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alina1380 [7]
3 years ago
8

Please help exponents and scientific notation

Mathematics
1 answer:
Anna007 [38]3 years ago
6 0
Alright! When you have a constant to a power times another constant to a power (ex. [x^3 times x^3] ) you simply add the powers and keep the base [x^6]. When you have a power to a power (ex. [(12^3)^3] ) you multiply the powers and keep the base [12^9]. When you have a constant to a power divided by a constant to a power (ex. [ x^2 divided by x^5] ) you subtract the powers and keep the base. It's hard to see the questions, so I'll leave this here for you to use as a guide.
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I need help ASAP please
RSB [31]

Answer:

5:10

6 (-2,0)

7 (-5,6)

8 (5,3)

9 No, ab=8 CD=6

Step-by-step explanation:

4 0
3 years ago
Solve solve the following equations 2x (x minus 5) close + 3(x-2)=8+7(x-4)​
stiv31 [10]

Step-by-step explanation:

<em>2</em><em>x</em><em>(</em><em>x-5</em><em>)</em><em>+</em><em>3</em><em>(</em><em>x-2</em><em>)</em><em>=</em><em>8</em><em>+</em><em>7</em><em>(</em><em>x-4</em><em>)</em>

<em>2</em><em>x</em><em>²</em><em>-10x</em><em>+</em><em>3</em><em>x</em><em>-</em><em>6</em><em>=</em><em>8</em><em>+</em><em>7</em><em>x</em><em>-</em><em>2</em><em>8</em><em>(</em><em>Group</em><em> </em><em>like</em><em> </em><em>terms</em><em>)</em>

<em>2</em><em>x</em><em>²</em><em>-</em><em>1</em><em>0</em><em>x</em><em>+</em><em>3</em><em>x</em><em>-</em><em>7</em><em>x</em><em>=</em><em>8</em><em>-</em><em>2</em><em>8</em><em>+</em><em>6</em>

<em>2</em><em>x</em><em>²</em><em>-</em><em>7</em><em>x</em><em>-</em><em>7</em><em>x</em><em>=</em><em>-</em><em>2</em><em>0</em><em>+</em><em>6</em>

<em>2</em><em>x</em><em>²</em><em>-</em><em>1</em><em>4</em><em>x</em><em>=</em><em>-</em><em>1</em><em>4</em><em>(</em><em>Divi</em><em>de</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em><em>by</em><em> </em><em>-</em><em>1</em><em>4</em><em>)</em>

2x²<em>-</em><em>x</em><em>=</em><em>1</em>

<em>2</em><em>x</em><em>=</em><em>1</em>

<em>x</em><em>=</em><em>½</em>

<em>Hope</em><em> </em><em>you </em><em>get</em><em> </em><em>it</em><em> </em><em>please</em><em> </em><em>someone</em><em> </em><em>shou</em><em>ld</em><em> </em><em>verify</em><em>.</em><em>.</em><em>.</em><em>.</em>

7 0
2 years ago
. Use Lagrange multipliers to find the maximum and minimum values of the function, f, subject to the given constraint, g. (Place
zzz [600]

Answer:

Minimum value of f(x, y, z) = (1/3)

Step-by-step explanation:

f(x, y, z) = x⁴ + y⁴ + z⁴

We're to maximize and minimize this function subject to the constraint that

g(x, y, z) = x² + y² + z² = 1

The constraint can be rewritten as

x² + y² + z² - 1 = 0

Using Lagrange multiplier, we then write the equation in Lagrange form

Lagrange function = Function - λ(constraint)

where λ = Lagrange factor, which can be a function of x, y and z

L(x,y,z) = x⁴ + y⁴ + z⁴ - λ(x² + y² + z² - 1)

We then take the partial derivatives of the Lagrange function with respect to x, y, z and λ. Because these are turning points, each of the partial derivatives is equal to 0.

(∂L/∂x) = 4x³ - λx = 0

λ = 4x² (eqn 1)

(∂L/∂y) = 4y³ - λy = 0

λ = 4y² (eqn 2)

(∂L/∂z) = 4z³ - λz = 0

λ = 4z² (eqn 3)

(∂L/∂λ) = x² + y² + z² - 1 = 0 (eqn 4)

We can then equate the values of λ from the first 3 partial derivatives and solve for the values of x, y and z

4x² = 4y²

4x² - 4y² = 0

(2x - 2y)(2x + 2y) = 0

x = y or x = -y

Also,

4x² = 4z²

4x² - 4z² = 0

(2x - 2z) (2x + 2z) = 0

x = z or x = -z

when x = y, x = z

when x = -y, x = -z

Hence, at the point where the box has maximum and minimal area,

x = y = z

And

x = -y = -z

Putting these into the constraint equation or the solution of the fourth partial derivative,

x² + y² + z² = 1

x = y = z

x² + x² + x² = 1

3x² = 1

x = √(1/3)

x = y = z = √(1/3)

when x = -y = -z

x² + y² + z² = 1

x² + x² + x² = 1

3x² = 1

x = √(1/3)

y = z = -√(1/3)

Inserting these into the function f(x,y,z)

f(x, y, z) = x⁴ + y⁴ + z⁴

We know that the two types of answers for x, y and z both resulting the same quantity

√(1/3)

f(x, y, z) = x⁴ + y⁴ + z⁴

f(x, y, z) = (√(1/3)⁴ + (√(1/3)⁴ + (√(1/3)⁴

f(x, y, z) = 3 × (1/9) = (1/3).

We know this point is a minimum point because when the values of x, y and z at turning points are inserted into the second derivatives, all the answers are positive! Indicating that this points obtained are

S = (1/3)

Hope this Helps!!!

6 0
3 years ago
He nine ring wraiths want to fly from barad-dur to rivendell. rivendell is directly north of barad-dur. the dark tower reports t
kiruha [24]

This problem is better understood with a given figure. Assuming that the flight is in a perfect northwest direction such that the angle is 45°, therefore I believe I have the correct figure to simulate the situation (see attached).

 

Now we are asked to find for the value of the hypotenuse (flight speed) given the angle and the side opposite to the angle. In this case, we use the sin function:

sin θ = opposite side / hypotenuse

sin 45 = 68 miles per hr / flight

flight = 68 miles per hr / sin 45

<span>flight = 96.17 miles per hr</span>

6 0
3 years ago
HEY GUYS I NEED HELP ASAP PLZZ! 20 points to the person who can give me the right answer first!!
Ivanshal [37]

Answer:

28 inches of the board

3 0
3 years ago
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