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timofeeve [1]
3 years ago
6

Divide. Write the quotient in lowest terms. 5 divide 3 1/3

Mathematics
1 answer:
Step2247 [10]3 years ago
3 0

Answer:

3/2 or 1 1/2

Step-by-step explanation:

5÷3 1/3

5/1 ÷ 10/3 because you have to get it into an improper fraction form in order to divide

5/1 × 3/10 because you have to multiply the first number by the reciprocal

5  and 10 cancel out so you would have 2 at the bottom

3/2 or 1 1/2

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Step-by-step explanation:


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Determine the number of possible solutions for a triangle with B=37 degrees, a=32, b=27
vladimir1956 [14]

Answer:

Two possible solutions

Step-by-step explanation:

we know that

Applying the law of sines

\frac{a}{sin(A)}=\frac{b}{Sin(B)}=\frac{c}{Sin(C)}

we have

a=32\ units

b=27\ units

B=37\°

step 1

Find the measure of angle A

\frac{a}{sin(A)}=\frac{b}{Sin(B)}

substitute the values

\frac{32}{sin(A)}=\frac{27}{Sin(37\°)}

sin(A)=(32)Sin(37\°)/27=0.71326

A=arcsin(0.71326)=45.5\°

The measure of angle A could have two measures

the first measure-------> A=45.5\°

the second measure -----> A=180\°-45.5\°=134.5\°

step 2

Find the first measure of angle C

Remember that the sum of the internal angles of a triangle must be equal to  180\°

A+B+C=180\°

substitute the values

A=45.5\°

B=37\°

45.5\°+37\°+C=180\°

C=180\°-(45.5\°+37\°)=97.5\°

step 3

Find the first length of side c

\frac{a}{sin(A)}=\frac{c}{Sin(C)}

substitute the values

\frac{32}{sin(37\°)}=\frac{c}{Sin(97.5\°)}

c=Sin(97.5\°)\frac{32}{sin(37\°)}=52.7\ units

therefore

the measures for the first solution of the triangle are

A=45.5\° , a=32\ units

B=37\° , b=27\ units

C=97.5\° , b=52.7\ units

step 4    

Find the second measure of angle C with the second measure of angle A

Remember that the sum of the internal angles of a triangle must be equal to  180\°

A+B+C=180\°

substitute the values

A=134.5\°

B=37\°

134.5\°+37\°+C=180\°

C=180\°-(134.5\°+37\°)=8.5\°

step 5

Find the second length of side c

\frac{a}{sin(A)}=\frac{c}{Sin(C)}

substitute the values

\frac{32}{sin(37\°)}=\frac{c}{Sin(8.5\°)}

c=Sin(8.5\°)\frac{32}{sin(37\°)}=7.9\ units

therefore

the measures for the second solution of the triangle are

A=45.5\° , a=32\ units

B=37\° , b=27\ units

C=8.5\° , b=7.9\ units

6 0
3 years ago
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