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asambeis [7]
3 years ago
9

How to do isosceles triangle

Mathematics
1 answer:
nata0808 [166]3 years ago
4 0

An isosceles triangle has 2 equal sides and 2 equal angles

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Let θ
konstantin123 [22]

Answer:

θ is decreasing at the rate of \frac{21}{16} units/sec

or \frac{d}{dt}(θ) = \frac{-21}{16}

Step-by-step explanation:

Given :

Length of side opposite to angle θ is y

Length of side adjacent to angle θ is x

θ is part of a right angle triangle

At this instant,

x =  8 , \frac{dx}{dt} = 7

( \frac{dx}{dt} denotes the rate of change of x with respect to time)

y = 8 , \frac{dy}{dt} = -14

( The negative sign denotes the decreasing rate of change )

Here because it is a right angle triangle,

tanθ = \frac{y}{x}-------------------------------------------------------------------1

At this instant,

tanθ = \frac{8}{8} = 1

Therefore θ = π/4

We differentiate equation (1) with respect to time in order to obtain the rate of change of θ or \frac{d}{dt}(θ)

\frac{d}{dt} (tanθ) = \frac{d}{dt} (y/x)

( Applying chain rule of differentiation for R.H.S as y*1/x)

sec^{2}θ\frac{d}{dt}(θ) = \frac{1}{x}\frac{dy}{dt} - \frac{y}{x*x}\frac{dx}{dt}-----------------------2

Substituting the values of x , y , \frac{dx}{dt} , \frac{dy}{dt} , θ at that instant in equation (2)

2\frac{d}{dt}(θ) = \frac{1}{8}*(-14)- \frac{8}{8*8}*7

\frac{d}{dt}(θ) = \frac{-21}{16}

Therefore θ is decreasing at the rate of \frac{21}{16} units/sec

or  \frac{d}{dt}(θ) = \frac{-21}{16}

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3 years ago
I need help please!!!
MAVERICK [17]

Answer:

1). 10. 2). 9. 3). 2(square root)14. 4). (square root)6. 5). right triangle. 6). not a right triangle. 7). 13. 8). 3(square root)34. 9). acute. 10). acute. 11). right. 12). obtuse

Step-by-step explanation:

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