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anzhelika [568]
3 years ago
13

144 miles on 4.5 gallons

Mathematics
2 answers:
Zigmanuir [339]3 years ago
7 0
144 miles on 4.5 gallons
Solution: 144mi                         4.5            32mi
             ------------   divided by             =  -------------
                4.5gal                        4.5            1 gal
konstantin123 [22]3 years ago
5 0

Answer:

32 miles per gallon.

Step-by-step explanation:

We are supposed to find unit rate for the given scenario.

144 miles on 4.5 gallons.

To find unit rate, we will divide 144 by 4.5 as:

\text{Unit rate}=\frac{144\text{ miles}}{\text{4.5 gallons}}

\text{Unit rate}=\frac{32\text{ miles}}{\text{gallon}}

Therefore, unit rate for our given situation is 32 miles per gallon.

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Show with work please.
kolbaska11 [484]

Answer:

$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$

Step-by-step explanation:

The identity you will use is:

$\csc \left(x\right)=\frac{1}{\sin \left(x\right)}$

So,

$\csc \left(\theta-\frac{\pi }{2}\right)$

$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{\sin \left(-\frac{\pi }{2}+\theta\right)}$

Now, using the difference of sin

Note: state that \text{sin}(\alpha\pm \beta)=\text{sin}(\alpha) \text{cos}(\beta) \pm \text{cos}(\alpha) \text{sin}(\beta)

$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)}$

Solving the difference of sin:

$-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)$

-\cos \left(\theta\right) \cdot 1+0\cdot \sin \left(\theta\right)

-\text{cos} \left(\theta\right)

Then,

$\csc \left(\theta-\frac{\pi }{2}\right)=-\frac{1}{\cos \left(\theta\right)}$

Once

\text{sec}(-\theta)=\text{sec}(\theta)

And, \text{sec}(\theta)=-0.73

$-\frac{1}{\cos \left(\theta\right)}=-\text{sec}(\theta)$

$-\frac{1}{\cos \left(\theta\right)}=-(-0.73)$

$-\frac{1}{\cos \left(\theta\right)}=0.73$

Therefore,

$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$

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