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Gre4nikov [31]
3 years ago
8

Solve for z. z−4/9−1/3=5/9

Mathematics
2 answers:
uysha [10]3 years ago
7 0

Answer:  The required value of z is \dfrac{4}{3}.

Step-by-step explanation:  We are given to solve the following equation for z :

z-\dfrac{4}{9}-\dfrac{1}{3}=\dfrac{5}{9}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

To solve the given equation for z, we need to take all the constant terms on the right-hand side of the equation.

From equation (i), we have

z-\dfrac{4}{9}-\dfrac{1}{3}=\dfrac{5}{9}\\\\\\\Rightarrow z=\dfrac{5}{9}+\dfrac{1}{3}+\dfrac{4}{9}\\\\\\\Rightarrow z=\dfrac{5+3+4}{9}\\\\\\\Rightarrow z=\dfrac{12}{9}\\\\\Rightarrow z=\dfrac{4}{3}.

Thus, the required value of z is \dfrac{4}{3}.

laila [671]3 years ago
4 0
Z-4/9-1/3=5/9
z-4 =5/9(9-1/3)

z-4 =4.414814815

z =8.814
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Answer:  1) 5040 and 2) 165

Step-by-step explanation:

1) Here total number of letters = 10

The number of permutations that can be formed using 4 letters at a time

= P (10, 4)

= 10_P_4

= \frac{10!}{(10-4)!}

=  \frac{10!}{6!}

= \frac{10\times 9\times 8\times 7\times 6!}{6!}

= 10 × 9 × 8 × 7

= 5040

2) Here the total number of machine = 11

The different combinations of machines can Geoff choose from to use

= 11_C_3

= \frac{11!}{(11-3)!3!}

= \frac{11!}{8!3!}

= \frac{11\times 10\times 9\times 8!}{8!\times 6}

= 11 × 5 × 3

= 165

5 0
3 years ago
Write the expression in radical form. <img src="https://tex.z-dn.net/?f=%2836x%29%5Cfrac%7B1%7D%7B2%7D" id="TexFormula1" title="
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√36x

All under the radical
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3 years ago
A landscaping company placed two orders with a nursery. First order was 5 bushes and 8 trees,and totaled $374.The second order w
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Step-by-step explanation:185 + 189 = 374

8 0
3 years ago
The sum of two numbers is negative. The product of these two same numbers is also negative. What can you conclude about these tw
lara [203]

Answer:

5 and -8

Step-by-step explanation:

One number must be negative since the product of the 2 number is negative (5 x -8 = -40). They both cannot be negative, if they were the product would then be positive. The negative number must have a absolute value that is larger than the positive, the negative numbers distance from 0 must be larger than the positive, -8 has a distance of 8 and 5 has a distance of 5. The sum of the two numbers is

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3 years ago
This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the ex
azamat

Answer:

Maximum at points (8,0),(-8,0).Minimum at points (0,8), (0,-8).

Step-by-step explanation:

There are multiple ways of using lagrange multipliers. Most of them are equivalent.

Consider the function F(x,y) = x^2-y^2-\lambda(x^2+y^2-64). We want the following \frac{\partial F}{\partial x} = \frac{\partial F}{\partial y} = \frac{\partial F}{\partial \lambda} = 0.

Then, we have

\frac{\partial F}{\partial x} = 2x-2x\lambda= 2x(1-\lambda)=0

\frac{\partial F}{\partial y} = -2y-2y\lambda = -2y(1+\lambda)=0

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From the first two equations, we can see that if \lambda =1 then necessarily y=0. IN that case, from the third equation (which is the restriction) gives us that x=\pm 8.

On the other hand, if \lambda=-1 then necessarily x=0. Again, using the restriction this gives us that y=\pm 8.

if we evaluate the original function in this points, we have that f(0,\pm 8) = -64, f(\pm 8,0)=64. Then, we have Maximum at points (8,0),(-8,0) and Minimum at points (0,8), (0,-8).

3 0
3 years ago
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