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3 years ago

ABCD is a quadrilateral. Work out the length of BC.

Mathematics

1 answer:

Pani-rosa [81]3 years ago

8 1

The answer is B.C. =8.1cm
The working is on the picture

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Let P and Q be polynomials with positive coefficients. Consider the limit below. lim x→[infinity] P(x) Q(x) (a) Find the limit i

jenyasd209 [6]

Answer:

If the limit that you want to find is $\lim_{x\to \infty}\dfrac{P(x)}{Q(x)}$ then you can use the following proof.

Step-by-step explanation:

Let $P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0}$ and $Q(x)=b_{m}x^{m}+b_{m-1}x^{n-1}+\cdots+b_{1}x+b_{0}$ be the given polinomials. Then

$\dfrac{P(x)}{Q(x)}=\dfrac{x^{n}(a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n})}{x^{m}(b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m})}=x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}$

Observe that

$\lim_{x\to \infty}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\dfrac{a_{n}}{b_{m}}$

and

$\lim_{x\to \infty} x^{n-m}=\begin{cases}0& \text{if}\,\, nm\end{cases}$

Then

$\lim_{x\to \infty}=\lim_{x\to \infty}x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\begin{cases}0 & \text{if}\,\, nm \end{cases}$

3 0

2 years ago

3x+30+x=10+2x+5x+2 <br> i need help fast

kupik [55]

Answer:

x=6

Step-by-step explanation:

Group Like Terms:

3x+x+30=10+2x+5x+2

Add similar elements 3x+x=4x:

4x+30=10+2x+5x+2

Add similar elements 2x+5x=7x:

4x+30=10+7x+2

Group like terms:

4x+30=7x+10+2

Add the numbers 10+2=12:

4x+30=7x+12

Subtract 30 from both sides:

4x+30-30=7x+12-30

Simplify:

4x=7x-18

Subtract 7x from both sides:

4x-7x=7x-18-7x

Simplify:

-3x=-18

Divide both sides by -3:

$\frac{-3x}{-3} =\frac{-18}{-3}$

Simplify:

x=6

Hence, the correct answer is 6

4 0

2 years ago

Someone please help me with question 2

alukav5142 [94]

Answer:

v = s/t

v = (381.59 miles) / (5.5 hours)

v = 69.38 mph

8 0

2 years ago

True/False: Money that is usable can be easily moved from your home to the store.

egoroff_w [7]

Answer:

true

Step-by-step explanation:

4 0

2 years ago

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I need to find x in these two problems in the picture.

forsale [732]

Answer:

for the first one do 15 divided by 10 and the second one 18 divided by 8.

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers