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Sonja [21]
3 years ago
12

In the given figure, angle APC =angle BQD. Prove that: AB //CD.​

Mathematics
1 answer:
aniked [119]3 years ago
3 0

1. <APC = <DQB [ Given]

2. Arc(AC = BD) [ Equal angles subtend equal arcs]

3. AB//CD [From 2]

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Find the area between the graph of the function and the x-axis over the given interval, if possible.
vodomira [7]

Answer:

A= -\frac{5}{-1} - \lim_{x\to\infty} \frac{5}{x-2} = 5-0 = 5

So then the integral converges and the area below the curve and the x axis would be 5.

Step-by-step explanation:

In order to calculate the area between the function and the x axis we need to solve the following integral:

A = \int_{-\infty}^1 \frac{5}{(x-2)^2}

For this case we can use the following substitution u = x-2 and we have dx = du

A = \int_{a}^b \frac{5}{u^2} du = 5\int_{a}^b u^{-2}du

And if we solve the integral we got:

A= -\frac{5}{u} \Big|_a^b

And we can rewrite the expression again in terms of x and we got:

A = -\frac{5}{x-2} \Big|_{-\infty}^1

And we can solve this using the fundamental theorem of calculus like this:

A= -\frac{5}{-1} - \lim_{x\to\infty} \frac{5}{x-2} = 5-0 = 5

So then the integral converges and the area below the curve and the x axis would be 5.

7 0
3 years ago
A penguin can dive 48 meters below the surface of the water to reach a fish. It dives 2% of the total depth every 1 second. What
nevsk [136]
3.84 meters because 2% of 48 is 0.96, 0.96*4, which is 3.84
8 0
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A quiz contains five true or false questions.if mason guesses ,what is the probability that he gets all five correct?
astraxan [27]

Answer:

1 out of 25

Step-by-step explanation:

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3 years ago
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Gnesinka [82]

Answer:

Step-by-step explanation:

In statistics, a simple random sample is a subset of individuals (a sample) chosen from a larger set (a population). Each individual is chosen randomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process, and each subset of k individuals has the same probability of being chosen for the sample as any other subset of k.

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5x^2=11x-2 quadratic equation
hjlf

Given data:

The given equation is 5x^2= -11x-2.

The given equation can be written as,

\begin{gathered} 5x^2=-11x-2 \\ 5x^2+11x+2=0^{} \\ 5x^2+10x+x+2^{} \\ 5x(x+2)+1(x+2)=0 \\ (5x+1)(x+2)=0 \\ x=-\frac{1}{5},\text{ x=-2} \end{gathered}

Thus, the values of x are x=-1/5, and x= -2.

4 0
1 year ago
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