Use the diagram. AB is a diameter and AB perpendicular to CD. The figure is not drawn to scale. Which statement is NOT true?

Mathematics

2 answers:

drek231 [11]3 years ago

8 0

A. The arc length AC is not congruent to arc BD.

Sindrei [870]3 years ago

4 0

Answer:

arc AC is congruent to arc BD

Step-by-step explanation:

By drawing the perpendicular CD we get some congruent triangles, first we have ΔACP = ΔADP.

Thus, since these two triangles are congruent, we have that their sides and angles are congruent.

So, AC = AD

But we also got the congruent triangles ΔCPB and ΔDPB, where we will have congruent angles and sides:

So, ∠PBC = ∠DBP = ∠DBA

Finally, we get the congruent triangles ΔABC and ΔABD where ∠BDA = ∠ACB

Thus the statement which is not true is that arc AC is congruent to arc BD

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The slope of the tangent line to the curve x^3y+y^2-x^2=5 at the point (2,1) is

zheka24 [161]

Answer:

-4/5

Step-by-step explanation:

To find the slope of the tangent to the equation at any point we must differentiate the equation.

x^3y+y^2-x^2=5

3x^2y+x^3y'+2yy'-2x=0

Gather terms with y' on one side and terms without on opposing side.

x^3y'+2yy'=2x-3x^2y

Factor left side

y'(x^3+2y)=2x-3x^2y

Divide both sides by (x^3+2y)

y'=(2x-3x^2y)/(x^3+2y)

y' is the slope any tangent to the given equation at point (x,y).

Plug in (2,1):

y'=(2(2)-3(2)^2(1))/((2)^3+2(1))

Simplify:

y'=(4-12)/(8+2)

y'=-8/10

y'=-4/5

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If f(x)=x^3−x, what is the average rate of change of f(x) over the interval [1, 5]? a)29.5 b)30 c)43 d)120

avanturin [10]

$\bf slope = m = \cfrac{rise}{run} \implies 
\cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby 
\begin{array}{llll}
average~rate\\
of~change
\end{array}\\\\
-------------------------------\\\\
f(x)= x^3-x \qquad 
\begin{cases}
x_1=1\\
x_2=5
\end{cases}\implies \cfrac{f(5)-f(1)}{5-1}
\\\\\\
\cfrac{[5^3-5]~-~[1^3-1]}{4}\implies \cfrac{125-5~~-~~0}{4}\implies \cfrac{120}{4}\implies 30$