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Alecsey [184]
3 years ago
14

Hiro bought a small carton of milk at lunch. If the approximate dimensions of the milk carton are shown what is the minimum amou

nt of cardboard needed to make the milk carton? Round to the nearest whole number.
A. 65 in2
B. 95in2
C. 104in2
D.119in2

Mathematics
2 answers:
anyanavicka [17]3 years ago
8 0

Answer:

C) 104

Step-by-step explanation:

it was right on edu 2020

faltersainse [42]3 years ago
5 0

Answer:

C.\ 104\ in^2

Step-by-step explanation:

At first, the question looks like an optimization problem, but since all the dimensions of the carton are given, we only have to compute the total area of the given figure.

Let's calculate the front (and back) areas, which are rectangles

A_1=(6.5)(3)=19.5\ in^2

Now with the lateral rectangles which happen to have the very same dimensions

A_2=19.5\ in^2

Next, we compute the front and back triangles of base 3 in and height 1.5 in

A_3=\frac{1}{2}(3)(1.5)=2.25\ in^2

Now, the lateral inclined rectangles of base 3 in and height 2 in

A_4=(3)(2)=6\ in^2

Finally, the base rectangle who happens to be a square of side 3 in

A_5=(3)(3)= 9\ in^2

This last area, unlike all others, is not doubled because its counterpart is inside the carton and is not part of the lateral area

Our total area of cardboard is

A_t=2(19.5)+2(19.5)+2(2.25)+2(6)+9=103.5\ in^2

The closest option to this answer is

C.\ 104\ in^2

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Step-by-step explanation: |x − y| = 1, ok lets play as Alice, my number is y, and the bob number is x.

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3 years ago
Evaluate each trigonometric equation for θ.
liberstina [14]

Answer:

sinФ = 8/17

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tan Ф = 8/15

csc Ф = 17/8

sec Ф = 17/15

cot Ф = 15/8

Step-by-step explanation:

Let us revise the trigonometry functions

  • Sin(x) = opposite/hypotenuse
  • Cos(x) = adjacent/hypoteouse
  • Tan(x) = opposite/adjacent
  • Csc(x) = hypotenuse/opposit
  • Sec(x) = hypotenues/adjacent
  • Cot(x) = adjacent/opposite

In the given figure

The opposite side to angle Ф = 8

The adjacent side to angle Ф = 15

Find the hypotenuse using Pythagoras' theorem

Hypotenuse = \sqrt{8^{2}+15^{2}  }

Hypotenuse = \sqrt{64+225}

Hypotenuse = \sqrt{289}

Hypotenuse = 17

Let us use the rules above to find the trigonometry functions

sinФ = 8/17

cosФ = 15/17

tan Ф = 8/15

csc Ф = 17/8

sec Ф = 17/15

cot Ф = 15/8

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3 years ago
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Step-by-step explanation:

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3 years ago
What is the volume of the composite figure? Explain your work. A complete answer should include how you broke up the figure, whi
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Answer:

15,000\:\mathrm{mm^3}

Step-by-step explanation:

The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.

The volume of the square prism is given by V=s^2\cdot h, where s is the base length and h is the height. Substituting given values, we have: V=14^2\cdot 30=196\cdot 30=5,880\:\mathrm{mm^3}

The volume of a trapezoidal prism is given by V=\frac{b_1+b_2}{2}\cdot l\cdot h, where b_1 and b_2 are bases of the trapezoid, l is the length of the height of the trapezoid and h is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases (\frac{b_1+b_2}{2}) multiplied by the trapezoid's height (l).

Substituting given values, we get:

V=\frac{14+24}{2}\cdot (30-14)\cdot 30,\\V=19\cdot 16\cdot 30=9,120\:\mathrm{mm^3}}

Therefore, the total volume of the composite figure is 5,880+9,120=\boxed{15,000\:\mathrm{mm^3}} (ah, perfect)

Alternatively, we can break the figure into a larger square prism and a triangular prism to verify the same answer:

V=30^2\cdot 14+\frac{1}{2}\cdot10\cdot 16\cdot 30=\boxed{15,000\:\mathrm{mm^3}}\checkmark

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