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WARRIOR [948]
3 years ago
6

Solve. Enter your answer as a mixed number. The driving distance from the sports arena to Kristina's house is 11 7 10 miles. The

distance from the sports arena to Luke's house is 5 2 10 miles. How much greater is the driving distance between the sports arena and Kristina's house than between the sports arena and Luke's house? The driving distance between the sports arena and Kristina's house is miles greater than between the sports arena and Luke's house.
Mathematics
1 answer:
sineoko [7]3 years ago
3 0

Answer: 6\frac{1}{2} miles

Step-by-step explanation:

From the sports arena to Kristina's house = 11\frac{7}{10}miles

From the sports arena to Luke's house = 5\frac{2}{10} miles

Subtract Luke from Kristina

5\frac{2}{10}-11\frac{7}{10}

There's a confusing but easy way to solve this. However, I'm going to convert into improper fractions to make it easier.

To convert to improper fraction, take the whole number, multiply it by the denominator and add it to the numerator. All over the same denominator.

\frac{5*10+2}{10} -\frac{11*10+7}{10}

\frac{50+2}{10}-\frac{110+7}{10}\\\frac{52}{10}-\frac{117}{10}

Subtract them.

\frac{52-117}{10}

-\frac{65}{10}

Convert to mixed number by dividing.

65/10=6

60

----

5

The 6 is the whole number, 5 the numerator and 10 the denominator. Remember the negative sign that we had.

6\frac{5}{10}

5 and 10 can be simplified

5/5=1

10/5=2

Our final answer would be:

6\frac{1}{2}

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5 0
3 years ago
Rewrite the Cartesian equation y=-3 as a polar equation.
andreev551 [17]

r

sin

θ

=

−

3

Explanation:

Imagine we have a point  

P

with Rectangular (also called Cartesian) coordinates  

(

x

,

y

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and Polar coordinates  

(

r

,

θ

)

.

The following diagram will help us visualise the situation better:

https://keisan.casio.com/exec/system/1223526375

https://keisan.casio.com/exec/system/1223526375

We can see that a right triangle is formed with sides  

x

,  

y

and  

r

, as well as an angle  

θ

.

We have to find the relation between the Cartesian and Polar coordinates, respectively.

By Pythagora's theorem, we get the result

r

2

=

x

2

+

y

2

The only properties we can say about  

θ

are its trigonometric functions:

sin

θ

=

y

/

r

⇒

y

=

r

sin

θ

cos

θ

=

x

/

r

⇒

x

=

r

cos

θ

So we have the following relations:

⎧

⎪

⎨

⎪

⎩

r

2

=

x

2

+

y

2

y

=

r

sin

θ

x

=

r

cos

θ

Now, we can see that saying  

y

=

−

3

in the Rectangular system is equivalent to say

r

sin

θ

=

−

3

Answer link

Jim G.

May 19, 2018

r

=

−

3

sin

θ

Explanation:

to convert from  

cartesian to polar

∙

x

x

=

r

cos

θ

and  

y

=

r

sin

θ

⇒

r

sin

θ

=

−

3

⇒

r

=

−

3

sin

θ

4 0
2 years ago
I need help again please 5/6-1/6
Murljashka [212]
The answer is 2/3 in lowest terms.
6 0
3 years ago
What is the volume of the square pyramid? Round to the nearest tenth.
goldfiish [28.3K]

Answer:

V=718.7\ cm^{3}

Step-by-step explanation:

we know that

The volume of the square pyramid is equal to

V=\frac{1}{3}b^{2}h

we have

b=14\ cm ----> the length of the base of the square pyramid

h=11\ cm ---> the height of the pyramid

substitute the values in the formula

V=\frac{1}{3}(14)^{2}(11)

V=718.7\ cm^{3}

4 0
2 years ago
The cost for a pack of 9 padlock is $25.20 find the unit price in dollars per padlock if necessary round your answer to the near
Elena-2011 [213]

Answer:

2.80

Step-by-step explanation:

Take the cost and divide by the number of padlocks

25.20/9

2.80

Each padlock costs 2.80

8 0
3 years ago
Read 2 more answers
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