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3 years ago

Ex) A nursery plants a new tree and attaches a guy wire to help support the tree

Mathematics

2 answers:

o-na [289]3 years ago

8 0

Answer:

d = 5,35 ft

Step-by-step explanation: See annex

Figure in annex is clear,

sin ∠42⁰ = d / 8

And

sin ∠42⁰ = 0.669

d/8 = 0,669

d = 0,669*8

d = 5,35 ft

nordsb [41]3 years ago

6 0

Answer:

a ≈ 5.4 ft

Step-by-step explanation:

A guy wire is used to hold a tree firmly to the ground to avoid bending or falling due to earth natural phenomenon like wind.

The guy wire is tied to a stake and attached to the tree. The illustration above forms a right angle triangle. The angle of elevation from the stake in the ground with the tree is 42°.

The tree forms the opposite side of the right angle triangle starting from the point the guy wire was attached down to the base of the tree. The guy wire attached from the tree to the stake forms the hypotenuse of the right angle triangle.

The height of the connection point on the tree is the height of the tree starting from where the guy wire was tied to the tree to the base. Let us call the height a.

hypotenuse = 8 ft

opposite side(a) = ?

angle of elevation = 42°

Using the SOHCAHTOA principle

sin ∅ = opposite/hypotenuse

sin 42° = a/8

cross multiply

a = 8 sin 42°

a = 8 × 0.6691306064

a = 5.3530448509

a ≈ 5.4 ft

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/// WORTH 70 points /// ASAP ////

belka [17]

A community is developing plans for a pool and hot tub. The community plans to form a swim team, so the pool must be built to certain dimensions. Answer the questions to identify possible dimensions of the deck around the pool and hot tub.

Part I: The dimensions of the pool are to be 25 yards by 9 yards. The deck will be the same width on all sides of the pool. Including the deck, the total pool area has a length of (x + 25) yards, and a width of (x + 9) yards.

Write an equation representing the total area of the pool and the pool deck. Use y to represent the total area. Hint: The area of a rectangle is length times width. (1 point)

$y = (x+25)(x+9)$

Rewrite the area equation in standard form. Hint: Use the FOIL method. (1 point)

$y = x^2 + 9x + 25x + 9(25)$

$y = x^2 +34x + 225$

Rewrite the equation from Part b in vertex form by completing the square. Hint: Move the constant to the other side, add to each side, rewrite the right side as a perfect square trinomial, and finally, isolate y. (4 points: 1 point for each step in the hint)

$y-225 = x^2 +34x$

$y-225 + 17^2 = x^2 +34x + 17^2$

$y-225 + 289 = (x+17)^2$

$y = (x+17)^2 - 64$

What is the vertex of the parabola? What are the x- and y-intercepts? Hint: Use your answer from Part a to identify the x-intercepts. Use your answer from Part b to identify the y-intercept. Use your answer from Part c to identify the vertex. (4 points: 1 point for each coordinate point)

The vertex is where the squared term is zero, x=-17 , y =-64, (-17,-64)

The y intercept is y at x=0, so (0,225)

The x intercepts are the zeros; so at x=-25 and x=-9, aka (-25,0), (-9,0)

Graph the parabola. Use the key features of the graph that you identified in Part d. (3 points)

[Plot the points we generated and connect the dots. I'll leave the graphing to you]

In this problem, only positive values of x make sense. Why? (1 point)

x is the width of the pool edge; it must be positive.

What point on your graph shows a total area that includes the pool but not the pool deck? (1 point)

x=0, y=225 i.e. (0,225)

The community decided on a pool area that adds 6 yards of pool deck to both the length and the width of the pool. What is the total area of the pool and deck when x = 6 yards? (2 points)

(9+6)(25+6)=15(31)=465

Part II: A square hot tub will be placed in the center of an enclosed area near the pool. Each side of the hot tub measures 6 feet. It will be surrounded by x feet of deck on each side. The enclosed space is also square and has an area of 169 square feet. Find the width of the deck space around the hot tub, x.

Step 1: Write an equation for the area of the enclosed space in the form y = (side length)2. Hint: Don't forget to add x to each side of the hot tub. (1 point)

$y=(x+6)(x+6)=(x+6)^2$