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xeze [42]
3 years ago
8

B.

Mathematics
1 answer:
denis23 [38]3 years ago
5 0

Hey!

-----------------------------------------------------

Question B:

12 tenths + 9 tenths

~Turn into decimal

1.2 + 0.9

~Add

1.2 + 0.9 = 2.1

~Answer

one(s): 2

tenth(s): 1

-----------------------------------------------------

Question C:

3 hundredths + 4 hundredths

Turn into decimal

0.03 + 0.04

~Add

0.03 + 0.04 = 0.07

~Answer

hundredth(s): 7

-----------------------------------------------------

Hope This Helped! Good Lucked!

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Use lagrange multipliers to find the shortest distance, d, from the point (4, 0, −5 to the plane x y z = 1
Varvara68 [4.7K]
I assume there are some plus signs that aren't rendering for some reason, so that the plane should be x+y+z=1.

You're minimizing d(x,y,z)=\sqrt{(x-4)^2+y^2+(z+5)^2} subject to the constraint f(x,y,z)=x+y+z=1. Note that d(x,y,z) and d(x,y,z)^2 attain their extrema at the same values of x,y,z, so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.

The Lagrangian is

L(x,y,z,\lambda)=(x-4)^2+y^2+(z+5)^2+\lambda(x+y+z-1)

Take your partial derivatives and set them equal to 0:

\begin{cases}\dfrac{\partial L}{\partial x}=2(x-4)+\lambda=0\\\\\dfrac{\partial L}{\partial y}=2y+\lambda=0\\\\\dfrac{\partial L}{\partial z}=2(z+5)+\lambda=0\\\\\dfrac{\partial L}{\partial\lambda}=x+y+z-1=0\end{cases}\implies\begin{cases}2x+\lambda=8\\2y+\lambda=0\\2z+\lambda=-10\\x+y+z=1\end{cases}

Adding the first three equations together yields

2x+2y+2z+3\lambda=2(x+y+z)+3\lambda=2+3\lambda=-2\implies \lambda=-\dfrac43

and plugging this into the first three equations, you find a critical point at (x,y,z)=\left(\dfrac{14}3,\dfrac23,-\dfrac{13}3\right).

The squared distance is then d\left(\dfrac{14}3,\dfrac23,-\dfrac{13}3\right)^2=\dfrac43, which means the shortest distance must be \sqrt{\dfrac43}=\dfrac2{\sqrt3}.
7 0
3 years ago
Is -2.7 an irrational number
ololo11 [35]

Answer:

No

Step-by-step explanation:

An irrational number is a number that never ends or repeats. This decimal ends and it doesn't repeat.

6 0
2 years ago
Read 2 more answers
Select the correct solution set. 50 ≥ 15x
Semenov [28]
The answer (i think) is 3 <span>≥</span> x. hope i helped
7 0
3 years ago
You don't have to answer if you don't want to lol, but you just gotta simplify.
saveliy_v [14]

Answer:

question 8 is 178cmcubed I think

4 0
2 years ago
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Solve the system of equations. y=23x–19 x2–y= – 6x–23 Write the coordinates as integers, simplified proper or improper fractions
forsale [732]

Answer:

(3, 50) and (14,303)

Step-by-step explanation:

Given the system of equations;

y=23x–19 ....1

x²–y= – 6x–23 ...2

Substitute 1 into 2;

x²–(23x-19)= – 6x–23

x²–23x+19= – 6x–23 .

x²-23x + 6x + 19 + 23  = 0

x² - 17x + 42 = 0

Factorize;

x² - 14x - 3x + 42 = 0

x(x-14)-3(x-14) = 0

(x-3)(x-14) = 0

x = 3 and 14

If x = 3

y = 23(3) - 19

y = 69-19

y = 50

If x = 14

y = 23(14) - 19

y = 322-19

y = 303

Hence the coordinate solutions are (3, 50) and (14,303)

8 0
3 years ago
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