Answer: Time taken by him in going = 8 hours
Time taken by him in returning = 9 hours
Step-by-step explanation:
Let the total distance from home to New York is x miles,
Also, he drove his car from his home to New York at the rate of 45 mph,
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And, returned over the same road at the rate of 40 mph.
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According to the question,
Time taken by him in returning - Time taken by him in going = 30 minutes = 1/2 hours, ( 1 hours = 60 minutes )
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Hence, the total distance from home to New York = x miles = 360 miles
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a. 9/10
explanation:
• the denominators (bottom number) are the same so there is no need to change to a common factor
• because the fractions have common factors, you add the top numbers (3+6) to get 9
• then you put the top number over the 10 (9/10) and it’s simplified as much as possible
b. 3/4
explanation:
• each denominator (bottom term) is a factor of 12 so you have to change each fraction to #/12
• to change 1/3, you multiply the top and bottom numbers by 4 (1x4 & 3x4 = 4/12)
• to change 1/4, you multiply the top and bottom numbers by 3 (1x3 & 4x3 = 3/12)
• to change 1/6, you multiple the top and bottom numbers by 2 (1x2 & 6x2 = 2/12)
• then you add each of the top numbers (4+3+2) and put it over the common denominator (12) to get 9/12
- both 9 & 12 are divisible by 3, so you simply by dividing both by 3 to get 3/4
c. 1/3
explanation:
•the denominators are the same, so you subtract 5-3 without changing the denominator & you get 2/6
• then, because both numbers are divisible by 2, you divide both by 2 and get 1/3
Answer:
<em>MQ = 16 units</em>
Step-by-step explanation:
= 
x = 
= 2
<em>MQ</em> = 14 + 2 = <em>16 units</em>
Answer:
-937.5π
Step-by-step explanation:
F (r) = r = (x, y, z) the surface equation z = 3(x^2 + y^2) z_x = 6x, z_y = 6y the normal vector n = (- z_x, - z_y, 1) = (- 6x, - 6y, 1)
Thus, flux ∫∫s F · dS is given as;
∫∫ <x, y, z> · <-z_x, -z_y, 1> dA
=∫∫ <x, y, 3x² + 3y²> · <-6x, -6y, 1>dA , since z = 3x² + 3y²
Thus, flux is;
= ∫∫ -3(x² + y²) dA.
Since the region of integration is bounded by x² + y² = 25, let's convert to polar coordinates as follows:
∫(θ = 0 to 2π) ∫(r = 0 to 5) -3r² (r·dr·dθ)
= 2π ∫(r = 0 to 5) -3r³ dr
= -(6/4)πr^4 {for r = 0 to 5}
= -(6/4)5⁴π - (6/4)0⁴π
= -937.5π
Answer:
B: x=-2
Step-by-step explanation:
This is because x=-2 is where the parabola is split into two equal halves.
