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2 years ago

14

Sam will place three of his eight model trucks on a shelf. In how many different orders can you please three model trucks on the

shelf

1 answer:

mr Goodwill [35]2 years ago

5 0

Answer: 336 ways

Step-by-step explanation:

Given

Sam has 8 models and he needs to place 3 on a shelf

3 models can be selected out of 8 in $^8C_3$ ways

It can further be arranged among themselves in $3!$ ways

Therefore, total number of ways are

$\Rightarrow 3!\times ^8C_3\\\\\Rightarrow 3!\times \dfrac{8!}{3!5!}\\\\\Rightarrow 8\times 7\times 6=336\ \text{ways}$

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For the equation:
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Answer:
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3 years ago

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3 years ago

PLEASE HELP 25 POINTS!!!

miss Akunina [59]

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Here Given Sum to Infinity

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a1 = 2

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2 years ago

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

$A=45.5\°$ , $a=32\ units$

$B=37\°$ , $b=27\ units$

$C=8.5\°$ , $b=7.9\ units$

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3 years ago