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4 years ago

If f(x) = 2/x and g(x) = x^2 what is f of g

Mathematics

2 answers:

alekssr [168]4 years ago

7 0

I think f of g = 2/x^2
is that right?

Mekhanik [1.2K]4 years ago

3 0

Answer: The required value is $f(g(x))=\dfrac{2}{x^2}.$

Step-by-step explanation: We are given two functions as follows :

$f(x)=\dfrac{2}{x},~~~~~~~g(x)=x^2.$

We are to find f of g, i.e., f(g(x)).

To find the required value, first we have to find the f value of the function g(x).

We have

$f(g(x))=f(x^2)=\dfrac{2}{x^2}.$

Thus, the required value is $f(g(x))=\dfrac{2}{x^2}.$

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find the equation of a straight line passing through the point(4,5) and equally inclined to the lines 3x = 4y +7 and 5y= 12x +6

galina1969 [7]

First we have to determine the slope of each lines by transforming to the slope-intercept form:

y=(3x-7/)4; m2= ¾y=(12x+6)/5, m3 = 12/5

The formula to be used in the proceeding steps is a=tan^-1(m1-m2)/1+m1m2=tan^-1(m1-m2)/1+m1m2
substituting, a=tan^-1(m1-3/4)/1+3m1/4=tan^-1(m1-12/5)1+12m1/5) =>(4m1-3)/(4+3m1)=(5m1-12)/(5+12m1)m1 = -1applying this slope

y -y1 = m(x-x1)
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3 0

4 years ago

The half-life of a certain radioactive substance is 45 days. There are 6.2 grams present initially. On what day

kvasek [131]

Answer:

There will be less than 1 gram of the radioactive substance remaining by the elapsing of 118 days

Step-by-step explanation:

The given parameters are;

The half life of the radioactive substance = 45 days

The mass of the substance initially present = 6.2 grams

The expression for evaluating the half life is given as follows;

$N(t) = N_0 \left (\dfrac{1}{2} \right )^{\dfrac{t}{t_{1/2}}$

Where;

N(t) = The amount of the substance left after a given time period = 1 gram

N₀ = The initial amount of the radioactive substance = 6.2 grams

$t_{1/2}$ = The half life of the radioactive substance = 45 days

Substituting the values gives;

$1 = 6.2 \left (\dfrac{1}{2} \right )^{\dfrac{t}{45}$

$\dfrac{1}{6.2} = \left (\dfrac{1}{2} \right )^{\dfrac{t}{45}$

$ln\left (\dfrac{1}{6.2} \right ) = {\dfrac{t}{45} \times ln \left (\dfrac{1}{2} \right )$

$t = 45 \times \dfrac{ln\left (\dfrac{1}{6.2} \right ) }{ln \left (\dfrac{1}{2} \right )} \approx 118.45 \ days$

The time that it takes for the mass of the radioactive substance to remain 1 g ≈ 118.45 days

Therefore, there will be less than 1 gram of the radioactive substance remaining by the elapsing of 118 days.

3 0

3 years ago

Simplify the expression... 0.04(0.7). hi

ale4655 [162]

Answer:

0.028

Step-by-step explanation:

Just multiply

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6 0

3 years ago

Triangle XYZ is shown, where n ≥ 5. Triangle X Y Z is shown. The length of side X Y is n + 4, the length of side Y Z is 2 n, and

motikmotik

Answer:

The longest side of the triangle is YZ, the shortest side is ZX, the largest angle is ∠X and the smallest angle is ∠Y.

Step-by-step explanation:

The lengths of the sides of the triangle XYZ are as follows:

XY = n + 4

YZ = 2n

ZX = n - 2

According to the triangle inequality theorem, the sum of two sides of a triangle is always greater than the third side.

Then,

XY < YZ + ZX ⇒ n + 4 < 2n + n - 2 ⇒ n + 4 < 3n - 2 ⇒ 2n > 6 ⇒ n > 3

YZ < XY + ZX ⇒ 2n < n + 4 + n - 2 ⇒ 2n < 2n + 2 ⇒ 0 < 2

ZX < XY + YZ ⇒ n - 2 < n + 4 + 2n ⇒ n - 2 < 3n + 4 ⇒ 2n > -6 ⇒ n > -3

It is provided that n ≥ 5.

Then the sides of the triangle are:

XY = n + 4 ≥ 5 + 4 = 9

YZ = 2n ≥ 2 × 5 = 10

ZX = n - 2 ≥ 5 - 2 = 3

So, the longest side of the triangle is YZ. And the shortest side is ZX.

The largest angle of a triangle is opposite to the longest side.

The angle opposite to YZ would be X. So, the largest angle is ∠X.

The smallest angle of a triangle is opposite to the shortest side.

The angle opposite to ZX would be Y. So, the smallest angle is ∠Y.

Thus, the longest side of the triangle is YZ, the shortest side is ZX, the largest angle is ∠X and the smallest angle is ∠Y.

6 0

4 years ago

Find the length of x.

xenn [34]

130° use the formula that your teacher gives you, a calculator can help too

8 0

3 years ago