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2 years ago

The quotient of 7 more than three times a number m and the number 27 less than n

Mathematics

1 answer:

nalin [4]2 years ago

6 0

The given statement can be modeled as an algebraic expression (3m+7)/27 < n.

<h3>What is an Expression?</h3>

In mathematics, an expression is a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The statement is given as "The quotient of 7 more than three times a number m and the number 27 less than n" can be modeled as an algebraic expression.

(3m+7)/27 < n

Hence, the given statement can be modeled as an algebraic expression (3m+7)/27 < n.

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Consider F and C below. F(x, y) = x4y5i + x5y4j, C: r(t) = t3 − 2t, t3 + 2t , 0 ≤ t ≤ 1 (a) Find a function f such that F = ∇f.

vovikov84 [41]

$\mathbf f(x,y)=x^4y^5\,\mathbf i+x^5y^4\,\mathbf j$

We want a scalar function $f(x,y)$ whose gradient is equivalent to the vector field. That means

$\dfrac{\partial f}{\partial x}=x^4y^5\implies f(x,y)=\dfrac{x^5y^5}5+g(y)$
$\dfrac{\partial f}{\partial y}=x^5y^4\implies x^5y^4=x^5y^4+\dfrac{\mathrm dg}{\mathrm dy}$
$\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=C$

So (a)

$f(x,y)=\dfrac{x^5y^5}5+C$

which means (b)

$\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f(\mathbf r(1))-f(\mathbf r(0))=f(-1,3)-f(0,0)=-\dfrac{243}5-0=-\dfrac{243}5$

5 0

3 years ago

Find rate of change help show work.

sukhopar [10]

Answer:

rise/run = 2/-4 or it is rise/run = -2/4

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2 years ago

A 3

Andrew [12]

Answer:

There are (63) combinations. The notation means "six choose three". Out of six items (flavors) choose three.

(nk)=n!k!(n−k)!.

(63)=6!3!3!.

Think of it this way. There are 6 ways to choose a flavor. Once you choose, there are 5 ways to choose the next. After that, there are 4 flavors left. which is 6!/3!=6⋅5⋅4⋅3⋅2⋅13⋅2⋅1=6⋅5⋅4=120.

But, you could have chosen {chocolate,vanilla,strawberry} and you get the same combination as {vanilla, strawberry, chocolate} so we have to divide by 3!=3⋅2⋅1=6 to account for the order of choosing.

So the number of combinations of flavors is (63)=1206=20.

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7 0

2 years ago

PLZZZ HELP WILL GIVE BRAINN

Hatshy [7]

Answer:

Whole numbers: 56

Rational numbers: 1/3

Integer: -5

Irrational numbers: 1.17513698

Natural numbers: 0

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3 years ago

Please answer for me!

vekshin1

Part b is $638.40
Part c is $1,641.6

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3 years ago