Four fifts times what equals two thirds

What is the range of the function f(x) = –2|x + 1|?

beks73 [17]

Answer:

Range $\rightarrow$ all real numbers less than or equal to 0 $\rightarrow$ ( - ∞ , 0 ]

Step-by-step explanation:

For visual understanding a graph of the function is attached with the answer.

For calculating the range of any modulus function you need to know that if modulus is there across any function then the output will be always positive.

For example: x has a range of ( - ∞ , + ∞ ) but |x| has a range of [ 0 , + ∞ ). Similarly range of |x + 1| is [ 0 , + ∞ ).

If you multiply the modulus function with a negative sign then the output will always be negative.

For example: Range of |x| is [ 0 , + ∞ ) but range of -|x| is ( - ∞ , 0 ]. Similarly range of -|x + 1| is ( - ∞ , 0 ]

Range in this case won't be affected on multiplying a positive constant with the modulus function.

Therefore the range of f(x) = -2|x + 1| will be ( - ∞ , 0 ].

(NOTE : [a,b] means all the numbers between 'a' and 'b' including 'a' and 'b'.

(a,b) means all the numbers between 'a' and 'b' excluding 'a' and 'b'.

(a,b] means all the numbers between 'a' and 'b' including only 'b' not 'a'.

[a,b) means all the numbers between 'a' and 'b' including only 'a' not 'b'.

{a,b} means only 'a' and 'b'.

{a,b] or (a,b} doesn't mean anything. )

6 0

3 years ago

Read 2 more answers

A cylinder and a cone have the same volume. The cylinder has radius x and height y. The cone has radius 2x. Find the height of t

n200080 [17]

$\bf \textit{volume of a cylinder}\\\\
V_c=\pi r^2h\qquad 
\begin{cases}
r=radius\\
h=height\\
------\\
r=x\\
h=y
\end{cases}\implies V_c=x^2y\pi 
\\\\\\
\textit{volume of a cone}\\\\
V_n=\cfrac{\pi r^2h}{3}\qquad r=2x\implies V_n=\cfrac{\pi \cdot (2x)^2h}{3}
\\\\\\
V_n=\cfrac{\pi \cdot 2^2x^2h}{3}\implies V_n=\cfrac{4x^2h\pi }{3}\\\\
-------------------------------\\\\$

$\bf V_c=V_n\implies x^2y\pi =\cfrac{4x^2h\pi }{3}\implies 3x^2y\pi =4x^2h\pi 
\\\\\\
\cfrac{3x^2y\pi }{4x^2\pi }=h\implies \boxed{\cfrac{3y}{4}=h}$

5 0

3 years ago

Please help with this

WINSTONCH [101]

Answer:

x = 25

Step-by-step explanation:

Step 1: Make a proportion

40/20 = 50/x

Step 2: Solve your proportion

2 = 50/x

2x = 50

x = 25

3 0

3 years ago

Read 2 more answers

Use the method of lagrange multipliers to find

Yanka [14]

Answer:

a) The function is: f(x, y) = x + y.

The constraint is: x*y = 196.

Remember that we must write the constraint as:

g(x, y) = x*y - 196 = 0

Then we have:

L(x, y, λ) = f(x, y) + λ*g(x, y)

L(x, y, λ) = x + y + λ*(x*y - 196)

Now, let's compute the partial derivations, those must be zero.

dL/dx = λ*y + 1

dL/dy = λ*x + 1

dL/dλ = (x*y - 196)

Those must be equal to zero, then we have a system of equations:

λ*y + 1 = 0

λ*x + 1 = 0

(x*y - 196) = 0

Let's solve this, in the first equation we can isolate λ to get:

λ = -1/y

Now we can replace this in the second equation and get;

-x/y + 1 = 0

Now let's isolate x.

x = y

Now we can replace this in the last equation, and we will get:

(x*x - 196) = 0

x^2 = 196

x = √196 = 14

then the minimum will be:

x + y = x + x = 14 + 14 = 28.

b) Now we have:

f(x) = x*y

g(x) = x + y - 196

Let's do the same as before:

L(x, y, λ) = f(x, y) + λ*g(x, y)

L(x, y, λ) = x*y + λ*(x + y - 196)

Now let's do the derivations:

dL/dx = y + λ

dL/dy = x + λ

dL/dλ = x + y - 196

Now we have the system of equations:

y + λ = 0

x + λ = 0

x + y - 196 = 0

To solve it, we can isolate lambda in the first equation to get:

λ = -y

Now we can replace this in the second equation:

x - y = 0

Now we can isolate x:

x = y

now we can replace that in the last equation

y + y - 196 = 0

2*y - 196 = 0

2*y = 196

y = 196/2 = 98

The maximum will be:

x*y = y*y = 98*98 = 9,604

6 0

3 years ago

The admission to a local fair is $10 for each adult and $6 for each child. Each ride costs $1.50 for an adult and $1 for a child

S_A_V [24]

So first start out by writing an expression for the cost of the child and the adult separately.

Child:
6 + 1r ($6 + $1 per ride)

Adult:
10 + 1.5r ($10 + $1.50 per ride)

to find how much more the adult will spend, just do Adult Expression - Child Expression which will be:

10 + 1.5r - (6 + 1r) just simplify this

For Part B, use your equation from part A where r = 7

6 0

2 years ago