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laiz [17]
3 years ago
7

The base of a ladder is 25 meters due west of a burning building. If the angle of elevation of the ladder is 51°, how long is th

e ladder (round to the nearest meter)?
Mathematics
1 answer:
Tanzania [10]3 years ago
5 0

Answer: the length of the ladder is 40 meters.

Step-by-step explanation:

The ladder forms a right angle triangle with the wall and the ground.

The length of the ladder represents the hypotenuse of the right angle triangle.

The distance of the base of the ladder due west of the burning building represents the adjacent side of the right angle triangle.

To determine the length of the ladder, h, we would apply the cosine trigonometric ratio. It is expressed as

Cos θ = adjacent side/hypotenuse. Therefore,

Cos 51 = 25/h

h = 25/Cos 51 = 25/0.6293

h = 40 meters to the nearest meter.

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Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°.
umka2103 [35]
A polar coordinate is that which can be written as (r, θ) where r is the radius and θ is the angle. 

The radius, r, is also the hypotenuse of the right triangle that can be formed. Hence, it can be calculated through the equation,
    
                   r² = x² + y²
If we are to simplify this for the r alone, we have,
                     r = sqrt (x² + y²)

Substituting the known values,
               r = sqrt ((4)² + (-4)²) = 4√2

The x and y can be related through the trigonometric function, tangent. 
      tan θ = y/x
To solve for θ
   θ = tan⁻¹(y/x) = tan⁻¹(-4/4) = -45° = 315°

Hence, the polar coordinate is <em>(4√2, 315°)</em>
5 0
3 years ago
Given the expression: 3x^10 − 48x^2
photoshop1234 [79]

Answer:

Part A: 3x²(x⁸ - 16)

Part B: 3x²(x² - 2)(x² + 2) (x² - 2x + 2)(x² + 2x + 2)  

Step-by-step explanation:

Part A. Factor out the greatest common factor

3x¹⁰ - 48 x²

= 3x²(x⁸ - 16)

Part B. Factor the expression completely

(i) Factor the difference of squares

x⁸ - 16

= (x⁴ - 4)(x⁴ + 4)

= (x² - 2)(x² + 2)(x⁴ + 4)

3x¹⁰ - 48 x² = 3x²(x² - 2)(x² + 2)(x⁴ + 4)

(ii) Factor the sum of squares

Use the Sophie Germain Identity to factor x⁴ + 4.

x⁴ + 4

= (x²)² + 2²           (Still a sum of squares)

= (x² + 2)² - 4x²    (Factor this as a difference of squares)

= (x² + 2 - 2x)(x² + 2 + 2x)

3x¹⁰ - 48 x² = 3x² (x² - 2)(x² + 2) (x² - 2x + 2)(x² + 2x + 2)

8 0
3 years ago
Which system is equivalent to 3x squared - 4y squared = 25 over -6x squared -2y squared = 11
TEA [102]
So we are given the following system:
3x^2-4y^2=25\\&#10;-6x^2-2y^2=11\\\text{Multiply the second equation by -2:}\\12x^2+4y^2=-22\\\text{Add to the first equation we get:}\\15x^2=3&#10;\text{ therefore }x=\pm \sqrt{ \frac{1}{5} }
Using the first equation again we get:
3x^2-4y^2=25\\&#10;3x^2=4y^2+25\\&#10;x^2= \frac{1}{3}(4y^2+25)\\x^2= \frac{1}{3}(4 \frac{1}{5} +25)\\= \frac{43}{5}\\x=\pm \sqrt{ \frac{43}{5} }
3 0
3 years ago
What value makes the two expressions equivalent?<br> 45x + 72y<br> __(5x + 8y)
zimovet [89]

Answer:

9

Step-by-step explanation:

This is because of the distributive property.

The outside number is multiplied by each inside number.

So, if it's 9(5x+8y), then do 9*5x which is 45x and 9*8y which is 72y.

3 0
3 years ago
A health-food store owner buys new products for his store by borrowing against a credit line of $4,500 from one of his wholesale
tresset_1 [31]

Answer:

Loan Amount= $4500

Monthly Payment= $600

9 months= $600*9= $5400

Interest = $5400-$4500= $900

4 0
2 years ago
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