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Whitepunk [10]
3 years ago
5

The sum of two numbers is 42, and one of the numbers is 5 times the other. Find the two numbers.

Mathematics
1 answer:
PolarNik [594]3 years ago
8 0

5x+x=42
6x=42
x=7
So the numbers are 7 and 35 (5*7)

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Which of these ordered pairs is a solution to the linear inequality 3y – 2x ≥ 8? (1, 3) (3, 1) (–4, 2) (2, –4)
MA_775_DIABLO [31]
The ordered pair is (-4,2)
7 0
2 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
velikii [3]

Answer:

The maximum value= 36

Minimum value = - 36

Step-by-step explanation:

Given that

f(x, y, z) = 8 x + 8 y + 4 z

h(x,y,z)=4 x² + 4 y² + 4 z² - 36

From Lagrange multipliers

Δf = λ Δh

Δf = < 8 ,8 , 4>

Δh = < 8 x ,8 y  , 8 z>

Δf = λ Δh

So

< 8 ,8 , 4> = < 8  λ x ,8 λ y  , 8 λ z>

8 = 8  λ x                     -------------1

8 = 8 λ y                      ----  ------2

4 = 8 λ z                    ----------------3

From equation 1 ,2 and 3

Now by putting the value of x,y and z in the following equation

4 x² + 4 y² + 4 z² = 36

4\times \dfrac{1}{\lambda^2 }+4\times \dfrac{1}{\lambda^2 }+4\times \dfrac{1}{(2\lambda)^2 }=36

\dfrac{4}{\lambda^2 }+ \dfrac{4}{\lambda^2 }+ \dfrac{1}{\lambda^2 }=36

So the value of λ is

\lambda =\pm \dfrac{1}{2}

When λ = 1/2

x = 1 / λ   , y=1 / λ   ,  z= 1 /2 λ

x= 2 , y = 2 , z=1

So

f(x, y, z) = 8 x + 8 y + 4 z

f(2, 2, 1) = 8 x 2 + 8 x 2 + 4 x 1

f(2, 2, 1) =36

When λ = - 1/2

x = 1 / λ   , y=1 / λ   ,  z= 1 /2 λ

x= - 2 , y = - 2 , z= - 1

So

f(x, y, z) = 8 x + 8 y + 4 z

f(-2, -2, -1) = 8 x (-2) + 8 x (-2) + 4 x (-1)

f(-2, -2, -1) = - 36

The maximum value= 36

Minimum value = - 36

7 0
3 years ago
Read 2 more answers
Ms. Lynch has 21 coins in nickels and dimes. Their total value is $1. 65. How many of each coin does she have? Please answer!!
timama [110]

Hi, there

<u>Question:Ms. Lynch has 21 coins in nickels and dimes. Their total value is $1. 65. How many of each coin does she have?</u>

Explanation:

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Answer 34.65

3 0
3 years ago
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Express 0.000216 in scientific notation
damaskus [11]
2.16 x 10 to the power of -4
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3 years ago
If a car drove 180 miles in 3 hours and a truck drove 150 miles in 2 hours, what is the speed (in miles per hour) of the faster
grigory [225]

Step-by-step explanation:

Divide 180 by 3 = 60

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The faster vehicle is truck and its speed is 75 mph

6 0
2 years ago
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