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Katarina [22]
3 years ago
6

Four fifts times what equals two thirds

Mathematics
1 answer:
SVEN [57.7K]3 years ago
7 0
(4/5)*what = (2/3)
Multiply by 5/4
.. what = (2/3)*(5/4)
.. what = 5/6
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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 : <em>[a,b] means all the numbers between 'a' and 'b' including 'a' and 'b'.</em>

<em>(a,b) means all the numbers between 'a' and 'b' excluding 'a' and 'b'.</em>

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

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

<em>{a,b} means only 'a' and 'b'.</em>

<em>{a,b] or (a,b} doesn't mean anything.</em> )

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
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\bf \textit{volume of a cylinder}\\\\&#10;V_c=\pi r^2h\qquad &#10;\begin{cases}&#10;r=radius\\&#10;h=height\\&#10;------\\&#10;r=x\\&#10;h=y&#10;\end{cases}\implies V_c=x^2y\pi &#10;\\\\\\&#10;\textit{volume of a cone}\\\\&#10;V_n=\cfrac{\pi r^2h}{3}\qquad r=2x\implies V_n=\cfrac{\pi \cdot (2x)^2h}{3}&#10;\\\\\\&#10;V_n=\cfrac{\pi \cdot 2^2x^2h}{3}\implies V_n=\cfrac{4x^2h\pi }{3}\\\\&#10;-------------------------------\\\\

\bf V_c=V_n\implies x^2y\pi =\cfrac{4x^2h\pi }{3}\implies 3x^2y\pi =4x^2h\pi &#10;\\\\\\&#10;\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
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