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expeople1 [14]
3 years ago
9

If z = f(x, y), where f is differentiable, and x = g(t) y = h(t) g(9) = 6 h(9) = 4 g' (9) = −6 h' (9) = 4 fx(6, 4) = 9 fy(6, 4)

= 1 find dz/dt when t = 9.
Mathematics
1 answer:
horsena [70]3 years ago
6 0

Answer:

dz / dt = -50

Step-by-step explanation:

To solve the chain rule must apply, we have all the necessary values to make the calculation, as follows:

using the chain rule, we find:

dz / dt = (∂z / ∂x) * (∂x / ∂t) + (∂z / ∂y) * (∂y / ∂t)

Evaluating when t = 9, we have to:

fx (6, 4) * g '(9) + fy (6, 4) * h '(9)

We know that g '(9) = −6; h '(9) = 4; fx (6, 4) = 9; fy (6, 4) = 1

Replacing:

(9 * -6) + (1 * 4) = -50

Por lo tanto dz / dt = -50

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4 0
2 years ago
Solve the following absolute value equations. Show the solution set and check your answers. |0.3-3/5k|-0.4=1.2
9966 [12]

Answer:

**The equation is not clear, so I have provided both options**

<h3><u>Option 1</u></h3>

\left|0.3-\dfrac{3}{5}k\right|-0.4=1.2

\implies \left|0.3-\dfrac{3}{5}k\right|=1.6

<u>Solution 1</u>

\implies 0.3-\dfrac{3}{5}k=1.6

\implies -\dfrac{3}{5}k=1.3

\implies k=-\dfrac{13}{6}

<u>Solution 2</u>

\implies -(0.3-\dfrac{3}{5}k)=1.6

\implies -0.3+\dfrac{3}{5}k=1.6

\implies \dfrac{3}{5}k=1.9

\implies k=\dfrac{19}{6}

<h3><u>Option 2</u></h3>

\left|0.3-\dfrac{3}{5k}\right|-0.4=1.2

\implies \left|0.3-\dfrac{3}{5k}\right|=1.6

<u>Solution 1</u>

\implies 0.3-\dfrac{3}{5k}=1.6

\implies -\dfrac{3}{5k}=1.3

\implies -3=6.5k

\implies k=-\dfrac{6}{13}

<u>Solution 2</u>

\implies -(0.3-\dfrac{3}{5k})=1.6

\implies -0.3+\dfrac{3}{5k}=1.6

\implies \dfrac{3}{5k}=1.9

\implies 3=9.5k

\implies k=\dfrac{6}{19}

6 0
2 years ago
One sample has Aa Aa One sample has n 10 scores and a variance of s2 20, and a second sample has n 15 scores and a variance of s
siniylev [52]

Answer:

option (a) It will be closer to 30 than to 20

Step-by-step explanation:

Data provided in the question:

For sample 1:

n₁ = 10

variance, s₁² = 20

For sample 2:

n₂ = 15

variance, s₂² = 30

Now,

The pooled variance is calculated using the formula,

S^{2}_{p} = \frac{(n_{1}-1)\times s^{2}_{1} +(n_{2}-1)\times s^{2}_{2}}{n_{1}+n_{2}-2}

on substituting the given respective values, we get

S^{2}_{p} = \frac{(10-1)\times 20 +(15-1)\times 30}{10+15-2}

or

S^{2}_{p} = 26.0869

Hence,

the pooled variance will be closer to 30 than to 20

Therefore,

The correct answer is option (a) It will be closer to 30 than to 20

4 0
3 years ago
Kianna lives in a town where the streets are laid out in a grid. She uses a coordinate plane to draw a map of the town, with her
Dmitrij [34]

Answer:

1. The coordinates of Jo’s house are (-4,-2).

2. Kianna walks 8 blocks west, and 2 blocks south.

3. The coordinates of Elena’s house are (4,-2).

4. Kianna is incorrect.

Step-by-step explanation:

1. Since Jo’s house is reflected across both axes, we must reflect the coordinates two times. So we can reflect the coordinates of Kianna’s house across the x-axis first, which would give you the coordinates (4,-2). Then we reflect (4,-2) across the y axis, giving us the coordinates (-4,-2). So Jo’s house has the coordinates (-4,-2).

3. Since Elena’s house is only a reflection of Jo’s house across the x-axis only,  we can reflect Kianna’s house’s coordinates (4,2). When we reflect (4.2) over the x-axis, that gives us the coordinates (4,-2). So therefore Elena’s house has the coordinates (4,-2).

4. Kianna is incorrect, if Elena’s house was a reflection of her house across the y-axis, the coordinates would be (-4,2).

(A reflection can be thought of as folding or "flipping" an object over the line of reflection. The original object is called the pre-image, and the reflection is called the image.)

Hope this helps.

7 0
2 years ago
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(Assuming no deaths occur)

5 0
3 years ago
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