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lilavasa [31]
4 years ago
6

Find the value of x in the triangle shown below.

Mathematics
1 answer:
Fittoniya [83]4 years ago
8 0

Answer:

20

Step-by-step explanation:

This triangle can be solved using the Pythagorean theorem. 16^2+12^2=x^2. 16^2+12^2=400. If we set 400 equal to x^2, x=20.

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A fence 6 ft high runs parallel to the wall of a house at a distance of 5 ft. Find the length of the shortest ladder that extend
Anettt [7]

Answer:

L = 15.53 ft

Step-by-step explanation:

using diagram which is attached below

now, using Pythagoras theorem

L² = b²  + (5 + x)²...............(1)

using similarity of triangle

\dfrac{x}{6}=\dfrac{5+x}{b}

b=\dfrac{5+x}{x}6

from equation (1)

L^2 = (\dfrac{5+x}{x}6)^2 + (5 + x)^2

     = (5+x)^2(1+\dfrac{36}{x^2})

\frac{\mathrm{d} L^2}{\mathrm{d} x}= 2(5+x)(1+\dfrac{36}{x^2})+(5+x)^2(\dfrac{-2\times 36}{x^3})

\frac{\mathrm{d} L^2}{\mathrm{d} x}= (5+x)(2-\dfrac{72\times 5}{x^3})

for maxima or minima

\frac{\mathrm{d} L^2}{\mathrm{d} x}=0

x = -5 and x =  ∛190  = 5.74

on second derivative 5.74 is the value which comes out to be minimal value which is the distance between the fence and ladder

now,

L² = 241.38

L = 15.53 ft

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3 years ago
What number, c, completes the square? X^2 + 8x + c
barxatty [35]

Answer:

16

Step-by-step explanation:

If you divide 8 by 2 it is 4 and 4 times itself is 16. Because to complete the square you find half of b and square it for c.

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3 years ago
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