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3 years ago

5

Daniel is using apple juice to make juice pops. He has 3 cups of juice, and each juice pop uses 1/2 of a cup of juice. How many

juice pops can he make.

1 answer:

Gennadij [26K]3 years ago

6 0

Answer:

6

Step-by-step explanation:

2 halves make a whole so multiply 2 by 3. the answer is six. you can also add the halves. 1/2+1/2+1/2+1/2+1/2+1/2=3.

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3 years ago

How do the expressions 8+k2−6 and 8(k+2)−4k compare when k = 7?

Andreas93 [3]

Answer:

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Step-by-step explanation:

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2 years ago

Find the directional derivative of f(x,y,z)=2z2x+y3f(x,y,z)=2z2x+y3 at the point (−1,4,3)(−1,4,3) in the direction of the vector

Feliz [49]

$f(x,y,z)=2z^2x+y^3$

$f$ has gradient

$\nabla f(x,y,z)=2z^2\,\vec\imath+3y^2\,\vec\jmath+4xz\,\vec k$

which at the point (-1, 4, 3) has a value of

$\nabla f(-1,4,3)=18\,\vec\imath+48\,\vec\jmath-12\,\vec k$

I'm not sure what the given direction vector is supposed to be, but my best guess is that it's intended to say $\vec u=15\,\vec\imath+25\,\vec\jmath$ , in which case we have

$\|\vec u\|=\sqrt{15^2+25^2}=5\sqrt{34}$

Then the derivative of $f$ at (-1, 4, 3) in the direction of $\vec u$ is

$D_{\vec u}f(-1,4,3)=\nabla f(-1,4,3)\cdot\dfrac{\vec u}{\|\vec u\|}=\boxed{\dfrac{294}{\sqrt{34}}}$

4 0

3 years ago