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3 years ago

Which of the sets of ordered pairs represents a function?

1 answer:

6 0

A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.

A = {(1, -2); (3, -5), (5, 2), (7, 5)} - it's a function

B = {(4, 2), (4, -2), (9, 3), (9, -3)} - it's not a function

<h3>Answer: Only A</h3>

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When a swimmer dives into the pool, an angle measurement is created. What is an approximate measurement of this swimmer upon ent

AleksandrR [38]

The Answer would be C because the person is diving in at a 55° angle and when they hit the water it would decrease.

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3 years ago

Read 2 more answers

D/d{cosec^-1(1+x²/2x)} is equal to

SIZIF [17.4K]

Step-by-step explanation:

$\large\underline{\sf{Solution-}}$

$\rm :\longmapsto\:\dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)$

Let assume that

$\rm :\longmapsto\:y = {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)$

We know,

$\boxed{\tt{ {cosec}^{ - 1}x = {sin}^{ - 1}\bigg( \dfrac{1}{x} \bigg)}}$

So, using this, we get

$\rm :\longmapsto\:y = sin^{ - 1} \bigg( \dfrac{2x}{1 + {x}^{2} } \bigg)$

Now, we use Method of Substitution, So we substitute

$\red{\rm :\longmapsto\:x = tanz \: \rm\implies \:z = {tan}^{ - 1}x}$

So, above expression can be rewritten as

$\rm :\longmapsto\:y = sin^{ - 1} \bigg( \dfrac{2tanz}{1 + {tan}^{2} z} \bigg)$

$\rm :\longmapsto\:y = sin^{ - 1} \bigg( sin2z \bigg)$

$\rm\implies \:y = 2z$

$\bf\implies \:y = 2 {tan}^{ - 1}x$

So,

$\bf\implies \: {cosec}^{ - 1}\bigg( \dfrac{1 + {x}^{2} }{2x} \bigg) = 2 {tan}^{ - 1}x$

Thus,

$\rm :\longmapsto\:\dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)$

$\rm \: = \: \dfrac{d}{dx}(2 {tan}^{ - 1}x)$

$\rm \: = \: 2 \: \dfrac{d}{dx}( {tan}^{ - 1}x)$

$\rm \: = \: 2 \times \dfrac{1}{1 + {x}^{2} }$

$\rm \: = \: \dfrac{2}{1 + {x}^{2} }$

<u>Hence, </u>

$\purple{\rm :\longmapsto\:\boxed{\tt{ \dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg) = \frac{2}{1 + {x}^{2} }}}}$

<u>Hence, Option (d) is </u><u>correct.</u>

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3 years ago

Ananya's is 7 year 8 months 16 days and Abha's age is 4 years 10 months 25 days . By how much Abha is younger than Ananya ?

Alexxandr [17]

Answer:

<h3><em>2 year 9 months 21 days</em></h3><h3><em></em></h3>

If a month is 30 days;

Year/ Months/Days

7 8 16 \

<h3> If we subtract = <em>2 year 9 months 21 days</em></h3>

4 10 25 /

6 0

3 years ago

Factor the greatest common factor out of 8x^3 + 28x^2 + 40x

Liula [17]

Answer: $4x(2x^2+7x+10)$

Step-by-step explanation:

The Greatest Common Factor (GCF) of a polynomial is defined as the largest monomial that is a factor of all the terms of the polynomial.

In this case, given this polynomial:

$8x^3 + 28x^2 + 40x$

You can factor out the Greatest Common Factor applying this procedure:

1. Write the terms of the polynomial in prime factor form:

$8x^3=2*2*2*x*x*x\\\\28x^2=2*2*7*x*x\\\\40x=2*2*2*5*x$

2. Identify the factors the terms have in common (this will be the Greatest Common Factor). In this case this is:

$GCF=2*2*x=4x$

3. Finally, rewrite the expression in factor form:

$4x(2x^2+7x+10)$

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3 years ago

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Distribute: 9(3x^3-2)

allochka39001 [22]

The answer is 27x^3 - 18

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3 years ago