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2 years ago

These ordered pairs, {(2,4) (3,6) (4,8) (5,10)}, are a function. True False

Mathematics

1 answer:

ki77a [65]2 years ago

8 0

Answer:

True

Step-by-step explanation:

In order for a relation (a set of ordered pairs) to be considered a function, every value in the domain (the set of all the first numbers in the pair) is associated with one value in the range (the set of all second numbers in the pair). This is easiest to see visually. Our domain is the set {2, 3, 4, 5} and our range is the set {4, 6, 8, 10}, and we can visualize the ordered pair (2, 4) as an "arrow" starting a 2 in the domain and ending at 4 in the range. When seen this way, a relation is a function if every value in the domain only has one arrow coming out of it. We can see from the attached picture that the ordered pairs in the problem are a function, so this statement is true.

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Find the length of the unknown side. Round your answer to the nearest tenth.

Paraphin [41]

Answer:

The correct option is: 11.5

Step-by-step explanation:

Suppose, the length of the unknown side is $x$

So, here the length of hypotenuse is 14 and the lengths of other two sides are 8 and $x$ .

As the given triangle is right angle triangle, so using Pythagorean theorem, we will get.........

$8^2+x^2= 14^2\\ \\ 64+x^2=196\\ \\ x^2=196-64=132\\ \\ x=\sqrt{132}=11.489...\approx 11.5$

(Rounded to the nearest tenth)

So, the length of the unknown side is 11.5

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2 years ago

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Question 2

Slav-nsk [51]

Answer:

wanna help, but please specify what the (2) means.

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2 years ago

Quadrilateral LMNO is a parallelogram, and LM=24-9 and NO=y-2, find the value of "y" and the length of NO.

Slav-nsk [51]

Answer:

y = 7

NO = 5

Step-by-step explanation:

Let the side of the parallelogram LM and NO given be 2y - 9 and y - 2

Since LMNO is a parallelogram, hence;

LM = NO

2y - 9 = y - 2

2y - y = -2 + 9

y = 7

Since NO = y - 2

NO = 7 - 2

NO = 5

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2 years ago

Which operation is used to solve for x? x/5=15

Ulleksa [173]

Answer:

x = 75

Step-by-step explanation:

x/5 = 15

x = 75 Multiply 5 on both sides

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2 years ago

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Calculus 2

FinnZ [79.3K]

Answer:

See Below.

Step-by-step explanation:

We want to estimate the definite integral:

$\displaystyle \int_1^47\sqrt{\ln(x)}\, dx$

Using the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule with six equal subdivisions.

The trapezoidal rule is given by:

$\displaystyle \int_{a}^bf(x)\, dx\approx\frac{\Delta x}{2}\Big(f(x_0)+2f(x_1)+...+2f(x_{n-1})+f(x_n)\Big)$

Our limits of integration are from x = 1 to x = 4. With six equal subdivisions, each subdivision will measure:

$\displaystyle \Delta x=\frac{4-1}{6}=\frac{1}{2}$

Therefore, the trapezoidal approximation is:

$\displaystyle =\frac{1/2}{2}\Big(f(1)+2f(1.5)+2f(2)+2f(2.5)+2f(3)+2f(3.5)+2f(4)\Big)$

Evaluate:

$\displaystyle =\frac{1}{4}(7)(\sqrt{\ln(1)}+2\sqrt{\ln(1.5)}+...+2\sqrt{\ln(3.5)}+\sqrt{\ln(4)})\\\\\approx18.139337$

The midpoint rule is given by:

$\displaystyle \int_a^bf(x)\, dx\approx\sum_{i=1}^nf\Big(\frac{x_{i-1}+x_i}{2}\Big)\Delta x$

Thus:

$\displaystyle =\frac{1}{2}\Big(f\Big(\frac{1+1.5}{2}\Big)+f\Big(\frac{1.5+2}{2}\Big)+...+f\Big(\frac{3+3.5}{2}\Big)+f\Big(\frac{3.5+4}{2}\Big)\Big)$

Simplify:

$\displaystyle =\frac{1}{2}(7)\Big(f(1.25)+f(1.75)+...+f(3.25)+f(3.75)\Big)\\\\ =\frac{1}{2}(7) (\sqrt{\ln(1.25)}+\sqrt{\ln(1.75)}+...+\sqrt{\ln(3.25)}+\sqrt{\ln(3.75)})\\\\\approx 18.767319$

Simpson's Rule is given by:

$\displaystyle \int_a^b f(x)\, dx\approx\frac{\Delta x}{3}\Big(f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+...+4f(x_{n-1})+f(x_n)\Big)$

So:

$\displaystyle =\frac{1/2}{3}\Big((f(1)+4f(1.5)+2f(2)+4f(2.5)+...+4f(3.5)+f(4)\Big)$

Simplify:

$\displaystyle =\frac{1}{6}(7)(\sqrt{\ln(1)}+4\sqrt{\ln(1.5)}+2\sqrt{\ln(2)}+4\sqrt{\ln(2.5)}+...+4\sqrt{\ln(3.5)}+\sqrt{\ln(4)})\\\\\approx 18.423834$

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2 years ago