How to simplify 6x^2y^-3/x^-5

On a trip, Duke encounters some road construction that slows him down. While he is able to go 60 mph on the highway and 40 mph t

natulia [17]

Answer:

Time taken by Duke on the highway = 3 hours

Time spent on the construction = 6 hours

Time spent in the city = 2 hours

Step-by-step explanation:

Speed by which Duke travels a distance on highway $d_1$ = 60 mph

Let the time taken to travel on highway = $t_1$ hours

Distance traveled = $60t_1$ miles

Speed in the city = 40 mph

Let the time taken = $t_2$ hours

Distance traveled in the city = $40t_2$ miles

Speed on the construction = 20 mph

Let the time spend on the construction = $t_3$ hours

Distance traveled on the construction = $20t_3$ miles

Since, total distance covered = 380 miles

$d_1+d_2+d_3=60t_1+40t_2+20t_3$

He spends one half the time on the highway as he does on the construction,

$t_3=2t_1$

Total time spent in the trip = 11 hours

Therefore, $t_1+t_2+t_3=11$

$t_1+t_2+2t_1=11$

$t_2=11-3t_1$

From equation (1),

$60t_1+40(11-3t_1)+20(2t_1)=380$

$60t_1-120t_1+40t_1+440=380$

$440-20t_1=380$

$20t_1=440-380$

$t_1=\frac{60}{20}$

$t_1=3$ hours

$t_2=11-3t_1=2$ hours

$t_3=2t_1=6$ hours

Therefore, time taken by Duke on the highway = 3 hours

Time spent on the construction = 6 hours

Time spent in the city = 2 hours

3 0

3 years ago

Which of the following is a polynomial with roots 2, 3i, and −3i? f(x) = x3 − 2x2 + 6x − 9 f(x) = x3 − 6x2 + 9x − 18 f(x) = x3 −

Andreas93 [3]

F(x) = x3 − 2x2 + 9x − 18

4 0

3 years ago

Read 2 more answers

5x=-4y+4;x= 1,2,3 solve equation then find value of y

nadezda [96]

x = 1 5(1)= -4y + 4 5= -4y + 4 -4. -4 1 = -4y y = -¼ x = 2... 10 = -4y + 4 6 = -4y y = -3/2 x = 3.. 15 = -4y + 4 11 = -4y y = -11/4

7 0

3 years ago

Read 2 more answers

PLEASE SHOW ALL THE STEPS THAT YOU USE TO SOLVE THIS PROBLEM

Mademuasel [1]

Answer:

{x = 1 , y=1, z=0

Step-by-step explanation:

Solve the following system:

{-2 x + 2 y + 3 z = 0 | (equation 1)

{-2 x - y + z = -3 | (equation 2)

{2 x + 3 y + 3 z = 5 | (equation 3)

Subtract equation 1 from equation 2: