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2 years ago

What is the slope of a line perpendicular to the line whose equation is x+ 3y = -15 Fully simplify your answer.

Mathematics

1 answer:

alukav5142 [94]2 years ago

3 0

Answer:

Step-by-step explanation:

We can find the slope of the given line in this two way:

1) the faster is calculate -a/b where a is the number the multiply x and b is the number the multiply y. In this case we have -1/3

2) the second method is rewrite the equation in slope intercept form and find the therm that multiply x

3y = -x-15

y = -1/3x - 5

Also in this case we have -1/3

Two perpendicular lines have the the product of the their slope that is -1

So the slope that we are finding is 3

In fact = 3 x -1/3 = -1

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12.7 centimeters is times big as 2.54 centimeters

lapo4ka [179]

Answer:

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2 years ago

What is the output value for the following function if the input value is 3.2?

mars1129 [50]

For functions, there is only many input values, but there can be only one output value, and there can be no identical x values. For this, x=3.2. If y= 2*3.2 - 1, then y=5.4.

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3 years ago

Water is flowing into and out of two vats, Vat A and Vat B. The amount of water, in gallons, in Vat A at time t hours is given b

svetoff [14.1K]

Note: The first file attached contains the clear and complete question

Answer:

a) The times at which the graph of A(t) has horizontal tangent are t = 1 and t = 7

A(t) has a local maximum at t=7

A(t) has a local minimum at t=1

b) The times at which the graph of D(t) has horizontal tangent are t = 1.59 and t = 7.74

D(t) has a local maximum at t=1.59

D(t) has a local minimum at t=7.74

c) A(t) = (-t^3) + 8(t^2) -21t + 40

d) The water level in vat A is rising most rapidly at t = 4 hrs

e) 138 gallons

f) 18 gallons per hour

g) 98 gallons

Step-by-step explanation:

For clarity and easiness of expression, the calculations are handwritten and attached as files below.

Each step is neatly expressed and solutions to each part of the question are clearly written

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 <em>directional</em> 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 <em>directional</em> 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 <em>partial</em> 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 <em>directional</em> 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

an experiment consists of rolling a six sided die to select a number between 1 and 6 and drawing a card at random from a set of

dsp73

probabiltity is

outcome/total possible outcomes

hence probability is 1/6×10= 1/60

4 0

3 years ago