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lisabon 2012 [21]
3 years ago
10

Triangle ABC is isosceles, with ab = CB

Mathematics
1 answer:
patriot [66]3 years ago
6 0
I’m pretty sure the correct answer is B.
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what is the rate of change for the linear relationship modeled in the table? x y −1 10 1 9 3 8 5 7 -1/2 0 1/2 2
Vesnalui [34]

Answer:

Rate of change for the linear relationship modeled is \dfrac{-1}{2}

Step-by-step explanation:

As the there is a linear relationship in the points, so all these points will be on a single straight line. Hence the slope will be same throughout all the points.

We know that, the slope of the line joining (x₁, y₁) and (x₂, y₂) is,

m=\dfrac{y_2-y_1}{x_2-x_1}

Putting the points as (-1, 10) and (1, 9), we get

m=\dfrac{9-10}{1-(-1)}

=\dfrac{9-10}{1+1}

=\dfrac{-1}{2}

Rate of change is the slope of the line joining all these points.

7 0
3 years ago
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Derivative of tan(2x+3) using first principle
kodGreya [7K]
f(x)=\tan(2x+3)

The derivative is given by the limit

f'(x)=\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h

You have

\displaystyle\lim_{h\to0}\frac{\tan(2(x+h)+3)-\tan(2x+3)}h
\displaystyle\lim_{h\to0}\frac{\tan((2x+3)+2h)-\tan(2x+3)}h

Use the angle sum identity for tangent. I don't remember it off the top of my head, but I do remember the ones for (co)sine.

\tan(a+b)=\dfrac{\sin(a+b)}{\cos(a+b)}=\dfrac{\sin a\cos b+\cos a\sin b}{\cos a\cos b-\sin a\sin b}=\dfrac{\tan a+\tan b}{1-\tan a\tan b}

By this identity, you have

\tan((2x+3)+2h)=\dfrac{\tan(2x+3)+\tan2h}{1-\tan(2x+3)\tan2h}

So in the limit you get

\displaystyle\lim_{h\to0}\frac{\dfrac{\tan(2x+3)+\tan2h}{1-\tan(2x+3)\tan2h}-\tan(2x+3)}h
\displaystyle\lim_{h\to0}\frac{\tan(2x+3)+\tan2h-\tan(2x+3)(1-\tan(2x+3)\tan2h)}{h(1-\tan(2x+3)\tan2h)}
\displaystyle\lim_{h\to0}\frac{\tan2h+\tan^2(2x+3)\tan2h}{h(1-\tan(2x+3)\tan2h)}
\displaystyle\lim_{h\to0}\frac{\tan2h}h\times\lim_{h\to0}\frac{1+\tan^2(2x+3)}{1-\tan(2x+3)\tan2h}
\displaystyle\frac12\lim_{h\to0}\frac1{\cos2h}\times\lim_{h\to0}\frac{\sin2h}{2h}\times\lim_{h\to0}\frac{\sec^2(2x+3)}{1-\tan(2x+3)\tan2h}

The first two limits are both 1, and the single term in the last limit approaches 0 as h\to0, so you're left with

f'(x)=\dfrac12\sec^2(2x+3)

which agrees with the result you get from applying the chain rule.
7 0
3 years ago
Let P be a predicate. Determine whether or not each of the following implications is true and give a brief English explanation f
den301095 [7]

Answer:

See answer below

Step-by-step explanation:

1), Probably, your implication is ∀x∃yP(x,y)⇒∃x∀yP(x,y).

This implication is false. Consider the predicate P(x,y):="x<y" for real numbers x,y. Then, ∀x∃yP(x,y) is true: for all real x, there exists some y greater than x (take y=x+1 for example). However, ∃x∀yP(x,y) is false, as it would imply that there exists some real number x such that x is smaller than all real numbers, which is not true (real numbers do not have a minimum or a lower bound).

A short explanation would be, even if for all elements you can find one that makes a predicate true, you can not find one element that makes the predicate true for all elements.

2) Again, I assume that the predicate is ∃x∀yP(x,y)⇒∀x∃yP(x,y)

This implication is false. Consider the predicate P(x,y):="x is integer and xy=0 " for real numbers x,y. Then ∃x∀yP(x,y) is true, we need to take x=0. However, ∀x∃yP(x,y) is false, if you take x=1/2, 1/2 will never be an integer, no matter the value of y.

A short explanation would be, even if you can find one element that makes a predicate true for all elements, you can not always take an arbitrary element and find some element that makes the predicate true.

6 0
3 years ago
Linda's rental car cost $198
Vsevolod [243]
I got $258.44 but it may be different if the six percent tax was off the entire total which included the insurance, I only took the 6% tax for the cost of the rental car
8 0
3 years ago
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18 students at woodworth school. 1/2 as many girls as boys. how many girls
Ganezh [65]
9 girls and 9 boys equals 18 students
8 0
3 years ago
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