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2 years ago

Suppose you earned 7t -1 dollars on monday and 8t + 5 on tuesday. what are your total earnings? simplify your answer

Mathematics

1 answer:

ira [324]2 years ago

5 0

You are correct! You added the two amounts together. Combined the like terms, 7t +8t=15t and -1+5=4

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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

Josh works for a construction company that uses 150 pounds of gravel for each driveway they pour. He can buy a dump truck load w

Pavlova-9 [17]

Answer:

Josh should by the dump truck with 30,000 pounds of gravel in it

Step-by-step explanation:

the easiest way to find this out is divide 30,000 and 2,500 by 150 and if the answer is a whole number, then you know that is the correct answer.

30,000/150 = 200

2,500/150 = 16.6666666666666

May I have brainliest please? :)

5 0

2 years ago

Ming used the calculations shown to find out how much he would spend on 6 pounds of ground beef if 10 pounds of ground beef cost

Angelina_Jolie [31]

Answer:

He determined pounds per dollar by dividing 10 by 25 but wrote the unit rate as a dollar value.

Step-by-step explanation:

Given

$\frac{10\ pounds}{\$25} = \frac{10\ pounds}{25} / \frac{\$25}{25} = \frac{0.4}{1}$

$Unit\ Price = 40\ cents$

$40\ cents * 6 = \$2.40$

Required

Determine Ming's error

Ming's error is from here

$\frac{10\ pounds}{\$25} = \frac{10\ pounds}{25} / \frac{\$25}{25} = \frac{0.4}{1}$

He calculated the unit rate as pound per dollar.

So, after calculating the unit rate, the unit should be:

$Unit\ Rate = 0.4\ pound/\$$

But instead, he solved as:

$Unit\ Rate = \$0.4/ pound$

<em>Hence, (a) is correct</em>

5 0

2 years ago

Read 2 more answers

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, t

maksim [4K]

Answer:

Boat traveled 553.24 feet towards the lighthouse.

Step-by-step explanation:

In the figure attached AB is the light house of height 200 feet.

Angle of depression of the boat from the top of a lighthouse = angle of elevation of the lighthouse from the boat = 14°52'

so 1' = $\frac{1}{60}$ degree

so angle of elevation at point C = 14 + $\frac{52}{60}$

So angle of elevation from C = (14 + 0.87) = 14.87°

Similarly, when boat arrives at point D angle of elevation = 45°10' = 45 + $\frac{10}{60}$ = 45.17°

Now we have to calculate the distance CD, traveled by the boat.

In ΔABC

tan14.87 = $\frac{200}{BC}$

0.2655 = $\frac{200}{BC}$

BC = $\frac{200}{0.26552}$

BC = 753.239 feet

Similarly in ΔABD

tan45.17 = $\frac{200}{BD}$

1 = $\frac{200}{BD}$

BD = 200 feet

So distance CD = BC - BD

CD = 753.239 - 200

= 553.24 feet

Therefore, Boat traveled 553.24 feet towards the lighthouse.

7 0

2 years ago

Read 2 more answers

*31. Priya and Ravish planned to participate in a cycle race to be organised for National integration. They decided

Julli [10]

Answer:

36 minutes

2 rounds for Priya

3 rounds for Ravish

Step-by-step explanation:

The answer is the LCM (least common multiple) of 12 and 18.

12 = 2^2 x 3

18 = 3^2 x 2

=>LCM of 12 and 18 = 2^2 x 3^2 = 4 x 9 = 36

=> After 36 minutes they meet again at the starting point

=> At that time, Priya has completed: 36/18 = 2 rounds

=> At that time, Ravish has completed: 36/12 = 3 rounds

7 0

2 years ago