How to find the measure of yz

Mathematics

1 answer:

stira [4]3 years ago

4 0

Use the Law of Sines (sina/A=sinb/B=sinc/C for any triangle)

YZ/sin30=50/sin90

YZ=50sin30 (sin90=1 :P)

YZ=25m

Use the 30,60,90° triangle ratios 1, √3, 2

YZ/1=50/2

YZ=25m

Using the Pythagorean Theorem....

(2*25)^2=YZ^2+(√3*YZ)^2

2500=YZ^2+3YZ^2

2500=4YZ^2

625=YZ^2

25m=YZ

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A. x(x +4)(3 -x) . . . . a cubic will have 3 linear factors

B. The dimensions are x, x+4, 3 -x, or 1.694 ft, 5.694 ft, 1.306 ft

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Step-by-step explanation:

A. The first attachment shows the synthetic division of the given polynomial by x+4. The result is -x^2 +3x = x(3 -x). Hence the factored polynomial is ...

x(3-x)(x+4) . . . . . . shown as positive

Since the polynomial is a cubic, we know there will be 3 roots. For this problem, that means we expect 3 factors.

B. We are apparently to assume that the dimensions of the tank correspond to the three factors:

For the maximum size tank (see part C), the corresponding measurements in feet are