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2 years ago

Simplify (2/3)^2∙81 please explain 2

Mathematics

1 answer:

SVETLANKA909090 [29]2 years ago

8 0

Answer:

Step-by-step explanation:

Simplify the following:

(2/3)^2 81

Hint: | Simplify (2/3)^2 using the rule (p/q)^n = p^n/q^n.

(2/3)^2 = 2^2/3^2:

2^2/3^2 81

Hint: | Evaluate 2^2.

2^2 = 4:

4/3^2 81

Hint: | Evaluate 3^2.

3^2 = 9:

4/9×81

Hint: | Express 4/9×81 as a single fraction.

4/9×81 = (4×81)/9:

(4×81)/9

Hint: | In (4×81)/9, divide 81 in the numerator by 9 in the denominator.

81/9 = (9×9)/9 = 9:

4×9

Hint: | Multiply 4 and 9 together.

4×9 = 36:

Answer: 36

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Are both a function or not ?

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Answer:

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Step-by-step explanation:

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1 year ago

Evaluate the integral Integral ∫ from (1,2,3 ) to (5, 7,-2 ) y dx + x dy + 4 dz by finding parametric equations for the line seg

n200080 [17]

$\vec F(x,y,z)=y\,\vec\imath+x\,\vec\jmath+3\,\vec k$

is conservative if there is a scalar function $f(x,y,z)$ such that $\nabla f=\vec F$ . This would require

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

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

$\dfrac{\partial f}{\partial z}=3$

(or perhaps the last partial derivative should be 4 to match up with the integral?)

From these equations we find

$f(x,y,z)=xy+g(y,z)$

$\dfrac{\partial f}{\partial y}=x=x+\dfrac{\partial g}{\partial y}\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)$

$f(x,y,z)=xy+h(z)$

$\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=3z+C$

$f(x,y,z)=xy+3z+C$

so $\vec F$ is indeed conservative, and the gradient theorem (a.k.a. fundamental theorem of calculus for line integrals) applies. The value of the line integral depends only the endpoints:

$\displaystyle\int_{(1,2,3)}^{(5,7,-2)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz=\int_{(1,2,3)}^{(5,7,-2)}\nabla f(x,y,z)\cdot\mathrm d\vec r$

$=f(5,7,-2)-f(1,2,3)=\boxed{18}$

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2 years ago

Brainly trash finish your own homework by yourself

Gennadij [26K]

Answer:

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2 years ago

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Solve the inequality for u. 22≤-4u-2 Simplify your answer as much as possible.

larisa [96]

Answer:

u ≤ -6

Step-by-step explanation:

Given :

22 ≤ -4u - 2

Add 2 on both sides :

22 + 2 ≤ -4u - 2 + 2
-4u ≥ 24

Divide both sides by -4 (remember the sign changes direction when divided by a negative number) :

-4u/-4 ≥ 24/-4
u ≤ -6

7 0

1 year ago

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The architects side view drawing of a saltbox-style house shows a post that supports the roof ridge. The support post is 10 ft t

pochemuha

These calculations are based on the drawing of the file enclosed.

There are three right triangles.

From the big right triangle:

a^2 + b^2 = 25^2

From the small right triangle on the left side:

(25-x)^2 + 10^2 = a^2

From the small right triangle on the right side

x^2 +10^2 = b^2

=> (25-x)^2 + 10^2 + x^2 + 10^2 = a^2 + b^2

=> (25-x)^2 + 10^2 + x^2 + 10^2 = 25^2

=> 25^2 - 50x + x^2 + 10^2 + 10^2 = 25^2

=> x^2 -50x + 100 =0

Use the quadratic formular to find the roots:

x = 2.1 and x = 47.9

Distance from back: 25 - 2.1 = 22.9 ft

Answer: 22.9 ft

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3 years ago

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