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zzz [600]
3 years ago
7

A ladder leans against the side of a house. The angle of elevation of the ladder is 68° when the bottom of the ladder is 16 it f

rom the side of the house. Find the
length of the ladder Round your answer to the nearest tenth.

Mathematics
1 answer:
choli [55]3 years ago
8 0

Answer:

The length of the ladder  = 6.5077 ft

Step-by-step explanation:

Given A ladder leans against the side of a house

Given the angle of elevation of the ladder is 68° when the bottom of the ladder is 16 ft from the side of the house

Let 'C' be the point of observation.

Given CA= 16 ft

 From right angle triangle

     

     

     x = 16 × cos 68°

    x = 16 × 0.4067

    x = 6.5077

  x = 6.5 ft

The length of the ladder = 6.5 ft

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2 years ago
Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same product
gregori [183]

Answer:

Generally the constraint that sets next week are shown below

Generally the constrain that sets next week maximum production of connecting rod for 4 cylinder  to  W_4 or  0 is  

     x_4 \le W_4 *  s_4

    x_4 \le 5000 *  s_4

Generally the constrain that sets next week maximum production of connecting rod for 6 cylinder  to  W_6 or  0  is  

     x_6 \le W_6 *  s_6

     x_6 \le 8,000 *  s_6

Generally the constrain that limits the production of connecting rods  for both 4 cylinder and 6 cylinders  is

     x_4 \le W_4 *  s_6

=>   x_4 \le 5000 *  s_6

     x_4 \le W_6 *  s_4

=>    x_4 \le 8000 *  s_4

     s_4 + s_6 = 1

The minimum cost of production for next week is  

   U  =  M_4 *  x_4 + M_6 * x_6 + C_4 * s_4 + C_6 * s_6

=>  U  =  13x_4 + 16x_6 + 2000 s_4 + 3500 s_6

Step-by-step explanation:

The cost for the four cylinder production line is  C_4 =  \$2,100

The cost for the six cylinder production line is  C_6 = \$3,500

The manufacturing cost for each four cylinder is  M_4= \$13

 The manufacturing cost for each six cylinder is M_6= \$16

  The weekly production capacity for 4 cylinder connecting rod is W_4 = 5,000

   The weekly production capacity for 6 cylinder connecting rod is W_6 = 8,000

Generally the constraint that sets next week are shown below

Generally the constrain that sets next week maximum production of connecting rod for 4 cylinder  to  W_4 or  0 is  

     x_4 \le W_4 *  s_4

    x_4 \le 5000 *  s_4

Generally the constrain that sets next week maximum production of connecting rod for 6 cylinder  to  W_6 or  0  is  

     x_6 \le W_6 *  s_6

     x_6 \le 8,000 *  s_6

Generally the constrain that limits the production of connecting rods  for both 4 cylinder and 6 cylinders  is

     x_4 \le W_4 *  s_6

=>   x_4 \le 5000 *  s_6

     x_4 \le W_6 *  s_4

=>    x_4 \le 8000 *  s_4

     s_4 + s_6 = 1

The minimum cost of production for next week is  

   U  =  M_4 *  x_4 + M_6 * x_6 + C_4 * s_4 + C_6 * s_6

=>  U  =  13x_4 + 16x_6 + 2000 s_4 + 3500 s_6

3 0
3 years ago
A math class and a science class have a total of 45 people in them. the math class has 5 more students than the science class. h
Marta_Voda [28]

Answer:

math class =25

Step-by-step explanation:

(45-5)÷2=20

math class =20+5

=25

5 0
3 years ago
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