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3 years ago

Lf 15 pounds of dog food costs $5.99, what is the price per pound?

Mathematics

2 answers:

snow_lady [41]3 years ago

6 0

Answer:

The answer is 0.39933333

spayn [35]3 years ago

3 0

2.5041 is I believe the answer, but I’m not for sure.

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Which equation is the inverse of y = 100 – x2?<br> A.y= +or- sqrt 100-x A. is the correct answer

GREYUIT [131]

I hope this helps you

100-y=x^2.

x= square root of 100-y

y^-1= square root of 100-x

4 0

3 years ago

(a) The plane y + z = 13 intersects the cylinder x2 + y2 = 25 in an ellipse. Find parametric equations for the tangent line to t

klemol [59]

Answer:

Step-by-step explanation:

We have a curve (an ellipse) written as the system of equations

$\begin{cases} y+z &= 13\\ x^2+y^2 &= 25\end{cases}$ .

And we want to calculate the tangent at the point (3,4,9).

The idea in this problem is to consider two variables as functions of the third. Usually we consider $y$ and $z$ as functions of $x$ . Recall that a curve in the space can be written in parametric form in terms of only one variable. In this case we are considering the ‘‘natural’’ parametrization $(x, y(x), z(x))$ .

Recall that the parametric equation of a line has the form

$r(t)=\begin{cases} x(t) &= x_0 + v_1t \\ y(t) &= y_0 +v_2t\\ z(t) &= z_0 +v_3t \end{cases}$ ,

where $(x_0,y_0,z_0)$ is a point on the line (in this particular case is (3,4,9)) and $(v_1,v_2,v_3)$ is the direction vector of the line. In this case, the direction vector of the line is the tangent vector of the ellipse at the point (3,4,9).

Now, if we have the parametric equation of a curve $(x, y(x), z(x))$ its tangent line will have direction vector $(1, y'(x), z'(x))$ . So, as we need to calculate the equation of the tangent line at the point $(3,4,9) = (3, y(3), z(3))$ , we must obtain the tangent vector $(1, y'(3), z'(3))$ . This part can be done taking implicit derivatives in the systems that defines the ellipse.

So, let us write the system as

$\begin{cases} y(x)+z(x) &= 13\\ x^2+y^2(x) &= 25\end{cases}$ .

Then, taking implicit derivatives:

$\begin{cases} y'(x)+z'(x) &= 0 \\ 2x+2y(x)y'(x) &= 0\end{cases}$ .

Now we substitute the values $x=3$ and $y(3)=4$ , and we get the system of linear equations

$\begin{cases} y'(3)+z'(3) &= 0 \\ 2\cdot 3+2\cdot 4y'(x) &= 0\end{cases}$ ,

where the unknowns are $y'(3)$ and $z'(3)$ .

The system is

$\begin{cases} y'(3)+z'(3) &= 0 \\ 6+8y'(x) &= 0\end{cases}$ ,

and its solutions are

$y'(3) = -\frac{3}{4}$ and $z'(3) = \frac{3}{4}$ .

Then, the direction vector of the tangent is

$(1, -\frac{3}{4}, -\frac{3}{4})$ .

Finally, the tangent line has parametric equation

$r(t)=\begin{cases} x(t) &= 3 + t \\ y(t) &= 4 -\frac{3}{4}t\\ z(t) &= 9 +\frac{3}{4}t \end{cases}$

where $t\in\mathbb{R}$ .

7 0

4 years ago

How did Gospel influence American popular music? can u give me 3-5 sentences thanks and hurry plz

borishaifa [10]

Answer:

Gospel Music frontiers Soul and Blues in American Music Industry. Gospel music has been a source of inspiration and solace for millions of listeners. Born out of traditional African American folk music and religious hymns, Gospel inspired a variety of American music

8 0

3 years ago

Whats the standard form of 2+8/15x =-2/3y

lara [203]

Standard Form looks like this:

$A_{x} + B_{y} = C$

Also, A cannot be negative and there are no fractions in Standard Form.

Now that we know the rules of Standard Form, let's get x and y on one side.

-2/3y = 2 + 8/15x
Subtract 8/15x from both sides.
-8/15x - 2/3y = 2
Multiply 2/3 by 5/5 to get a common denominator.
-8/15x - 10/15y = 2
Multiply everything by 15 to rid of the fractions.
-8x - 10y = 30
Multiply everything by -1 to make A positive.
8x + 10y = -30

8x + 10y = -30

7 0

4 years ago

During a four-day festival candies are lit only at the beginning of a daily gathering. They burn for a single hour each day and

yan [13]

Stsgsvs shgsgssjdnd. I don’t know

5 0

3 years ago