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3 years ago

On Monday your run on a treadmill for 1/2 hour at x miles. how do you solve it

Mathematics

1 answer:

fgiga [73]3 years ago

7 0

You ran 6 miles on the treadmill on Monday.

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Anyoneeee??????????

leva [86]

Your answer will be D

As y = -(x+2)(x-1)

Thus the external negative sign will flip the positive 2 into a negative & negative 1 into a positive; Resulting, y=(x-2)(x+1)

7 0

3 years ago

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The motorcycle engine on a kawasaki ninja 1000 has a displacement of 1043 cubic-centimeters (cm3). in order to calculate its eng

marishachu [46]

$\boxed{\boxed{ \ 0.061 \frac{inch^3}{cm^3}\ }}$

<h3>Further explanation</h3>

We will calculate the unit conversion factor used to convert its engine displacement from cubic-centimeters to cubic-inches.

The relationships between inch and cm are as follows:

$\boxed{ \ 1 \ inch = 2.54 \ cm\ }$

Inches and cm represent units of length.

Made into fractions, 1 inch as the denominator and 2.54 cm as the numerator.

$\boxed{ \ \frac{1 \ inch}{2.54 \ cm} \ }$

As a unit conversion factor of volume, the numerator and the denominator in cubic.

$\boxed{ \ \frac{(1 \ inch)^3}{(2.54 \ cm)^3} \ }$

$\boxed{ \ \frac{1 \ inch^3}{16.387 \ cm^3} \ }$

Thus, we get the unit conversion factor

$\boxed{\boxed{ \ 0.061 \frac{inch^3}{cm^3}\ }}$

Let's use this unit conversion factor to calculate its engine displacement in new units.

$\boxed{= 1,043 \ cm^3 \times 0.061 \ \frac{inch^3}{cm^3}}$

Note for cm³ units that have been crossed out.

The conversion result is $\ \boxed{ \ 63.623 \ inch^3\ }$

<h3>Learn more</h3>

Convert cubic-kilometers to cubic-meters brainly.com/question/1446243
How to write in scientific notation brainly.com/question/7263463
Calculating mass based on density and volume brainly.com/question/4053884

Keywords: the motorcycle engine, Kawasaki Ninja 1000, 1043 cubic-centimeters (cm³), to calculate, its engine displacement, in cubic-inches (in³), what unit conversion factor

5 0

3 years ago

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EXAMPLE 5 Find the maximum value of the function f(x, y, z) = x + 2y + 11z on the curve of intersection of the plane x − y + z =

Taya2010 [7]

Answer:

$\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}$

<em>Maximum value of f=2.41</em>

Step-by-step explanation:

<u>Lagrange Multipliers</u>

It's a method to optimize (maximize or minimize) functions of more than one variable subject to equality restrictions.

Given a function of three variables f(x,y,z) and a restriction in the form of an equality g(x,y,z)=0, then we are interested in finding the values of x,y,z where both gradients are parallel, i.e.

$\bigtriangledown f=\lambda \bigtriangledown g$

for some scalar $\lambda$ called the Lagrange multiplier.

For more than one restriction, say g(x,y,z)=0 and h(x,y,z)=0, the Lagrange condition is

$\bigtriangledown f=\lambda \bigtriangledown g+\mu \bigtriangledown h$

The gradient of f is

$\bigtriangledown f=$

Considering each variable as independent we have three equations right from the Lagrange condition, plus one for each restriction, to form a 5x5 system of equations in $x,y,z,\lambda,\mu$ .

We have

$f(x, y, z) = x + 2y + 11z\\g(x, y, z) = x - y + z -1=0\\h(x, y, z) = x^2 + y^2 -1= 0$

Let's compute the partial derivatives

$f_x=1\ ,f_y=2\ ,f_z=11\ \\g_x=1\ ,g_y=-1\ ,g_z=1\\h_x=2x\ ,h_y=2y\ ,h_z=0$

The Lagrange condition leads to

$1=\lambda (1)+\mu (2x)\\2=\lambda (-1)+\mu (2y)\\11=\lambda (1)+\mu (0)$

Operating and simplifying

$1=\lambda+2x\mu\\2=-\lambda +2y\mu \\\lambda=11$

Replacing the value of $\lambda$ in the two first equations, we get

$1=11+2x\mu\\2=-11 +2y\mu$

From the first equation

$\displaystyle 2\mu=\frac{-10}{x}$

Replacing into the second

$\displaystyle 13=y\frac{-10}{x}$

Or, equivalently

$13x=-10y$

Squaring

$169x^2=100y^2$

To solve, we use the restriction h

$x^2 + y^2 = 1$

Multiplying by 100

$100x^2 + 100y^2 = 100$

Replacing the above condition

$100x^2 + 169x^2 = 100$

Solving for x

$\displaystyle x=\pm \frac{10}{\sqrt{269}}$

We compute the values of y by solving

$13x=-10y$

$\displaystyle y=-\frac{13x}{10}$

For

$\displaystyle x= \frac{10}{\sqrt{269}}$

$\displaystyle y= -\frac{13}{\sqrt{269}}$

And for

$\displaystyle x= -\frac{10}{\sqrt{269}}$

$\displaystyle y= \frac{13}{\sqrt{269}}$

Finally, we get z using the other restriction

$x - y + z = 1$

Or:

$z = 1-x+y$

The first solution yields to

$\displaystyle z = 1-\frac{10}{\sqrt{269}}-\frac{13}{\sqrt{269}}$

$\displaystyle z = \frac{-23\sqrt{269}+269}{269}$

And the second solution gives us

$\displaystyle z = 1+\frac{10}{\sqrt{269}}+\frac{13}{\sqrt{269}}$

$\displaystyle z = \frac{23\sqrt{269}+269}{269}$

Complete first solution:

$\displaystyle x= \frac{10}{\sqrt{269}}\\\\\displaystyle y= -\frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{-23\sqrt{269}+269}{269}$

Replacing into f, we get

f(x,y,z)=-0.4

Complete second solution:

$\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}$

Replacing into f, we get

f(x,y,z)=2.4

The second solution maximizes f to 2.4

5 0

3 years ago

Each nickel is $0.05. Write and solve an equation to determine the total number of nickels needed to make $2.25

Alexeev081 [22]

Answer:

you need 45 nickels

Step-by-step explanation:

5 0

3 years ago

Alicia has 3/4 bag of cat food. Her cat eats 1/10 of the food per week. how many weeks will the food last

Sliva [168]

Answer:

It would last 7 1/2 weeks if i'm correct

5 0

3 years ago

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