Ask question

Ask question

All categories

3 years ago

9

Dedrick received $43 from his last birthday that he added to his piggy- bank already containing $52.60. He emptied it out so tha

t he could get his grandmother a present. If the perfume he purchased cost $37.59, how much money is remaining in his piggy-bank? $

1 answer:

mezya [45]3 years ago

8 0

Answer= $58.01

52.60
+43.00
95. 60. 95.60 - 37. 59= 58. 01

but, TECHNICALLY, there isn't anything in the piggy bank if he emptied it out.

You might be interested in

Which shape has two sets of parallel sides only?

soldier1979 [14.2K]

Answer:

all of the above to be honest

because they all have 2 pairs of parallel sides

5 0

3 years ago

I need help with this question

Sophie [7]

Answer:

C

Step-by-step explanation:

using the pythagorean theorem,

a²+b²=c²

8²+7²=c²

64+49=c²

113=c²

$\sqrt{113 = \sqrt{c}² }$

10.63=c

7 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

What is the length of the hypotenuse of the triangle?

sergey [27]

If you use the pothaorian theorym (A squared + B squared= C squared) youll be able to figure out the right answer is 65.

8 0

3 years ago

Read 2 more answers

Identify the product and express it in scientific notation. 4.7 x (6.02 x 10^23)

Anna11 [10]

Answer:

$\large\boxed{4.7\times(6.02\times10^{23})=2.8294\times10^{24}}$

Step-by-step explanation:

The scientific notation:

$a\times10^k\ \text{where}\ 1\leq a$

We have:

$4.7\times(6.02\times10^{23})=(4.7\times6.02)\times10^{23}=28.294\times10^{23}\\\\=2.8294\times10\times10^{23}=2.8294\times10^{24}$

6 0

3 years ago