In which quadrant will the following points be plotted (-4;-4) (5;2) (-6;11)

Interpreting composite functions in the real world The volume of air in a balloon is represented by the function v(r)=4/3 ³, whe

adoni [48]

There are two true statements:

When the function is composed with r, the composite function is V(t) = (1/48) · π · t⁶.
V(r(6)) shows that the volume is 972π cubic inches after 6 seconds.

<h3>How to use composition between two function</h3>

Let be f and g two functions, there is a composition of f with respect to g when the domain of f is equal to the range of g. In this question, the domain variable of the function V(r) is replaced by substitution.

If we know that V(r) = (4/3) · π · r³ and r(t) = (1/4) · t², then the composite function is:

V(t) = (4/3) · π · [(1/4) · t²]³

V(t) = (4/3) · π · (1/64) · t⁶

V(t) = (1/48) · π · t⁶

There are two true statements:

When the function is composed with r, the composite function is V(t) = (1/48) · π · t⁶.
V(r(6)) shows that the volume is 972π cubic inches after 6 seconds.

To learn on composition between functions: brainly.com/question/12007574

#SPJ1

7 0

2 years ago

Without calculating, which has a bigger volume. A cube that has a length, width, and height of 18 m. Or a sphere with a radius o

Evgesh-ka [11]

Weird. A period appears above this... huh.

Answer:

[Th]e cube has a greater value.

Step-by-step explanation:

What the word problem really wants us to get [is ]the question of 'Which is greater, A=6a^2 when 'a' [is] 18 or A=4 $\pi$ r^2 when r = 9? And here's how to solve that.

Starting with the[ c]ube we have A=6a^2. A bit t[o]o simple, right?

A=6(18)^2 Substitute numbers.

A=6(324) Solve ex[p]onents.

A=1944 Mult[i]ply.

So w[e] know that the cube is 1944 meters cube[d ] in area. But what about the more [f]ormidable sphere? Fo[r] it we need a slightly m[o]re co[m]plicated formula, A=4 $\pi$ r^2. However, instead of using the real pi I will be rounding to 3.14, since we have no calculator so anything more would take way too long and fry your[ bra]in.

A=4(3.14)(9)^2 Subst[i]tute numbers.

A=4(3.14)(81) Solve expone[n]ts.

A=12.56(81) Multip[ly].

A=1017.36 Multiply again[.]

Now, since I'm sure all of us can count, we know that 1944 is greater than 1017.36. Or in other words, the cube is bigger than the sphere.

And PLEASE don't copy this guys. Make your own iteration. Change it up!

3 0

3 years ago

Find the domain of the function. f(x) = -5x + 3

Sedaia [141]

Enter a problem...

Calculus Examples

Popular Problems Calculus Find the Domain and Range f(x)=5x-3

f

(

x

)

=

5

x

−

3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

(

−

∞

,

∞

)

Set-Builder Notation:

{

x

|

x

∈

R

}

The range is the set of all valid

y

values. Use the graph to find the range.

Interval Notation:

(

−

∞

,

∞

)

Set-Builder Notation:

{

y

|

y

∈

R

}

Determine the domain and range.

Domain:

(

−

∞

,

∞

)

,

{

x

|

x

∈

R

}

Range:

(

−

∞

,

∞

)

,

{

y

|

y

∈

R

}

3 0

3 years ago

Jack had 26 marbles and Jill had 12 marbles. How many marbles would Jack need to give to Jill in order for them to have equal am

rjkz [21]

Answer:

B. 7

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

How are the functions f(x)=16^x and g(x)=16^(1/2)x related? The output values of g(x) are one-half the output values of f(x) for

Goshia [24]

F(x) =16ˣ and g(x) = 16⁽ˣ/₂⁾

Since 16 = 2⁴, then we can write:

f(x) =2⁽⁴ˣ⁾ and g(x) = 2⁽⁴ˣ/₂⁾ = 2²ˣ

for x = 1 f(x) = 2⁴ = 16
for x = 1 g(x) = 2² = 4
(√16 = 4)

for x = 2 f(x) = 2⁸ = 256
for x = 2 g(x) = 2⁴ =16
(√256) = 16

for x = 3 f(x) = 2¹² = 4096
for x = 1 g(x) = 2⁶ = 64
(√4096 = 64)

We notice that:
The output values of g(x) are the square root of the output values of f(x) for the same value of x.

6 0

3 years ago

Read 2 more answers