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Afina-wow
1 month ago
12

Find the slope of a pipe that slopes down 2/5 inch per foot.

Mathematics
2 answers:
zzz [12.3K]1 month ago
8 0

Answer:

Step-by-step explanation:

Let's begin.

According to the problem, the pipe descends \frac{2}{5} inches per foot.

1 foot = 12 inches[/tex]

This means y=\frac{2}{5} inches

x=12 inches

Thus, the slope can be expressed as: \frac{y}{x}

So the slope equals \frac{\frac{2}{5} }{12}

the slope results in \frac{2}{12*5}

the slope evaluates to \frac{2}{60}

the slope is \frac{1}{30}: therefore the answer is \frac{1}{30}: Answer

babunello [11.8K]1 month ago
3 0

Answer:

m=\frac{1}{30}

Step-by-step explanation:

To determine the slope, divide the rise by the run to calculate the slope.

Note that

1 ft = 12 in

Let

y ----> the rise

x ----> the run

m ----> the slope

m=\frac{y}{x}

the values are given as

y=2/5\ in

x=1\ ft=12\ in

m=\frac{y}{x}

substituting these values gives

m=\frac{(2/5)}{12}

m=\frac{2}{60}

Simplifying further

m=\frac{1}{30}

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1 month ago
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A flat circular plate has the shape of the region x2 + y2≤1. The plate, including the boundary where x2 + y2 = 1, is heated such
Leona [12618]
Setting both partial derivatives to zero results in a single critical point at (x,y)=\left(\dfrac12,0\right), located within the unit disk.

At this given point, the derivative value of the Hessian matrix is

|H|=\begin{vmatrix}T_{xx}&T_{xy}\\T_{yx}&T_{yy}\end{vmatrix}=\begin{vmatrix}2&0\\0&4\end{vmatrix}=8>0

and the second-order partial derivative with respect to x yields

T_{xx}\bigg|_{(x,y)=(1/2,0)}=2>0

This suggests that the critical point represents a local minimum, marking it as the coldest area on the plate with a temperature of T\left(\dfrac12,0\right)=-\dfrac14.

To find the hottest area on the plate, it must be located along the boundary. Let x=\cos\theta and y=\sin\theta, so that

T(x,y)=T(\theta)=\cos^2\theta+2\sin^2\theta-\cos\theta
T(\theta)=\dfrac32-\cos\theta-\dfrac12\cos2\theta

Thus, the plate's boundary (the circle x^2+y^2=1) is treated as a single variable function \theta examined over \theta\in[0,2\pi). A single differentiation gives

T'(\theta)=\sin\theta+\sin2\theta=0
\implies\theta=0,\theta=\dfrac{2\pi}3,\theta=\pi,\theta=\dfrac{4\pi}3

You will discover that T(\theta) achieves three extrema on the interval (0,2\pi), with relative maxima occurring at \theta=\dfrac{2\pi}3 and \theta=\dfrac{4\pi}3, and a relative minimum at \theta=\pi (and \theta=0, if you wish to include that).

Our minimum has already been identified inside the plate - which you can check to have a lower temperature than at the points noted by T(\theta) - and we identify two maxima at \theta=\dfrac{2\pi}3 and \theta=\dfrac{4\pi}3, both showing a maximum temperature of T=\dfrac94.

Reverting to Cartesian coordinates, these points match up with \left(-\dfrac12,\pm\dfrac{\sqrt3}2\right).
4 0
22 days ago
A rectangular prism with integer side lengths has a height of $3$. If the surface area of the prism is equal to $52$, then what
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1 month ago
1-i need to mix 25% mineral spirits to the varnish i am using what ratio of spirit to varnish am i using? 2-if i use 240 ml of v
Svet_ta [12734]

Answer:

(1) The necessary proportion of spirit to varnish stands at 1:3.

(2) A total of 80 ml of mineral spirit is required.

(3) The ratio of the heights to the widths of the tapestries is 3:2.

Step-by-step explanation:

(1) To achieve a mixture containing 25% mineral spirit, the blend consists of 25% spirit and 75% varnish.

Therefore, \frac{spirit}{varnish}=\frac{25}{75}

=\frac{1}{3}

Consequently, the proportion of spirit to varnish is 1:3.

(2) Using 240ml of varnish indicates this is 75% of the entire solution, which means the ratio of varnish to the total solution is 3:4.

Let the total solution quantity be x.

Thus, 240:x=3:4.

⇒\frac{240}{x}=\frac{3}{4}

⇒3x=240*4

⇒x=\frac{240*4}{3}

⇒x=320

This means the total solution amounts to 320 ml.

Now, calculating Spirit = Total solution - Varnish

⇒Spirit = 320ml-240ml

⇒Spirit = 80ml

Therefore, when using 240 ml of varnish, you will require 80 ml of mineral spirit.

(3) The dimensions of Robison's tapestries are uniform at 1.5m in length and 1m in width. Initially, to obtain whole numbers, we multiply these dimensions by 10.

Thus, the dimensions become 15m long and 10m wide.

Now, the proportion of Height to Width is 15:10

⇒\frac{Height}{Width} =\frac{15}{10}

⇒\frac{Height}{Width} =\frac{3}{2}

Thus, the proportion of the heights of the tapestries to their widths is 3:2.

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Leona [12618]

Response: Yes, it is

Detailed explanation:

Since the average scores of both sets of students vary, evaluating the mean score in relation to their class will clarify which class supports or contradicts the professor's research

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24 days ago
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