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Nina [5.8K]
3 years ago
7

A delivery truck can transport packages weighing at most 3,800 pounds(lbs) and with a volume of no more than 400 cubic feet (ft^

3). The truck transports only two sizes of packages: A small package weighing 30 lbs with a volume of 4ft^3 and a large package weighing 65 lbs with a volume of 9ft^3. Let x represent the number of small packages and y represent the number of large packages. Which system of inequalities describes the possible numbers of packages the truck can transport at one time?
A. 6x+13y≥760 and 4x+9y≥ 400
B. 6x+ 13y ≤ 760 and 4x+9y≤400
C. 15x+2y≤ 1,900 and 65x + 9y≤ 400
D. 15x +12y≥ 1,900 and 65x+9y≥ 400
Mathematics
1 answer:
Makovka662 [10]3 years ago
7 0
Let's approach this problem by slowly eliminating choices.

First consider the keyword "at most" and "no more than". This means that the inequality should be less than or equal to the constant value stated. This will automatically eliminate two choices with the greater than symbol favoring the variables - choices A and D.

Next we associate the right constants to the right coefficients of variables. The two kinds of weight the truck transports are 30 and 65 lbs, and we know that this should not exceed 3,800 lbs. This is therefore our first inequality. The other inequality is for the volume. The combinations of the two volumes 4 and 9 cubic feet should not exceed 400 cubic feet when transported.

If you try to construct the inequality and miss it among the choices, don't worry! Let's try doing some simplifications first and see if it matches either B or C.

After simplification you can get 6x+13y \leq 760 from dividing the equation by 5 and 4x+9y \leq 400 for leaving it as it is.

Looking carefully, we can see that this is equivalent to option B.

ANSWER: B.
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You have been asked to design a can shaped like right circular cylinder that can hold a volume of 432π-cm3. What dimensions of t
rosijanka [135]

Answer:

Height = 12cm

Radius = 6cm

Step-by-step explanation:

Given

Represent volume with v, height with h and radius with r

V = 432\pi

Required

Determine the values of h and r that uses the least amount of material

Volume is calculated as:

V = \pi r^2h\\

Substitute 432π for V

432\pi = \pi r^2h

Divide through by π

432 = r^2h

Make h the subject:

h = \frac{432}{r^2}

Surface Area (A) of a cylinder is calculated as thus:

A=2\pi rh+2\pi r^2

Substitute \frac{432}{r^2} for h in A=2\pi rh+2\pi r^2

A=2\pi r(\frac{432}{r^2})+2\pi r^2

A=2\pi (\frac{432}{r})+2\pi r^2

Factorize:

A=2\pi (\frac{432}{r} + r^2)

To minimize, we have to differentiate both sides and set A' = 0

A'=2\pi (-\frac{432}{r^2} + 2r)

Set A' = 0

0=2\pi (-\frac{432}{r^2} + 2r)

Divide through by 2\pi

0= -\frac{432}{r^2} + 2r

\frac{432}{r^2} = 2r

Cross Multiply

2r * r^2 = 432

2r^3 = 432

Divide through by 2

r^3 = 216

Take cube roots of both sides

r = \sqrt[3]{216}

r = 6

Recall that:

h = \frac{432}{r^2}

h = \frac{432}{6^2}

h = \frac{432}{36}

h = 12

Hence, the dimension that requires the least amount of material is when

Height = 12cm

Radius = 6cm

3 0
3 years ago
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