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2 years ago

Please help me out please

Mathematics

1 answer:

Sliva [168]2 years ago

6 0

Answer:

Step-by-step explanation:

For rectangle ABCD, AC and BD are the lengths of the diagonals. The diagonals of a rectangle are congruent.

AC = BD

3x + 7 = 131 - x

Add x to both sides.

4x + 7 = 131

Subtract 7 from both sides.

4x = 124

Divide both sides by 4.

x = 31

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Find the linear approximation of the function f(x, y, z) = x2 + y2 + z2 at (3, 6, 6) and use it to approximate the number 3.022

sertanlavr [38]

Answer:

Step-by-step explanation:

<u>Linearization of Multivariable Functions</u>

Let f be a function that depends on the independent variables (x,y,z) and assume the following partial derivatives exist:

$\displaystyle \frac{\partial f}{\partial x}\ ,\ \frac{\partial f}{\partial y}\ ,\ \frac{\partial f}{\partial z}$

The function f can be linearized around a known point (xo,yo,zo) by the equation:

$\displaystyle f(x,y,z)\approx f(x_o,y_o,z_o)+\frac{\partial f(x_o,y_o,z_o)}{\partial x} (x-x_o)+\frac{\partial f(x_o,y_o,z_o)}{\partial y} (y-y_o)+\frac{\partial f(x_o,y_o,z_o)}{\partial z} (z-z_o)$

Given

$f(x, y, z) = x^2 + y^2 + z^2$

Evaluating in (3,6,6)

$f(x, y, z) = 3^2 + 6^2 + 6^2=81$

The partial derivatives are

$\displaystyle \frac{\partial f}{\partial x}=2x$

Evaluating at (3,6,6)

$\displaystyle \frac{\partial f}{\partial x}=2(3)=6$

$\displaystyle \frac{\partial f}{\partial y}=2y$

Evaluating at (3,6,6)

$\displaystyle \frac{\partial f}{\partial y}=2(6)=12$

$\displaystyle \frac{\partial f}{\partial z}=2z$

Evaluating at (3,6,6)

$\displaystyle \frac{\partial f}{\partial z}=2(6)=12$

The linearization of f is

$\displaystyle f(x,y,z)\approx 81+6 (x-3)+12 (y-6)+12 (z-6)$

Operating

$\displaystyle f(x,y,z)\approx 81+6 x-18+12y-72+12z-72$

$\displaystyle f(x,y,z)\approx 6 x+12y+12z-81$

Using the linearization to find f(3.022 , 5.992 , 5.972)

$\displaystyle f(3.022 , 5.992 , 5.972)\approx 6 (3.022)+12(5.992)+12(5.972)-81=80.70000$

7 0

2 years ago

-. In Ms. Nice's class of 9 students, the average

frutty [35]

Answer: 94.5

Step-by-step explanation:

If average of 9 students is 94, their total will be 94x 9 = 846

If the 10th student scores 99, the new total is 846 + 99 = 945

So, the new average will be

945/10 = 94.5

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2 years ago

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tekilochka [14]

Answer:

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Step-by-step explanation:

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2 years ago

Unit #2 - Lesson #7 Exit Ticket: Solve the equation shown below for the variable x. Place your answer in the answer box.

jolli1 [7]

Answer:

$x = bc + 2b$

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2 years ago

40 POINTS!

nata0808 [166]

-2x-4y = 2
-2x-4y+4y = 2+4y
-2x=4y+2

Divided by 2:
-2x/-2 = 4y +2/ -2
Answer: x=-2y-1

3x +4y =8
3x + 4y = -4y = 8+-4y
3x= -4y +8
Divided by 3
3x/3 = -4y + 8/3
x=-4/3y + 8/3

Bonus!
# of reserved seat tickets
r.
# of reserved admission ticket's
g
4r + 3g = 5792
r + g= 1787

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2 years ago