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rusak2 [61]
3 years ago
10

I need help with these three problems please​

Mathematics
2 answers:
lesya692 [45]3 years ago
5 0

Answer:

7) 8sqrt(2) in

8) 68sqrt(2) ft

9) 21sqrt(3) cm

Step-by-step explanation:

7) sqrt(8² + 8²) = 8sqrt(2) in

sqrt is square root

8) sqrt(x² + x²) = 34

2x² = 34²

x = 17sqrt(2)

Perimeter = 4x = 68sqrt(2) ft

9) 3s = 126

s = 42

Altitude² + 21² = 42²

Altitude² = 1323

Altitude = 21sqrt(3) cm

Liono4ka [1.6K]3 years ago
4 0

Answer:

Q7. 11.3 inches (3 s.f.)

Q8. 96.2 ft

Q9. 36.4cm

Step-by-step explanation:

Q7. Please see attached picture for full solution.

Q8. Let the length of a side of the square be x ft.

Applying Pythagoras' Theorem,

34^{2}  =  {x}^{2}  +  {x}^{2}  \\ 2 {x}^{2}  = 1156 \\  {x}^{2}  = 1156 \div 2 \\  {x}^{2}  = 578 \\ x =  \sqrt{578}  \\

Thus, the perimeter of the square is

= 4( \sqrt{578} ) \\  = 96.2 ft\:  \:  \: (3 \: s.f.)

Q9. Equilateral triangles have 3 equal sides and each interior angle is 60°.

Since the perimeter of the equilateral triangle is 126cm,

length of each side= 126÷3 = 42 cm

The green line drawn in picture 3 is the altitude of the triangle.

Let the altitude of the triangle be x cm.

sin 60°= \frac{x}{42}

\frac{ \sqrt{3} }{2}  =  \frac{x}{42}  \\ x =  \frac{ \sqrt{3} }{2}  \times 42 \\ x = 21 \sqrt{3}  \\ x = 36.4

(to 3 s.f.)

Therefore, the length of the altitude of the triangle is 36.4cm.

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According to the law of sines:

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Using the given values, we can find the angle B and find the number of possible triangles that can be formed.

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1 year ago
How to do surface area
Mars2501 [29]

Answer:

Step-by-step explanation:

Multiply the length and width, or c and b to find their area. Multiply this measurement by two to account for both sides. Add the three separate measurements together. Because surface area is the total area of all of the faces of an object, the final step is to add all of the individually calculated areas together.

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Answer:

360 cm^2

Step-by-step explanation:

Find the area of each face of the triangular prism.

Imagine the triangular prism as its net, it is composed with 2 triangular faces (these are tye bases of the prism) and 3 rectangular faces.

Areas of the 2 triangular bases (they are similar triangles):

1/2 x 8 cm x 6 cm = 24 cm^2

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Area of the rectangular face:

8 x 13 = 104 cm^2

Area of another rectangular face:

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Area of another rectangular face:

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A farmer wants to fence a rectangular area of 72 square feet next to a river. Find the length and width of the rectangle which u
Arlecino [84]

Answer:

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Step-by-step explanation:

The least fence is used when half the total fence is parallel to the river. That is, the shape of the rectangle is twice as long as it is wide.

72 = W(2W)

36 = W²

6 = W . . . . . . the width perpendicular to the river

12 = 2W . . . .  the length parallel to the river

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<em>Development of this relation</em>

Let T represent the total length of the fence for some area A. Then if x is the length along the river, the width is y=(T-x)/2, and the area is ...

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Note that the equation for area is that of a parabola with zeros at x=0 and at x=T. That is, for some fence length T, the area will be a maximum at the vertex of this parabola. That vertex is located halfway between the zeros, at ...

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The corresponding area width (y) is ...

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Equivalently, the fence length T will be a minimum for some area A when x=T/2 and y=T/4. This is the result we used above.

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