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3 years ago

5

Problem Solve 88 – (–35)

2 answers:

Rasek [7]3 years ago

7 0

Subtract negative = add
88 + 35 = 123
The solution is 123

Elodia [21]3 years ago

7 0

The answer is 124

Equation:

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Which expression makes the equation true?

valina [46]

Equation is y^20 = ( )^2

Answer:

y to the power of 10.

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3 years ago

MARSVECTORCALC6 3.4.020. My Notes A rectangular box with no top is to have a surface area of 64 m2. Find the dimensions (in m) t

ioda

Answer:

We would have

$l =w =\frac{8\sqrt{3}}{3} \\h = \frac{8\sqrt{3}}{6}$

where " l " is length, " w" is width and "h" is height.

Step-by-step explanation:

Step 1

Remember that

Surface area for a box with no top = $lw+2lh+2wh = 64$

where " l " is length, " w" is width and "h" is height.

Step 2.

Remember as well that

Volume of the box = $l*w*h$

Step 3

We can now use lagrange multipliers. Lets say,

$F(l,w,h) = lwh$

and

$g(l,w,h) = lw+2lh+2wh = 64$

By the lagrange multipliers method we know that

$\nabla F = \lambda \nabla g$

Step 4

Remember that

$\nabla F = (wh,lh,lw)$

and

$\nabla g = (w+2h,l+2h , 2w+2l)$

So basically you will have the system of equations

$wh = \lambda (w+2h)\\lh = \lambda (l+2h)\\lw = \lambda (2w+2l)$

Now, remember that you can multiply the first eqation, by "l" the second equation by "w" and the third one by "h" and you would get

$lwh = l\lambda (w+2h)\\\\lwh = w\lambda (l+2h)\\\\lwh = h\lambda (2w+2l)$

Then you would get

$l\lambda (w+2h) = w\lambda (l+2h) = h\lambda (2w+2l)$

You can get rid of $\lambda$ from these equations and you would get

$lw+2lh = lw+2wh = 2wh+2lh$

And from those equations you would get

$l = w =2h$

Now remember the original equation

$lw+2lh+2wh = 64$

If we plug in what we just got, we would have

$l^{2} + l^{2} + l^2 = 64 \\3l^{2} = 64 \\l = w = \frac{8\sqrt{3} }{3} \\h = \frac{8\sqrt{3} }{6}$

7 0

3 years ago

What is the difference between 2,386 and 7,000?<br> A. 9,386<br> B. 4,614<br> C. 5,614<br> D. 10,386

Anuta_ua [19.1K]

If you would like to know what is the difference between 7000 and 2386, you can calculate this using the following steps:

difference between 7000 and 2386:
7000 - 2386 = 4614

The correct result would be B. 4614.

7 0

3 years ago

Derive the equation of the parabola with a focus at (0, −4) and a directrix of y = 4.

CaHeK987 [17]

<u>Answer:</u>

$y=-\frac{1}{16} x^2$

<u>Step-by-step explanation:</u>

Equation of parabola with focus at (0,-4) and directrix is $y=4$ .

We know that parabola is the locus of all the points such that the distance from fixed point on the parabola to fixed line directrix is the same.

The parabola is opening downwards.

Let any point on parabola is (x,y).

Distance from focus(0,-4) to (x,y) = $\sqrt{(x-0)^2+(y-(-4))^2}=|y-4|$

$\sqrt{(x-0)^2+(y-+4)^2}=|y-4|$

$(x-0)^2+(y+4)^2=(y-4)^2$

$(x)^2+(y+4)^2=(y-4)^2$

$x^2+(y^2+4y+4y+16)=y^2-4y-4y+16$

$x^2+y^2+8y+16=y^2-8y+16$

$x^2+16y^2=0$

$16y=-x^2$

$y=-\frac{1}{16} x^2$

6 0

2 years ago

A telemarketer spent 7 hours during her 8-hour shift calling up new clients. What percentage of her time was spent on things oth

padilas [110]

1/8 of her time was spent on things other than working with clients. 1/8 = 0.125 * 100 = 12.5%

6 0

2 years ago