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3 years ago

Use thr Pythagorean theorem to find perimeter. What is the perimeter of the triangle??

Mathematics

1 answer:

kramer3 years ago

4 0

The base is 12cm and the height is 9cm.
b= 12cm
h=9cm

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If two 12-sided dice are rolled, what is the probability that both numbers will be even?

geniusboy [140]

1/4 I think, I’m not sure

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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

3 years ago

Find the function. f(-7) if f(x) = 8x+15 f(-7) = -4? 7 0

docker41 [41]

Answer:

-41.

Step-by-step explanation:

Replace the x by -7:

f(-7) = 8(-7) + 15

= -56 + 15

= -41.

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3 years ago

The larger the standard deviation is for a data set, the more variable the data in the set are. True or false?

erik [133]

True.

If the standard deviation value is larger, it means the data points are further away from the mean - which indicates that the data in the set are more variable.

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4 years ago

WILL MAKR BRAINLIEST IF GOTTEN RIGHT

Naya [18.7K]

Answer:

hmm give me more so I can answer it

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3 years ago

Read 2 more answers

Use thr Pythagorean theorem to find perimeter. What is the perimeter of the triangle??​

Use thr Pythagorean theorem to find perimeter. What is the perimeter of the triangle??