approaches positive infinity is positivie infinity, then the right end of the function heads off upward (toward + ∞).

6) To graph the function it is important to determine:
- x-intercepts
- y-intercepts
- critical points: local maxima, local minima, and inflection points.

7) x-intercepts ⇒ y = 0

⇒ 3(x + 2)³ - 3 = 0 ⇒ (x + 2)³ - 1 = 0


⇒ (x + 2)³ = -1 ⇒ x + 2 = 1 ⇒ x = - 1


8) y-intercepts ⇒ x = 0

y = 3(x + 2)³ - 3 = 3(0 + 2)³ - 3 = 0 - 3×8 - 3 = 24 - 3 = 21


9) Critical points ⇒ first derivative = 0


i) dy / dx = 9(x + 2)² = 0


⇒ x + 2 = 0 ⇒ x = - 2


ii) second derivative: to determine where x = - 2 is a local maximum, a local minimum, or an inflection point.


y'' = 18 (x + 2); x = - 2 ⇒ y'' = 0 ⇒ inflection point.


Then the function does not have local minimum nor maximum, but an inflection point at x = -2.


Using all that information you can graph the function, and I attache the figure with the graph.