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4 years ago

5

Use the gradient to find the directional derivative of the function at p in the direction of q. f(x, y) = 3x2 - y2 + 4, p(7, 1),

q(8, 8)

1 answer:

Fittoniya [83]4 years ago

5 0

Try this solution (attachment).Answer: 21

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valina [46]

Answer:

$(10, 0)$

Step-by-step explanation:

Let's try all the options:

$\left \{ {{2x + y = 20} \atop {4x-2y = 40} \right.$

Considering $(10, 0)$ :

$$\left \{ {{2(10) + 0 = 20} \atop {4(10)-2(0) = 40} \right. $\\$

$\left \{ {{20 + 0 = 20} \atop {40-0 = 40} \right.$

$\left \{ {{20= 20} \atop {40 = 40} \right.$

Considering $(0, 10)$ :

$$\left \{ {{2(0) + 10 = 20} \atop {4(0)-2(10) = 40} \right. $\\$

$\left \{ {{0 + 10 = 20} \atop {0-20 = 40} \right.$

$\left \{ {{10= 20} \atop {-20 = 40} \right.$

$\left \{ {{10\neq 20} \atop {-20 \neq 40} \right.$

Considering $(4, 2)$ :

$$\left \{ {{2(4) + 2 = 20} \atop {4(4)-2(2) = 40} \right. $\\$

$\left \{ {{8 + 2 = 20} \atop {8-4 = 40} \right.$

$\left \{ {{10= 20} \atop {4 = 40} \right.$

$\left \{ {{10\neq 20} \atop {4 \neq 40} \right.$

Considering $(10, -10)$ :

$$\left \{ {{2(10) -10 = 20} \atop {4(10)-2(-10) = 40} \right. $\\$

$\left \{ {{20 -10 = 20} \atop {40+20 = 40} \right.$

$\left \{ {{10= 20} \atop {60 = 40} \right.$

$\left \{ {{10\neq 20} \atop {60 \neq 40} \right.$

7 0

3 years ago

A total of $6000 was invested, part of it at 3% interest and the remainder at 8%. If the total yearly interest amounted to $380,

Nastasia [14]

$ 2000 is invested at 3 % interest and $ 4000 is invested at 8 % interest

<em><u>Solution:</u></em>

Given that, total of $6000 was invested

Let "x" be the amount invested at 3 % interest

Then, (6000 - x) is the amount invested at 8 % interest

Given that,

<em><u>The total yearly interest amounted to $380</u></em>

Then, we can frame a equation as:

$x \times 3 \% + (6000 - x) \times 8 \% = 380$

<em><u>Solve the above expression for "x"</u></em>

$x \times \frac{3}{100} + (6000-x) \times \frac{8}{100} = 380\\\\0.03x + (6000-x) \times 0.08 = 380\\\\0.03x + 480 - 0.08x = 380\\\\-0.05x = -100\\\\\text{Divide both sides by -0.05 }\\\\x = 2000$

Thus, $ 2000 is invested at 3 % interest

(6000 - x) = 6000 - 2000 = 4000

$ 4000 is invested at 8 % interest

4 0

4 years ago

Multiple choice. help ty

ki77a [65]

Answer:

Option B) is incorrect

Step-by-step explanation:

Looking at the graph the following points are to be noted.

<em>1) the graph has one maximum and one minimum within the interval.</em>

<em>2)the maximum value is attained at x=8, f(x) = 70</em>

<em>3)The least minimum value attained is at x=0, f(x) = -18</em>

<em>4) the y intercept is attained at x=0, f(x) = -18 ( thus option A is correct)</em>

as the graph decreases then increases within(3,6) and increases then decreases within (1,3) , so options A and D are correct.

And from above option B is wrong

7 0

3 years ago

Read 2 more answers

Solve for e. 5e=45 What is the value of e?

Mice21 [21]

Step-by-step explanation:

Given

5e = 45

e = 45 / 5

e = 9

Hope it will help :)

5 0

3 years ago

Steve took a 300 mile business trip and decided to travel by car. He drove the speed limit for half the trip until an accident o

svetoff [14.1K]

Answer:

He traveled for 2.5 hrs at 54 mi/hr

He traveled for 3 hrs at 61 mi/hr

------------------------------

check:

(1) +d+=+54t+

(1) +d+=+54%2A2.5+

(1) +d+=+135+ mi

3 0

3 years ago