Answer:
6.914miles (to 3 decimal places)
Step-by-step explanation:
Length of an arc = θ/360 *2πr
angle subtended by arc at the center of the earth = 6 minutes
1 minute =1/60 degree
6 minute= 6/60 degree =0.1°
θ=0.1°
radius of earth = 3960 miles
distance along the arc = 
=6.9142857143miles
Answer:
= 2x^4 + 6x^3 - 8x^2 + 24x
= 2x ( 2x^3 + 3x^2 - 4x + 12)
Step-by-step explanation:
(X^2 + x - 6) (2x^2 + 4x) =
Let's open the brackets carefully
x^2 * 2x^2 + x^2*4x + x*2x^2 + x*4x - 6*2x^2 - 24x
= 2x^4 + 4x^3 + 2x^3 + 4x^2 - 12x + 24x
= 2x^4 + 6x^3 - 8x^2 + 24x
= 2x ( 2x^3 + 3x^2 - 4x + 12)
Answer:
The number of friends that went out for dinner is 8
And their bill is $238
Step-by-step explanation:
Let's assume that the number of friends that went out for dinner to be x
And the bill for the dinner to be y
If each person contributed $32 and paid off the bill,they will have a balance of $18
32x - 18 = y_____equation 1
If each person contributed $35 and paid off the bill and also 15% tip,they will have a balance of $6.30
35x - 6.3 = y + (15% of y)
35x - 6.3 = y + (3y/20)
Open up the bracket
35x - 6.3 =(20y + 3y)/20
700x - 126 = 23y______equation 2
From equation 1,y = 32x - 18
Put the above in equation 2 and we have
700x - 126 = 23(32x -18)
700x - 126 = 736x - 414
collect like terms
36x = 288
x = 288/36
x = 8
Remember that equation 1 says that y = 32x - 18 and we now know that x = 8 .
Substitute and we have
(32 × 8) - 18
y = 238
The number of friends that went out for dinner is 8
And their bill is $238
