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Komok [63]
3 years ago
11

The length and width of a certain rectangle are both decreased by 50%. If the length and width of the new rectangle are then inc

reased by 40%, the area of the resulting rectangle is what percent less than the area of the original rectangle?
Mathematics
1 answer:
alina1380 [7]3 years ago
5 0
51% less.

The length is decreased by 50%, which is the same as being multiplied by 0.5, then it's increased by 40% which is another multiplication by 1.4. So the overall change is 0.5 * 1.4 = 0.7, or the newest rectangle is 70% of the size of the original rectangle. And since the area increases by the square, the newest rectangle has 0.7 * 0.7 = 0.49 of the area as the original rectangle. So it has 51% less area than the original rectangle.

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How do you do this question?
Lena [83]

Step-by-step explanation:

The Taylor series expansion is:

Tₙ(x) = ∑ f⁽ⁿ⁾(a) (x − a)ⁿ / n!

f(x) = 1/x, a = 4, and n = 3.

First, find the derivatives.

f⁽⁰⁾(4) = 1/4

f⁽¹⁾(4) = -1/(4)² = -1/16

f⁽²⁾(4) = 2/(4)³ = 1/32

f⁽³⁾(4) = -6/(4)⁴ = -3/128

Therefore:

T₃(x) = 1/4 (x − 4)⁰ / 0! − 1/16 (x − 4)¹ / 1! + 1/32 (x − 4)² / 2! − 3/128 (x − 4)³ / 3!

T₃(x) = 1/4 − 1/16 (x − 4) + 1/64 (x − 4)² − 1/256 (x − 4)³

f(x) = 1/x has a vertical asymptote at x=0 and a horizontal asymptote at y=0.  So we can eliminate the top left option.  That leaves the other three options, where f(x) is the blue line.

Now we have to determine which green line is T₃(x).  The simplest way is to notice that f(x) and T₃(x) intersect at x=4 (which makes sense, since T₃(x) is the Taylor series centered at x=4).

The bottom right graph is the only correct option.

3 0
2 years ago
Jake is baking cookies for a bake sale. He needs 134 cups of flour for each batch of cookies, and he needs to make 323 batches.
Fofino [41]
I am not going 100% sure but i think it is C
5 0
2 years ago
Read 2 more answers
Three sets Venn diagram
Anon25 [30]

Answer:

I hope this helps a little bit

8 0
2 years ago
A company makes and sells charm bracelets. The cost of producing x bracelets is represented by the function
Serggg [28]

P(x) = 12x – 180

Given:

A company makes and sells charm bracelets.

The cost of producing x bracelets is represented by the function C(x) = 180 +

8x

The revenue earned from selling x bracelets is represented by the function

R(x) = 20x.


Explanation of terms:

For x bracelets,

Cost of production is C(x); C(x) = 180 + 8x

Revenue earned is R(x); R(x) = 20x.Profit made is P(x); P(x) is unknown

Profit made = Revenue earned – Cost of production

∴ P(x) = R(x) – C(x)

P(x) = 20x – (180 + 8x)

P(x) = 20x – 180 – 8x

P(x) = 12x – 180

The profit made from selling x bracelets is represented by the function

<em> P(x) = 12x – 180</em>



8 0
3 years ago
Read 2 more answers
If a/b and c/d are rational expressions then a/b divided by c/d =a times d/b times c true or false
Tomtit [17]

Answer:

(a d)/(bc)

Step-by-step explanation:

a/b ÷ c/d

Copy dot flip

a/b * d/c

ad / bc

4 0
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