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enyata [817]
2 years ago
15

What is the slope of, (-2,1) and (5,4)?

Mathematics
1 answer:
Neporo4naja [7]2 years ago
5 0

Answer:

\frac{3}{7}

Step-by-step explanation:

\frac{4-1}{5--2} =

\frac{4-1}{5+2} =

\frac{3}{7}

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Write an equivalent expression for 8x + 9
siniylev [52]

Answer:

8+8+8+8+8+8+8+8+8.

Step-by-step explanation:

Just add 8 nine times.

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Rotate the point A (-3,4) 270°about the origin. Plot A' on the grid.
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Step-by-step explanation:

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A coin is tossed twice. What is the probability of getting a tail in the first toss and a tail in the second toss?
skelet666 [1.2K]

Answer:

<h2>1/4 Chances</h2><h2>25% Chances</h2><h2>0.25 Chances (out of 1)</h2>

Step-by-step explanation:

Two methods to answer the question.

Here are presented to show the advantage in using the product rule given above.

<h2>Method 1:Using the sample space</h2>

The sample space S of the experiment of tossing a coin twice is given by the tree diagram shown below

The first toss gives two possible outcomes: T or H ( in blue)

The second toss gives two possible outcomes: T or H (in red)

From the three diagrams, we can deduce the sample space S set as follows

          S={(H,H),(H,T),(T,H),(T,T)}

with n(S)=4 where n(S) is the number of elements in the set S

tree diagram in tossing a coin twice

The event E : " tossing a coin twice and getting two tails " as a set is given by

          E={(T,T)}

with n(E)=1 where n(E) is the number of elements in the set E

Use the classical probability formula to find P(E) as:

          P(E)=n(E)n(S)=14

<h2>Method 2: Use the product rule of two independent event</h2>

Event E " tossing a coin twice and getting a tail in each toss " may be considered as two events

Event A " toss a coin once and get a tail " and event B "toss the coin a second time and get a tail "

with the probabilities of each event A and B given by

          P(A)=12 and P(B)=12

Event E occurring may now be considered as events A and B occurring. Events A and B are independent and therefore the product rule may be used as follows

        P(E)=P(A and B)=P(A∩B)=P(A)⋅P(B)=12⋅12=14

NOTE If you toss a coin a large number of times, the sample space will have a large number of elements and therefore method 2 is much more practical to use than method 1 where you have a large number of outcomes.

We now present more examples and questions on how the product rule of independent events is used to solve probability questions.

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Find the equation of the line normal to the curve of y=3cos1/3x, Where x=\pi
sertanlavr [38]

Answer:

y = \frac{\sqrt{2}x}{3} - \frac{\sqrt{2}\pi}{3} + 1.5

Step-by-step explanation:

The equation to the line normal to the curve has the following format:

y - y(x_{0}) = m(x - x_{0})

In whicm m is the derivative of y at the point x_{0}

In this problem, we have that:

x_{0} = \pi

y(x) = 3\cos{\frac{x}{3}}

y(\pi) = 3\cos{\frac{\pi}{3}} = \frac{3}{2}

The derivative of \cos{ax} is a\sin{ax}

So

y(x) = 3\cos{\frac{x}{3}}

y'(x) = 3*\frac{1}{3}\sin{\frac{x}{3}} = \sin{\frac{x}{3}}

m = \sin{\frac{\pi}{3}} = \frac{\sqrt{2}}{3}

The equation of the line normal to the curve of y=3cos1/3x is:

y - y(x_{0}) = m(x - x_{0})

y - \frac{3}{2} = \frac{\sqrt{2}}{3}(x - \pi)

y = \frac{\sqrt{2}}{3}(x - \pi) +  \frac{3}{2}

y = \frac{\sqrt{2}x}{3} - \frac{\sqrt{2}\pi}{3} + 1.5

8 0
3 years ago
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