Answer:
9.5 gallons of gas
Step-by-step explanation:
Given that:
Each gallon gives 14 miles
Mrs giang wants to travel 133 miles
So
gallons she would need = 133 / 14 miles
gallons she would need = 9.5 gallons
So Mrs.giang will need 9.5 gallons of gas to visit her niece.
i hope it will help you!
Setup
0.8x + 0.4y = 50
0.1x + 0.2y = 10 - Multiply by -2 and add
get
0.6x = 30
x = 50 mg compound A
.1 (50) + .2y = 10
5 + .2y = 10
.2y = 5
y = 25 mg compound B
Step-by-step explanation:
To find a set of 3 leg lengths that will form a right-angled triangle, the square of the largest leg must be equal to the sum of the squares of the other 2 legs.
We try out all the options:
39² = 1521, 15² + 36² = 1521.
12² = 144, 8² + 4² = 80.
17² = 289, 13² + 9² = 250.
Since 39² equals 15² + 36², option A is the correct answer.
Answer:
- Base Length of 84cm
- Height of 42 cm.
Step-by-step explanation:
Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.
Step 1:
Let the side length of the base =x
Let the height of the box =h
Since the box has a square base
Volume, 
Surface Area of the box = Base Area + Area of 4 sides
Step 2: Find the derivative of A(x)
Step 3: Set A'(x)=0 and solve for x
![A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84](https://tex.z-dn.net/?f=A%27%28x%29%3D%5Cdfrac%7B2x%5E3-1185408%7D%7Bx%5E2%7D%3D0%5C%5C2x%5E3-1185408%3D0%5C%5C2x%5E3%3D1185408%5C%5C%24Divide%20both%20sides%20by%202%5C%5Cx%5E3%3D592704%5C%5C%24Take%20the%20cube%20root%20of%20both%20sides%5C%5Cx%3D%5Csqrt%5B3%5D%7B592704%7D%5C%5Cx%3D84)
Step 4: Verify that x=84 is a minimum value
We use the second derivative test
Since the second derivative is positive at x=84, then it is a minimum point.
Recall:
Therefore, the dimensions that minimizes the box surface area are:
- Base Length of 84cm
- Height of 42 cm.
Answer:
-13
Step-by-step explanation:
Given are two vectors v and w.
v=(6,7,-3) and
w=(-7,5,2)
We are to find the dot product of v.w
We have
Dot product is obtained by multiplying corresponding pairs and adding them
Here we have
v.w=6(-7)+7(5)-3(2)
=-13
