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3 years ago

keiko fills an aquarium to a depth of 3/5 meters in 7½ minutes. what is the unit ratr in minutes per meter?

Mathematics

2 answers:

zmey [24]3 years ago

8 0

Answer:

2/5 m ÷ by 6 minutes is the unit rate (can you do this division?)

On careful reading, I see that you're asked for minutes per meter, so that 6 min divided by 0.4 m, which is 2.5 times 6 min or 15 minutes per meter.

SOVA2 [1]3 years ago

7 0

Answer:

15 min

Step-by-step explanation:

2/5 divided by 6

=2/5 * 1/6

=2/30

=1/15

15 min

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In two or three sentences explain how you would solve for the real solutions of the following equation: please help asap!!

g100num [7]

the real solutions for the equation $x^{3}=-64$ are -

$x=4,2+-2\sqrt{3i}$

Step-by-step explanation:

$x^{3}$ = $- 64$

$x^{3} +64$ = 0

We can write 64 as $4^{3}$

$x^{3}$ + $4^{3}$ = 0

using the identity ( $x^{3}+y^{3} = (x+y)(x^{2} -xy+y^{2} )$ )

we get,

= $(x+4) (x^{2} -x*4+4^{2} )$

= $(x+4)(x^{2} -4x+16)$ ....................(1)

solving the quadratic equation ,

$x^{2} -4x+16$ =0

solutions of this quadratic equation can be obtained by

$x=-b +- \sqrt{b^{2}-4ac } /2a$

let use y for factors

$x=-(-4x)+-\sqrt{(-4x^{2} )-4*x^{2} *16} / 2*x^{2}$

$x=4x+-\sqrt{16x^{2} -64x^{2} } /2x^{2}$

$x=4+-\sqrt{16-64}/2$

$x=4+-4\sqrt{3i} /2$

<u /> $x=2+-2\sqrt{3i}$ ..................(2)

from the equation 1 we have,

$x-4=0$

which gives solution $x=4$

and from equation 2 we got $x=2+-2\sqrt{3i}$

so the real solutions for the equation $x^{3}=-64$ are -

$x=4,2+-2\sqrt{3i}$

3 0

3 years ago

A manufacturer produces televisions. He estimates that by selling them for x dollars each, he will be able to sell 230 – 3x each

poizon [28]

Answer:

Price per television =38.30

Step-by-step explanation:

Number of units sold in one week =230-3x

Price of one unit =x

Total money produced in one week =x(230 - 3x)

(Here it doesn't matter total money is taken for a week or day because after differentiating and equating to zero that factor disappear )

Differentiate total amount with respect to x.

$\frac{dM}{dt}=230-6x$

Now equate it equal to zero to get extremum.

230-6x=0

Then, x = 38.30

5 0

4 years ago

PLZZZZ HELP What is the slope of a line that is perpendicular to a line whose equation is 3y=−4x+2 ?

earnstyle [38]

$\bf 3y=-4x+2\implies y=\cfrac{-4x+2}{3} \\\\\\ y=\stackrel{\stackrel{slope}{\downarrow }}{-\cfrac{4}{3}}x+\cfrac{2}{3}\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

so the slope of that line above is really -4/3, now

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{4}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{3}{4}}\qquad \stackrel{negative~reciprocal}{+\cfrac{3}{4}\implies \blacktriangleright \cfrac{3}{4} \blacktriangleleft}}$