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LiRa [457]
3 years ago
13

Which equation could be used to solve the problem? Joan picked 4 bushels of apples in one hour. At that rate, how many bushels w

ould she pick in 8 hours (b)? * A. b = 8 + 4 B. b = 8 • 4C. b = 4 ÷ 8 D. b = 8 ÷ 4
Mathematics
1 answer:
jeka943 years ago
3 0
Hello!

Unit rates can be written as ratios. In this case, we have 4 bushels in one hour, or 4:1. In eight hours, we can multiply like a fraction, multiplying both by eight to get eight hours.

Our final answer is B) 8·4.

I hope this helps!
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Compute the directional derivative of the following function at the given point P in the direction of the given vector. Be sure
borishaifa [10]

Answer:

The directional derivate is given by: D_{u}(x,y) = \frac{6}{\ln{17}\sqrt{10}}

Step-by-step explanation:

The directional derivative at point (x,y) is given by:

D_{u}(x,y) = f_{x}(x,y)*a + f_{y}(x,y)*b

In which a is the x component of the unit vector and b is the y component of the unit vector.

Vector:

We are given the following vector: v = (3,1)

Its modulus is given by: \sqrt{3^2 + 1^2} = \sqrt{10}

The unit vector is given by each component divided by it's modulus. So

v_u = (\frac{3}{\sqrt{10}}, \frac{1}{\sqrt{10}})

This means that a = \frac{3}{\sqrt{10}}, b = \frac{1}{\sqrt{10}}

Partial derivatives:

f(x,y) = \ln{(2 + 3x^2 + 3y^2)}

So

f_x(x,y) = \frac{6x}{\ln{(2 + 3x^2 + 3y^2)}}

f_x(1,-2) = \frac{6(1)}{\ln{(2 + 3(1)^2 + 3(-2)^2)}} = \frac{6}{\ln{17}}

f_y(x,y) = \frac{6y}{\ln{(2 + 3x^2 + 3y^2)}}

f_y(1,-2) = \frac{6(-2)}{\ln{(2 + 3(1)^2 + 3(-2)^2)}} = -\frac{12}{\ln{17}}

Directional derivative:

D_{u}(x,y) = f_{x}(x,y)*a + f_{y}(x,y)*b

D_{u}(x,y) = \frac{6}{\ln{17}}\times\frac{3}{\sqrt{10}}-\frac{12}{\ln{17}}\times\frac{1}{\sqrt{10}}

D_{u}(x,y) = \frac{18}{\ln{17}\sqrt{10}} - \frac{12}{\ln{17}\sqrt{10}}[tex][tex]D_{u}(x,y) = \frac{6}{\ln{17}\sqrt{10}}

The directional derivate is given by: D_{u}(x,y) = \frac{6}{\ln{17}\sqrt{10}}

8 0
3 years ago
Order <br> 2.32, 2 1/3, 224%, 254%, 2 2/5<br><br><br> From least to greatest.
Kobotan [32]
2.32, 2 1/3, 2 2/5, 224, 254
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HELP PLSS QUICKLY!!!!
tigry1 [53]
3 cans!!!

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Answer:

x=−8 and y=−4

Step-by-step explanation:

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add eqn1 and 2

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x=-8

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