Answer:
No of city miles = 144 miles
No of highway miles = 110 miles.
Explanation:
Total distance traveled = 254 miles
Mileage of pickup truck in city = 16 mpg
Mileage of pickup truck in highway = 22 mpg
Total gas used = 14 gal
Let x be the number of city miles,
We have number of highway miles = 254-x
So gas used = ![\frac{254-x}{22} +\frac{x}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B254-x%7D%7B22%7D%20%2B%5Cfrac%7Bx%7D%7B16%7D)
Equating,
![\frac{254-x}{22} +\frac{x}{16} = 14\\ \\ 4064-16x+22x=4928\\ \\ 6x=864\\ \\ x=144 miles](https://tex.z-dn.net/?f=%5Cfrac%7B254-x%7D%7B22%7D%20%2B%5Cfrac%7Bx%7D%7B16%7D%20%3D%2014%5C%5C%20%5C%5C%204064-16x%2B22x%3D4928%5C%5C%20%5C%5C%206x%3D864%5C%5C%20%5C%5C%20x%3D144%20miles)
No of city miles = 144 miles
No of highway miles = 254 - 144 = 110 miles.
Answer:
7) 14✓2
8) 14
are the answers.
Step-by-step explanation:
in a triangle the sum of angles is 180 deg.
the third angle will be = 180 - 90 - 45
= 45 deg
since 2 angles in the triangle are 45 deg it means the triangle is isosceles
and in isosceles triangle the sides opposite to equal angles are equal which means
z = 14 (answer to question 8)
now in right angle triangle, by pythogoras theorem,
hypotenuse ² = base ² + height ²
thus
![{w}^{2} = {z}^{2} + {14}^{2} \\ {w}^{2} = {14}^{2} + {14 }^{2} \\ {w}^{2} = 2 \times {14}^{2} \\ w = \sqrt{2 \times {14}^{2} } \\ = \sqrt{2} \times 14 \\ = 14 \sqrt{2}](https://tex.z-dn.net/?f=%20%7Bw%7D%5E%7B2%7D%20%20%3D%20%20%7Bz%7D%5E%7B2%7D%20%20%2B%20%20%7B14%7D%5E%7B2%7D%20%20%5C%5C%20%20%7Bw%7D%5E%7B2%7D%20%20%3D%20%20%7B14%7D%5E%7B2%7D%20%20%2B%20%20%7B14%20%7D%5E%7B2%7D%20%20%5C%5C%20%20%20%7Bw%7D%5E%7B2%7D%20%3D%202%20%5Ctimes%20%20%7B14%7D%5E%7B2%7D%20%20%5C%5C%20w%20%3D%20%20%5Csqrt%7B2%20%5Ctimes%20%20%7B14%7D%5E%7B2%7D%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B2%7D%20%20%5Ctimes%2014%20%5C%5C%20%20%3D%2014%20%5Csqrt%7B2%7D%20)
answer to question 7
Answer:
Step-by-step explanation:
See attachment.
9514 1404 393
Answer:
7953.873
Step-by-step explanation:
The first derivative is ...
f'(x) = 4·3x²·e^x +4x³·e^x = e^x(4x³ +12x²)
Then the second derivative is ...
f''(x) = (12x² +24x)e^x +(4x³ +12x²)e^x
f''(x) = e^x(4x³ +24x² +24x)
So, f''(3) = (e^3)(4·27 +24·9 +24·3) = 396e^3 = 7953.87262158
Rounded to thousandths, this is ...
f''(3) = 7953.873