When the function f(x) = 5•2x is evaluated for x = 3, the output is:

Lisa has \dfrac{1}{3} 3 1 start fraction, 1, divided by, 3, end fraction of an hour to read and watch television. She wants to

ikadub [295]

Answer:

Lisa spends $\frac{1}{6}\ hrs$ in reading and $\frac{1}{6}\ hrs$ in watching television.

Step-by-step explanation:

Given:

Number of hours Lisa has = $\frac{1}{3}$

Now we need to find number of hours required to watch television and to read.

Given:

She splits her time equally between 2 activities.

Hence we can say;

Number of hours required to watch television and number of hours required to read both are half times equal to total number of hours.

Hence framing the equation we get;

Number of hours required to watch television = $\frac{1}{2} \times \textrm{Total Number of hours she has}$

Substituting the value we get;

Number of hours required to watch television = $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}\ hrs$

Number of hours required to read = $\frac{1}{2} \times \textrm{Total Number of hours she has}$

Substituting the values we get;

Number of hours required to read = $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}\ hrs$

Hence Lisa spends $\frac{1}{6}\ hrs$ in reading and $\frac{1}{6}\ hrs$ in watching television.

5 0

3 years ago

In a garden, 8 tulips were planted to every 9 dahlias. how many of each type of flower was planted if there were a total of 799

EastWind [94]

376 tulips and 423 Dahlias.
cause 8 times 47 is 376
And 9 times 47 is 423
And those answers together and you get 799

4 0

3 years ago

5 times 3 times 2 <br><br> show work

guajiro [1.7K]

Answer:

30

Step-by-step explanation:

5x3=p

px2 = a

5x3 = 15 x 2 = 30

8 0

3 years ago

Read 2 more answers

Need help ??????????????

lesantik [10]

Answer: the answer is the first one ,the third one , and the fourth

Step-by-step explanation:5x5 25

15x15 225

6 0

3 years ago

Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area that can be inscribed in the ell

Tanzania [10]

Answer:

Length (parallel to the x-axis): $2 \sqrt{2}$ ;

Height (parallel to the y-axis): $4\sqrt{2}$ .

Step-by-step explanation:

Let the top-right vertice of this rectangle $(x,y)$ . $x, y >0$ . The opposite vertice will be at $(-x, -y)$ . The length the rectangle will be $2x$ while its height will be $2y$ .

Function that needs to be maximized: $f(x, y) = (2x)(2y) = 4xy$ .

The rectangle is inscribed in the ellipse. As a result, all its vertices shall be on the ellipse. In other words, they should satisfy the equation for the ellipse. Hence that equation will be the equation for the constraint on x and y.

For Lagrange's Multipliers to work, the constraint shall be in the form: $g(x, y) =k$ . In this case

$\displaystyle g(x, y) = \frac{x^{2}}{4} + \frac{y^{2}}{16}$ .

Start by finding the first derivatives of $f(x, y)$ and $g(x, y)$ with respect to x and y, respectively:

$f_x = y$ ,
$f_y = x$ .

$\displaystyle g_x = \frac{x}{2}$ ,
$\displaystyle g_y = \frac{y}{8}$ .

This method asks for a non-zero constant, $\lambda$ , to satisfy the equations:

$f_x = \lambda g_x$ , and

$f_y = \lambda g_y$ .

(Note that this method still applies even if there are more than two variables.)

That's two equations for three variables. Don't panic. The constraint itself acts as the third equation of this system:

$g(x, y) = k$ .

$\displaystyle \left\{ \begin{aligned} &y = \frac{\lambda x}{2} && (a)\\ &x = \frac{\lambda y}{8} && (b)\\ & \frac{x^{2}}{4} + \frac{y^{2}}{16} = 1 && (c)\end{aligned}\right.$ .

Replace the $y$ in equation $(b)$ with the right-hand side of equation $(b)$ .

$\displaystyle x = \lambda \frac{\lambda \cdot \dfrac{x}{2}}{8} = \frac{\lambda^{2} x}{16}$ .

Before dividing both sides by $x$ , make sure whether $x = 0$ .

If $x = 0$ , the area of the rectangle will equal to zero. That's likely not a solution.

If $x \neq 0$ , divide both sides by $x$ , $\lambda = \pm 4$ . Hence by equation $(b)$ , $y = 2x$ . Replace the $y$ in equation $(c)$ with this expression to obtain (given that $x, y >0$ ) $x = \sqrt{2}$ . Hence $y = 2x = 2\sqrt{2}$ . The length of the rectangle will be $2x = 2\sqrt{2}$ while the height will be $2y = 4\sqrt{2}$ . If there's more than one possible solutions, evaluate the function that needs to be maximized at each point. Choose the point that gives the maximum value.

7 0

3 years ago