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2 years ago

Select the correct solution set. X + 17<-3

Mathematics

1 answer:

madam [21]2 years ago

8 0

Answer:

you didn't add the solution sets

Step-by-step explanation:

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a parallelogram has one side that is 4 centimeters long and one side that is 6 centimeters long. what is the perimeter of the pa

Ilia_Sergeevich [38]

Answer:

P = 20 cm

Step-by-step explanation:

The appropriate formula is P = 2W + 2L.

Here that comes to P = 2(6 cm) + 2(4 cm) = 20 cm

6 0

3 years ago

Find the directional derivative of the function at the given point in the direction of the vector v. G(r, s) = tan−1(rs), (1, 3)

alexandr1967 [171]

The directional derivative of $f$ at the given point in the direction indicated is $\frac{5}{2}$ .

<h3>How to calculate the directional derivative of a multivariate function</h3>

The directional derivative is represented by the following formula:

$\nabla_{\vec v} f = \nabla f (r_{o}, s_{o})\cdot \vec v$ (1)

Where:

$\nabla f (r_{o}, s_{o})$ - Gradient evaluated at the point $(r_{o}, s_{o})$ .
$\vec v$ - Directional vector.

The gradient of $f$ is calculated below:

$\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{\partial f}{\partial r}(r_{o},s_{o}) \\\frac{\partial f}{\partial s}(r_{o},s_{o}) \end{array}\right]$ (2)

Where $\frac{\partial f}{\partial r}$ and $\frac{\partial f}{\partial s}$ are the partial derivatives with respect to $r$ and $s$ , respectively.

If we know that $(r_{o}, s_{o}) = (1, 3)$ , then the gradient is:

$\nabla f(r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{s}{1+r^{2}\cdot s^{2}} \\\frac{r}{1+r^{2}\cdot s^{2}}\end{array}\right]$

$\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{3}{1+1^{2}\cdot 3^{2}} \\\frac{1}{1+1^{2}\cdot 3^{2}} \end{array}\right]$

$\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{3}{10} \\\frac{1}{10} \end{array}\right]$

If we know that $\vec v = 5\,\hat{i} + 10\,\hat{j}$ , then the directional derivative is:

$\nabla_{\vec v} f = \left[\begin{array}{cc}\frac{3}{10} \\\frac{1}{10} \end{array}\right] \cdot \left[\begin{array}{cc}5\\10\end{array}\right]$

$\nabla _{\vec v} f (r_{o}, s_{o}) = \frac{5}{2}$

The directional derivative of $f$ at the given point in the direction indicated is $\frac{5}{2}$ . $\blacksquare$

To learn more on directional derivative, we kindly invite to check this verified question: brainly.com/question/9964491

3 0

2 years ago

You want to wrap a gift shaped like the regular triangular prism shown. How many

kotegsom [21]

Answer:

$697.6 \ in^2$

Step-by-step explanation:

-Given the dimensions of the box is 8.7 in, 14 in and 10 in.

Let length=14 in, width=10 in and height =8.7 in

#The surface area of a rectangular prism is calculated as:

$Surface \ Area=2(wl+hl+hw)\\\\l=length, w=width, h=height\\\\\therefore Surface \ Area=2(14\times 10+10\times 8.7+14\times 8.7)\\\\=697.6 \ in^2$

Hence, the wrapping paper needed has an area of $697.6 \ in^2$

8 0

3 years ago

Graph the function f(x)=|x+1|+2

11111nata11111 [884]

Answer:

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Hope this helps!

3 0

3 years ago

Share £1000 in the ratio of 3 : 2

Delvig [45]

Answer:

$3 : 2 \\ £600 : £400$

Step-by-step explanation:

Total shares = 3+2 = 5

$\frac{1000}{5} = 200$

7 0

2 years ago