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2 years ago

Solve the equation for x. Write your answers as fractions. x^2 = 49/100 The solutions to the equation areand?

Mathematics

1 answer:

exis [7]2 years ago

4 0

Answer:

Step-by-step explanation:

x^2 = (49/100)

x = (7/10) and -(7/10)

If x = (7/10), then x^2 = 49/100

If x = -(7/10), then x^2 = 49/100

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How do I simplify (6^-2)(3^-3)(3 x 6)^4? Not the answer, just the simplified expression.

Mazyrski [523]

The simplification form of the provided expression is 108 after applying the integer exponent properties.

<h3>What is integer exponent?</h3>

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

We have an expression:

$=\left(6^{-2}\right)\left(3^{-3}\right)\left(3\:\cdot \:6\right)^4$

$=\dfrac{1}{36}\cdot \dfrac{1}{27}\left(3\cdot \:6\right)^4$

$=\dfrac{1}{36}\cdot \dfrac{1}{27}\cdot \:81\cdot \:1296$

$=\dfrac{1}{36}\cdot \dfrac{1}{27}\cdot \dfrac{104976}{1}$

$=\dfrac{104976}{972}$

= 108

Thus, the simplification form of the provided expression is 108 after applying the integer exponent properties.

Learn more about the integer exponent here:

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5 0

2 years ago

For each of the following vector fields

olga nikolaevna [1]

(A)

$\dfrac{\partial f}{\partial x}=-16x+2y$

$\implies f(x,y)=-8x^2+2xy+g(y)$

$\implies\dfrac{\partial f}{\partial y}=2x+\dfrac{\mathrm dg}{\mathrm dy}=2x+10y$

$\implies\dfrac{\mathrm dg}{\mathrm dy}=10y$

$\implies g(y)=5y^2+C$

$\implies f(x,y)=\boxed{-8x^2+2xy+5y^2+C}$

(B)

$\dfrac{\partial f}{\partial x}=-8y$

$\implies f(x,y)=-8xy+g(y)$

$\implies\dfrac{\partial f}{\partial y}=-8x+\dfrac{\mathrm dg}{\mathrm dy}=-7x$

$\implies \dfrac{\mathrm dg}{\mathrm dy}=x$

But we assume $g(y)$ is a function of $y$ alone, so there is not potential function here.

(C)

$\dfrac{\partial f}{\partial x}=-8\sin y$

$\implies f(x,y)=-8x\sin y+g(x,y)$

$\implies\dfrac{\partial f}{\partial y}=-8x\cos y+\dfrac{\mathrm dg}{\mathrm dy}=4y-8x\cos y$

$\implies\dfrac{\mathrm dg}{\mathrm dy}=4y$

$\implies g(y)=2y^2+C$

$\implies f(x,y)=\boxed{-8x\sin y+2y^2+C}$

For (A) and (C), we have $f(0,0)=0$ , which makes $C=0$ for both.

4 0

3 years ago

NEED HELP ASAP! MY GRADES ARE ON THE LINE

kumpel [21]

Answer:

2. and 4.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

One vegetable warehouse had 210 tons of potatoes, another one had 180 tons. 90 tons of potatoes were delivered to the first and

kow [346]

Answer:

The number of days in which the amount in warehouse #2 is 1.2 greater than warehouse #1 is 6 days.

Step-by-step explanation:

Let

x: number of days

y: amount of potatoes

We can express the amount of potatoes in each warehouse using linear equations:

Warehouse #1: $y_1 = 90x+210$

Warehouse #2: $y_2 = 120x+180$

We need to find the value of x when $1.2*y_{1} =y_{2}$

Substituting the expressions for y1 and y2 in $1.2*y_{1} =y_{2}$ :

$1.2*(90x+210) =120x+180$

Applying distributive law:

$108x+252 =120x+180$

Solving the equation by subtracting 108x and 180 on both sides:

$108x+252-108x-180 =120x+180-108x-180$

$252-180 =120x-108x$

$72 =12x$

Now we divide by 12 on both sides:

$\frac{72}{12} =\frac{12x}{12}\\6=x\\x=6$

Therefore, the number of days in which the amount in warehouse #2 is 1.2 greater than warehouse #1 is 6 days.

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3 years ago

The bacteria in a jar triple every 20 seconds. after three minutes, there are 275,562 bacteria in the jar. how many were in the

Lilit [14]

I believe this is correct

7 0

3 years ago

Solve the equation for x. Write your answers as fractions. x^2 = 49/100 The solutions to the equation are____and____?

Solve the equation for x. Write your answers as fractions. x^2 = 49/100 The solutions to the equation areand?