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3 years ago

Radius OA of circle O has a slope of 2.5. What is the slope of the line tangent to circle O to point A?

2 answers:

5 0

The tangent at A is perpendicular to OA, so has a slope that is the negative reciprocal of that of the radius: -1/2.5 = -2/5.

Mekhanik [1.2K]3 years ago

4 0

Answer: The required slope of the line tangent to the circle at point A is -0.4.

Step-by-step explanation: Given that the radius OA of a circle with center O has a slope of 2.5.

We are to find the slope of the line tangent to the circle at the point A.

We know that

The radius of a circle at a point on the circumference of a circle is perpendicular to the tangent line at the same point on the circumference of the circle.

Also, the product of the slopes of two perpendicular lines is -1.

So, if m is the slope of the tangent line at the point A, then we must have

$m\times 2.5=-1\\\\\Rightarrow m=-\dfrac{1}{2.5}\\\\\\\Rightarrow m=-\dfrac{10}{25}\\\\\Rightarrow m=-\dfrac{2}{5}\\\\\Rightarrow m=-0.4.$

Thus, the required slope of the line tangent to the circle at point A is -0.4.

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Three friends Kofi,Yaw and Musa are in partnership business in which Kofi and Yaw contributed 5/9 and 2/15 of the cost of 14000.

wlad13 [49]

Answer:

(a) $Total = 45000$

(b) Yaw, Musa and Kofi

Step-by-step explanation:

Given

$Kofi =5/9$

$Yaw = 2/15$

$Musa = 14000$

Solving (a): The cost of the business

First, we solve for the fraction of Musa

$Musa + Kofi + Yaw = 1$

$Musa = 1 - (Kofi + Yaw )$

$Musa = 1 - (5/9 + 2/15)$

$Musa = 1 - (\frac{25+6}{45})$

$Musa = 1 - \frac{31}{45}$

$Musa = \frac{45 - 31}{45}$

$Musa = \frac{14}{45}$

So, we have:

$\frac{14}{45} * Total = 14000$

Make Total the subject

$Total = 14000 * \frac{45}{14}$

$Total = 1000 * 45$

$Total = 45000$

Solving (b): Partners in ascending order

First, represent the fractions as decimals

$Kofi =5/9$ $= 0.5556$

$Yaw = 2/15$ $= 0.1333$

$Musa = \frac{14}{45}$ $= 0.3111$

From the conversion above, the least is 0.1333 (Yaw), then 0.3111 (Musa), then 0.5556 (Kofi).

<em>So, the order is: Yaw, Musa and Kofi</em>

6 0

3 years ago

Evaluate tan ( cos^-1 ( 1/8 ) ) , giving your answer as an exact value (no decimals)

vekshin1

$\bf cos^{-1}\left( \cfrac{1}{8} \right)=\theta \qquad \qquad cos(\theta )=\cfrac{\stackrel{adjacent}{1}}{\stackrel{hypotenuse}{8}}\impliedby \textit{let's find the \underline{opposite}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{8^2-1^1}=b\implies \pm\sqrt{63}=b ~\hfill tan(\theta )=\cfrac{\stackrel{opposite}{\pm\sqrt{63}}}{\stackrel{adjacent}{1}} \\\\\\ ~\hspace{34em}$