Find the common difference in the arithmetic sequence.

Mathematics

1 answer:

finlep [7]4 years ago

7 0

To find the common difference, subtract the 1st term from the 2nd term

1 8/9 - 2 =
17/9 - 2 =
17/9 - 18/9 =
-1/9 <==

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Your mom's new car gets 32 miles per gallon and gasoline costs $1.99 per gallon. You are going to see Uncle buck for Christmas,

Mashcka [7]

The gas cost will be $19.53 for this trip.

Step-by-step explanation:

Given,

Distance covered by car per gallon = 32 miles

Cost of one gallon = $1.99

Unit rate in terms of miles;

32 miles = $1.99

1 mile = $\frac{1.99}{32}\ Dollars$

Therefore,

314 miles = Unit rate of mile * 314 miles

314 miles = $\frac{1.99}{32}*314$

$314\ miles = \frac{624.86}{32}\\\\314\ miles=\$19.526$

Rounding off to nearest hundredth;

314 miles = $19.53

The gas cost will be $19.53 for this trip.

Keywords: unit rate, multiplication

Learn more about unit rate at:

#LearnwithBrainly

6 0

3 years ago

Given two vectors A=2i+3j+4k,B=i-2j+3k find the magnitude and direction of sum<br>(physics question)

Law Incorporation [45]

Answer:

$Magnitude =\sqrt{59} \\\\Direction \: of \: \overrightarrow{A + B} = \frac{3}{\sqrt {59}} , \:\frac{1}{\sqrt {59}} , \:\frac{7}{\sqrt {59}}$

Step-by-step explanation:

A=2i+3j+4k

B=i-2j+3k

Sum of the vectors:

A + B = 2i+3j+4k + i-2j+3k = 3i + j + 7k

$Magnitude =\sqrt{3^2 + 1^2+ 7^2} \\\\Magnitude =\sqrt{9+1+49} \\\\Magnitude =\sqrt{59}$

Direction of the sum of the vectors:

$\widehat{A + B} =\frac{\overrightarrow{A + B}}{Magnitude\: of \:\overrightarrow{A + B}} \\\\\widehat{A + B} =\frac{3i + j + 7k}{\sqrt {59}} \\\\\widehat{A + B} =\frac{3}{\sqrt {59}} i +\frac{1}{\sqrt {59}} j+\frac{7}{\sqrt {59}} k\\\\Direction \: of \: \overrightarrow{A + B} = \frac{3}{\sqrt {59}} , \:\frac{1}{\sqrt {59}} , \:\frac{7}{\sqrt {59}} \\\\$