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3 years ago

8

You have a pickle recipe that requires 3 ounces of sugar. You want to make a triple batch of pickles. How much sugar do you need

for the triple batch?

1 answer:

White raven [17]3 years ago

7 0

9 ounces of sugar needed

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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

2 years ago

What is the quotient of -8x^6/4x^-3 ?<br><br> A. x^9/32<br> B. 4x^9<br> C. -12/x^2<br> D. -2x^9

natka813 [3]

I believe the answer to the question is D.

5 0

3 years ago

Read 2 more answers

I need this please help

rjkz [21]

Answer:

a) sine
b) 9.8 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA helps you remember the definitions of the trig functions. In particular, the function that involves the Opposite side and the Hypotenuse is the Sine function:

... Sin = Opposite/Hypotenuse

In this problem that means ...

... sin(55°) = x/(12 ft)

Multiplying by 12 ft, we have ...

... (12 ft)·sin(55°) = x ≈ 9.82982 ft ≈ 9.8 ft

7 0

2 years ago

PLEASE help me with the answers!!!

jasenka [17]

100=1,478,300
1000=1,478,000
10,000=1,470,000

5 0

3 years ago

Read 2 more answers

What equation has a solution of 2/3 for x

Ahat [919]

Answer:

D

Step-by-step explanation:

Hope this helped! Please tell me if I'm wrong!

6 0

2 years ago