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3 years ago

7

How to find a missing measure of a triangle

1 answer:

bulgar [2K]3 years ago

3 0

Answer:

To determine to measure of the unknown angle, be sure to use the total sum of 180 degrees.

Step-by-step explanation:

if two angles are given , then add them together and the subtract from 180 degrees. if two angles are the same and unknow, subtract the know angle from 180 degrees and then divide by two hope this helps

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Consider the circle of radius 5 centered at (0, 0). Find an equation of the line tangent to the circle at the point (3, 4) in sl

Wittaler [7]

Answer:

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

Step-by-step explanation:

The equation of a circle of radius $5$ centered at $(0,0)$ is:

$x^{2} + y^{2} = 5^{2}$ .

$x^{2} + y^{2} = 25$ .

Differentiate implicitly with respect to $x$ to find the slope of tangents to this circle.

$\displaystyle \frac{d}{dx}[x^{2} + y^{2}] = \frac{d}{dx}[25]$

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(y^{2}) = 0$ .

Apply the power rule and the chain rule. Treat $y$ as a function of $x$ , $f(x)$ .

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(f(x))^{2} = 0$ .

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}(2f(x)\cdot f^{\prime}(x)) = 0$ .

That is:

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}\left(2y \cdot \frac{dy}{dx}\right) = 0$ .

Solve this equation for $\displaystyle \frac{dy}{dx}$ :

$\displaystyle \frac{dy}{dx} = -\frac{x}{y}$ .

The slope of the tangent to this circle at point $(3, 4)$ will thus equal

$\displaystyle \frac{dy}{dx} = -\frac{3}{4}$ .

Apply the slope-point of a line in a cartesian plane:

$y - y_0 = m(x - x_0)$ , where

$m$ is the gradient of this line, and
$(x_0, y_0)$ are the coordinates of a point on that line.

For the tangent line in this question:

$\displaystyle m = -\frac{3}{4}$ ,
$(x_0, y_0) = (3, 4)$ .

The equation of this tangent line will thus be:

$\displaystyle y - 4 = -\frac{3}{4} (x - 3)$ .

That simplifies to

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

3 0

3 years ago

Given the function f (x) = x2 – 52, find f (x - 3) f (x – 3)

Setler [38]

6 Why because my brain is huge

5 0

3 years ago

Read 2 more answers

I WILL UPVOTE!!!!! To make 1 1/2 dozen muffins, a recipe uses 1 cup of sugar.

maxonik [38]

Approximately 0.67 of a cup of sugar is needed. Let me know if this isn't right.

3 0

3 years ago

Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked

RUDIKE [14]

<em><u>The system of equations that represents this situation are:</u></em>

q + p = 2

4q + 5p = 8

<em><u>Solution:</u></em>

Let q be the number of hours it took Courtney to walk from her house to the beach

Let p be the number of hours it took her to walk from the beach to the park

<em><u>The entire walk took 2 hours</u></em>

Therefore,

q + p = 2 ------- eqn 1

<em><u>The total distance Courtney walked was 8 kilometers</u></em>

Total distance = 8 km

Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour

Then walked from the beach to the park at a constant speed of 5 kilometers per hour

<em><u>Distance is given as:</u></em>

$distance = speed \times time$

<em><u>From her house to the beach:</u></em>

$distance = 4 \times q = 4q$

<em><u>From the beach to the park:</u></em>

$distance = 5 \times p = 5p$

We know that,

Total distance = 8 km

Therefore,

4q + 5p = 8 ------ eqn 2

<em><u>Thus the system of equations that represents this situation are:</u></em>

q + p = 2

4q + 5p = 8

8 0

4 years ago

PLS HELP DUE TODAY (show work pls) i only have one attempt left

mr Goodwill [35]

Answer:

44 - 27 = 17

2hours 40min ---> 2 2/3

17 divided by 2 2/3 is equal to

<u>i d k f a m i got 6.375 km/hour </u>

5 0

3 years ago