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aksik [14]
3 years ago
12

Miles purchased 5/6 lbs. of bananas, Phillip purchased 8/9 lbs. of oranges.

Mathematics
2 answers:
Sav [38]3 years ago
5 0
They purchased a total of 1 13/18 pounds.
Elza [17]3 years ago
4 0

They purchased 1.7 pounds of fruit all together.

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A rectangle box with a square base and no top needs to be made using 300ft^2 of material. Find the dimensions of the box with th
Yuri [45]

The dimensions of the box are 10 ft and 5 ft

The maximum volume is 500 ft³

Step-by-step explanation:

A rectangle box with

  • A square base and no top
  • It needs to be made using 300 ft² of material
  • It has greatest volume

Surface area of a box without top (SA) = perimeter of base × height + area of the base

Volume of a box (V) = base area × height

Assume that the length of the side of the square base is x and the height of the box is y

∵ It needs to be made using 300 ft² of material

∴ The surface area of the box is 300 ft²

∵ Its base is a square of side length x ft

∴ Perimeter of the base = 4 × x = 4 x

∴ Area of the base = x²

∵ The height of the box = y ft

∵ SA = perimeter of base × height + area of the base

∵ SA = (4x)(y) + x²

∴ SA = 4xy + x²

∵ SA of the box = 300 ft²

- Equate the two expressions of SA

∴ 4xy + x² = 300

Now let us find y in terms of x

- Subtract x² from both sides

∴ 4xy = 300 - x²

- Divide each term by 4x to find y

∴ y=\frac{75}{x}-\frac{1}{4}x

∵ V = area of the base × height

∴ V = x² × y = x²y

- Substitute y by the equation of it above

∴ V=x^{2}(\frac{75}{x}-\frac{1}{4}x)

∴ V=75x-\frac{1}{4}x^{3}

∵ The volume of the box is greatest

- That means differentiate V and equate it by 0

∵ \frac{dV}{dx}=75-\frac{3}{4}x^{2}

∵ \frac{dV}{dx}=0 ⇒ greatest volume

∴ 75-\frac{3}{4}x^{2}=0

- Subtract 75 from both sides

∴ -\frac{3}{4}x^{2}=-75

- Divide both sides by -\frac{3}{4}

∴ x² = 100

- Take √ for both sides

∴ x = 10

Substitute the value of x in the equation of y

∵ y=\frac{75}{10}-\frac{1}{4}(10)

∴ y = 5

The dimensions of the box are 10 ft and 5 ft

∵ V=75x-\frac{1}{4}x^{3}

∵ x = 10

∴ V=75(10)-\frac{1}{4}(10)^{3}

∴ V=750-\frac{1}{4}(1000)

∴ V = 750 - 250

∴ V = 500 ft³

The maximum volume is 500 ft³

Learn more:

You can learn more about the volume in brainly.com/question/6443737

#LearnwithBrainly

6 0
3 years ago
May someone please help me on this math question
fenix001 [56]
He would need 2.8 bouquet's to make 20 dollars because i had to round 
i hope this helped

6 0
3 years ago
Determine the number of possible triangles, ABC, that can be formed given A = 30°, a = 7, and b = 18.
zzz [600]

Answer:

none

Step-by-step explanation:

We are given a triangle ABC with ∠A = 30°, sides a = 4 and b = 10.

According to the 'Law of Sines- Ambiguous Case', we have,

If a < b×sinA, then no triangle is possible.

If a = b×sinA, only one triangle is possible

If a > b×sinA, two triangles are possible.

So, we have,

b×sinA = 10 × sin30 = 10 × 0.5 = 5.

Now, as

4 = a < bsinA = 5.

We get, according to the rule, no triangle is possible.

8 0
2 years ago
Identify the slope and y intercept of the line having equation y=-8x-15
Harrizon [31]

Answer: the slope would be a negative slope with -15 as the y intercept.

Step-by-step explanation:

3 0
2 years ago
Answer to this please
xenn [34]

Answer:

(150 \times 75 - 75 \times 75 \times 3.14 \times 0.5) \times 0.5 = (11250 - 8831.25) \times 0.5 = 1209.375

5 0
3 years ago
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