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IceJOKER [234]
2 years ago
8

Match the vocabulary words with the right definitions. 1. a relation where for any given input value there is only one output va

lue mapping diagram 2. a group of two numbers written in an order (x, y) so that the first value represents a horizontal position and the second number represents a vertical position ordered pair 3. the independent values, or x values domain 4. a way of representing how the members of one group are related to the members of another group input 5. a value substituted in for the variable in a function which generates another value (the output) function
Mathematics
1 answer:
pochemuha2 years ago
3 0

Answer:

Step-by-step explanation:

1. Relation - a set of ordered pairs

2. Vertical line test - a test used to determine if a graph is a function; states that a vertical line can only go through one point on the graph to be a function

3. Function - a relation in which for any given input value, there is only one output value

4. Output -  value generated by a function when an input value is substituted into the function and evaluated

5. Ordered pair - a group of two numbers written in the form (x, y) where the x value represents a horizontal position and the y value represents a vertical position

6. Mapping Diagram - a table or diagram that represents a mathematical relation

7. Input - a value that is substituted in for the variable in a function in order to generate an output value

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Exercise 1: In the right triangle below, calculate the measurement of the unknown side. Show your work.
vekshin1

Answer:

Exercise 1:

base [b]=8cm

perpendicular [p]=6cm

hypotenuse [h]=?

<u>By</u><u> </u><u>using</u><u> </u><u>Pythagoras</u><u> </u><u>law</u>

h²=p²+b²

h²=6²+8²

h=√100

h=10cm

<u>So</u><u> </u><u>another</u><u> </u><u>side's</u><u> </u><u>length</u><u> </u><u>is</u><u> </u><u>1</u><u>0</u><u>c</u><u>m</u>

<u>Exercise</u><u> </u><u>2</u><u>:</u>

base [b]=6m

perpendicular [p]=bm

hypotenuse [h]=8m

By using Pythagoras law

h²=p²+b²

8²=b²+6²

b²=8²-6²

b=√28=2√7 0r 5.29 or 5.3

So height of kite is√<u>28</u><u>o</u><u>r</u><u> </u><u>2√7 0r 5.29 or 5.3 m</u>

Step-by-step explanation:

[Note: thanks for translating]

4 0
3 years ago
Which definite integral approximation formula is this: the integral from a to b of f(x)dx ≈ (b-a)/n * [<img src="https://tex.z-d
Stella [2.4K]

The answer is most likely A.

The integration interval [<em>a</em>, <em>b</em>] is split up into <em>n</em> subintervals of equal length (so each subinterval has width (<em>b</em> - <em>a</em>)/<em>n</em>, same as the coefficient of the sum of <em>y</em> terms) and approximated by the area of <em>n</em> rectangles with base (<em>b</em> - <em>a</em>)/<em>n</em> and height <em>y</em>.

<em>n</em> subintervals require <em>n</em> + 1 points, with

<em>x</em>₀ = <em>a</em>

<em>x</em>₁ = <em>a</em> + (<em>b</em> - <em>a</em>)/<em>n</em>

<em>x</em>₂ = <em>a</em> + 2(<em>b</em> - <em>a</em>)/<em>n</em>

and so on up to the last point <em>x</em> = <em>b</em>. The right endpoints are <em>x</em>₁, <em>x</em>₂, … etc. and the height of each rectangle are the corresponding <em>y </em>'s at these endpoints. Then you get the formula as given in the photo.

• "Average rate of change" isn't really relevant here. The AROC of a function <em>G(x)</em> continuous* over an interval [<em>a</em>, <em>b</em>] is equal to the slope of the secant line through <em>x</em> = <em>a</em> and <em>x</em> = <em>b</em>, i.e. the value of the difference quotient

(<em>G(b)</em> - <em>G(a)</em> ) / (<em>b</em> - <em>a</em>)

If <em>G(x)</em> happens to be the antiderivative of a function <em>g(x)</em>, then this is the same as the average value of <em>g(x)</em> on the same interval,

g_{\rm ave}=\dfrac{G(b)-G(a)}{b-a}=\dfrac1{b-a}\displaystyle\int_a^b g(x)\,\mathrm dx

(* I'm actually not totally sure that continuity is necessary for the AROC to exist; I've asked this question before without getting a particularly satisfying answer.)

• "Trapezoidal rule" doesn't apply here. Split up [<em>a</em>, <em>b</em>] into <em>n</em> subintervals of equal width (<em>b</em> - <em>a</em>)/<em>n</em>. Over the first subinterval, the area of a trapezoid with "bases" <em>y</em>₀ and <em>y</em>₁ and "height" (<em>b</em> - <em>a</em>)/<em>n</em> is

(<em>y</em>₀ + <em>y</em>₁) (<em>b</em> - <em>a</em>)/<em>n</em>

but <em>y</em>₀ is clearly missing in the sum, and also the next term in the sum would be

(<em>y</em>₁ + <em>y</em>₂) (<em>b</em> - <em>a</em>)/<em>n</em>

the sum of these two areas would reduce to

(<em>b</em> - <em>a</em>)/<em>n</em> = (<em>y</em>₀ + <u>2</u> <em>y</em>₁ + <em>y</em>₂)

which would mean all the terms in-between would need to be doubled as well to get

\displaystyle\int_a^b f(x)\,\mathrm dx\approx\frac{b-a}n\left(y_0+2y_1+2y_2+\cdots+2y_{n-1}+y_n\right)

7 0
3 years ago
Drag the names to match the geometric terms as shown in the diagram.
mamaluj [8]

Just so you know, there's no diagram

6 0
3 years ago
The parabola below is a graph of the equation, . -y^2+x=-4
serious [3.7K]
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+ All the points (x;y) satisfies: -y^2+x=-4 is on the <span>parabola.
</span>+ All the points (x;y) satisfies: -y^2+x< -4 is in part 1.
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3 years ago
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To calculate the mean we need x and f both

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3 years ago
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