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sveticcg [70]
2 years ago
11

A bird is flying at an elevation of 3 5/8 feet above sea level. A fish swims directly under the bird at a depth of 5 1/3 feet be

low sea level. How far apart are the two creatures?
Mathematics
1 answer:
Stells [14]2 years ago
3 0

Given :

Distance of bird from sea level, d_1 = 3\dfrac{5}{8} = \dfrac{29}{8}\ feet .

Distance between fish and sea level, d_2=5\dfrac{1}{3}=\dfrac{16}{3}\ feet .

To Find :

Distance between bird and fish.

Solution :

Distance between bird and fish is given by :

D=d_1+d_2\\\\D = \dfrac{29}{8}+\dfrac{16}{3}\\\\D=8.958\ feet

Therefore, distance between bird and fish is 8.958 feet.

Hence, this is the required solution.

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How to simplify -(-7y+12)
faust18 [17]
-(-7y + 12) = 7y - 12
u are distributing the -sign through the parenthesis...so u take the number outside of the parenthesis (and if it just a sign, the number is 1)...and u multiply it by everything in the parenthesis.
-1(-7y + 12) = -1 * -7y + (-1) * 12 = 7y + (-12) = 7y - 12
7 0
3 years ago
Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer d
andrey2020 [161]

Answer:

The maximum value is 1/27 and the minimum value is 0.

Step-by-step explanation:

Note that the given function is equal to (xyz)^2 then it means that it is positive i.e f(x,y,z)\geq 0.

Consider the function F(x,y,z,\lambda)=x^2y^2z^2-\lambda (x^2+y^2+z^2-1)

We want that the gradient of this function  is equal to zero. That is (the calculations in between are omitted)

\frac{\partial F}{\partial x} = 2x(y^2z^2 - \lambda)=0

\frac{\partial F}{\partial y} = 2y(x^2z^2 - \lambda)=0

\frac{\partial F}{\partial z} = 2z(x^2y^2 - \lambda)=0

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

Note that the last equation is our restriction. The restriction guarantees us that at least one of the variables is non-zero. We've got 3 options, either 1, 2 or none of them are zero.

If any of them is zero, we have that the value of the original function is 0. We just need to check that there exists a value for lambda.

Suppose that x is zero. Then, from the second and third equation we have that

-2y\lambda = -2z\lambda. If lambda is not zero, then y =z. But, since -2y\lambda=0 and lambda is not zero, this implies that x=y=z=0 which is not possible. This proofs that if one of the variables is 0, then lambda is zero. So, having one or two variables equal to zero are feasible solutions for the problem.

Suppose that only x is zero, then we have the solution set y^2+z^2=1.

If both x,y are zero, then we have the solution set z^2=1. We can find the different solution sets by choosing the variables that are set to zero.

NOw, suppose that none of the variables are zero.

From the first and second equation we have that

\lambda = y^2z^2 = x^2z^2 which implies x^2=y^2

Also, from the first and third equation we have that

\lambda = y^2z^2 = x^2y^2 which implies x^2=z^2

So, in this case, replacing this in the restriction we have 3z^2=1, which gives as another solution set. On this set, we have x^2=y^2=z^2=\frac{1}{3}. Over this solution set, we have that the value of our function is \frac{1}{3^3}= \frac{1}{27}

4 0
3 years ago
PLEASE HELP ASAP I’ll mark brainliest!!!
Andrej [43]

Answer:

yes it is a change of state since both hydrogen and oxygen are gas.

7 0
3 years ago
Is a multiple of a number is a power of the number
Valentin [98]
Yes it is a multiple
7 0
3 years ago
Kurt opened a savings account and deposited $3,000.00 as principal. The account earns 5%
stiv31 [10]

Answer:

Step-by-step explanation:

P = 3,000

r = 5% = 0.05

t = 9 years

Amount after 9 years is

A = P (1+ r)^t

A = 3,000(1+ 0.05)^9 = 3,000 * 1.05^9 = 4653.984648 ≈ $4,653.98

The balance after 9 years, rounded to the nearest cent is

$4,653 and 98 cents

7 0
2 years ago
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