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andrezito [222]

3 years ago

12

Keith ran in a marathon. It took him 3 hours and 2 minutes to run 26 miles. If he ran at the same rate for the whole race, how m

any minutes did it take him to run each mile? (1 hour = 60 minutes)
A.) 6 minutes

B.) 7 minutes

C.) 8 minutes

D.) 9 minutes

1 answer:

Lynna [10]3 years ago

5 0

Distance Keith ran = 26 miles

Time it took
= 3 hours 2 minutes = [(3 * 60) + 2] minutes = (180 + 2) minutes = 182 minutes

Hence,

Speed (Rate) = $\frac{Distance}{Time} = \frac{26}{182} = \frac{13}{91} = \frac{1}{7}$ miles per minute

Hence,

Time taken to complete 1 mile
= $\frac{Distance}{Speed} = \frac{1}{ \frac{1}{7} } = 1 * \frac{7}{1}$
= 7 minutes

Hence, the answer is B.

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What is the equation of the directrix of the parabola given by the equation y2 = -24x?

valentina_108 [34]

Hello!

The directrix of a parabola is a fixed line used in describing a curve or surface.

The standard form a parabola is 4p(x - h) = (y - k)². In this equation, h, k is the vertex, and p is the focal point.

To find the standard form, first, we would find p.

Since the equation given, y² = -24x, has a vertex at (0, 0), h, k would be zero. In this case, we can find p now.

4p = -24 (divide both sides by 4)

p = -6

4(-6)(x - 0) = (y - 0)² which can be simplified to: 4(-6)(x) = y².

Looking at the graph of the parabola, it is symmetric around the x-axis, so therefore, the directrix is a line parallel to the y-axis. To find the directrix, use the formula: x = 0 - p, and we know that p = -6.

x = 0 - (-6)

x = 6

Therefore, the directrix of the parabola is choice D, x = 6.

3 0

4 years ago

a box with a square base and open top must have a volume of 70304 c m 3 cm3 . we wish to find the dimensions of the box that min

Dmitriy789 [7]

The box should have base 52 cm by 52 cm and height 26 cm.

What is volume?

A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume definition and length definition are connected.

The Volume of a box with a square base x by x cm and height h cm is

$V = x^2h$

Since the surface area directly affects the amount of material used, we can reduce the amount of material by reducing the surface area.

The surface area of the box described is $A = x^2 + 4xh$

We need A as a function of x alone, so we'll use the fact that

$V = x^2h= 70304 cm^3$

⇒ $h = \frac{70304}{x^2}$

So, the area becomes,

$A = x^2+4x(\frac{70304}{x^2})\\ A = x^2 + \frac{281216}{x}$

We want to minimize A, so

$A' = 2x - \frac{281216}{x^2} =0\\\frac{2x^3-281216}{x^2}=0\\ {2x^3-281216} = 0\\x^3 - 140608=0\\x^3 = 140608\\x = 52$

The second derivative test verifies that A has a minimum at this critical number:

$A'' = 2+\frac{562432}{x^3}$ which is positive at x = 52.

Now,

$h = \frac{70304}{x^2}= \frac{70304}{(52)^2}=26$

Hence, The box should have base 52 cm by 52 cm and height 26 cm.

To know more about volume, click on the link

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8 0

2 years ago

Use the procedures developed to find the general solution of the differential equation. (Let x be the independent variable.)

makkiz [27]

Solution :

Given :

2y''' + 15y'' + 24y' + 11y= 0

Let x = independent variable

$(a_0D^n + a_1D^{n-1}+a_2D^{n-2} + ....+ a_n) y) = Q(x)$ is a differential equation.

If $Q(x) \neq 0$

It is non homogeneous then,

The general solution = complementary solution + particular integral

If Q(x) = 0

It is called the homogeneous then the general solution = complementary solution.

2y''' + 15y'' + 24y' + 11y= 0

$(2D^3+15D^2+24D+11)y=0$

Auxiliary equation,

$2m^3+15m^2+24m +11 = 0$

-1 | 2 15 24 11

<u> | 0 -2 - 13 -11 </u>

2 13 11 0

∴ $2m^2+13m+11=0$

The roots are

$=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$=\frac{-13\pm \sqrt{13^2-4(11)(2)}}{2(2)}$

$=\frac{-13\pm9}{4}$

$=-5.5, -1$

So, $m_1, m_2, m_3 = -1, -1, -5.5$

Then the general solution is :

$= (c_1+c_2 x)e^{-x} + c_3 \ e^{-5.5x}$

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3 years ago

Which of the following give the highest future value is 6000000 is invested at 6% for 3 years

Blababa [14]

Answer:

$5084745.76271

Step-by-step explanation:

Given data

Final amount= $6000000

Rate=6%

Time= 3 years

Now let us find the initial amount which is the principal

using the simple interest formula we have

6000000 = P(1+0.06*3)

6000000 =P(1+0.18)

6000000 =P*1.18

P= 6000000 /1.18

P=$5084745.76271

Hence the initial deposite is $5084745.76271

3 0

3 years ago

Work out and simplify where possible 5/18 + 4/9

Fittoniya [83]

Answer:

0.73

Step-by-step explanation:

$\\ \frac{5}{18 } + \frac{4}{9}$

$\\ = \frac{5 + 8}{18}$

$\\ = \frac{13}{18}$

$\\ = 0.73$

3 0

3 years ago