Find the slope of -8x+5y=0<br><br> can anyone help with finding the slope i don't understand

9. A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

SSSSS [86.1K]

Answer:

Part 4) $r=84\ units$

Part 9) $sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) $sin(\theta)=-\frac{9\sqrt{202}}{202}$

Step-by-step explanation:

Part 4) A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

we know that

The circumference of a circle subtends a central angle of 360 degrees

The circumference is equal to

$C=2\pi r$

using proportion

$\frac{2\pi r}{360^o}=\frac{56\pi}{120^o}$

simplify

$\frac{r}{180^o}=\frac{56}{120^o}$

solve for r

$r=\frac{56}{120^o}(180^o)$

$r=84\ units$

Part 9) Given cos(∅)=-2/3 and ∅ lies in Quadrant III. Find the exact value of sin(∅) in simplified form

Remember the trigonometric identity

$cos^2(\theta)+sin^2(\theta)=1$

we have

$cos(\theta)=-\frac{2}{3}$

substitute the given value

$(-\frac{2}{3})^2+sin^2(\theta)=1$

$\frac{4}{9}+sin^2(\theta)=1$

$sin^2(\theta)=1-\frac{4}{9}$

$sin^2(\theta)=\frac{5}{9}$

square root both sides

$sin(\theta)=\pm\frac{\sqrt{5}}{3}$

we know that

If ∅ lies in Quadrant III

then

The value of sin(∅) is negative

$sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) The terminal side of ∅ passes through the point (11,-9). What is the exact value of sin(∅) in simplified form?

see the attached figure to better understand the problem

In the right triangle ABC of the figure

$sin(\theta)=\frac{BC}{AC}$

Find the length side AC applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$AC^2=11^2+9^2$

$AC^2=202$

$AC=\sqrt{202}\ units$

so

$sin(\theta)=\frac{9}{\sqrt{202}}$

simplify

$sin(\theta)=\frac{9\sqrt{202}}{202}$

Remember that

The point (11,-9) lies in Quadrant IV

then

The value of sin(∅) is negative

therefore

$sin(\theta)=-\frac{9\sqrt{202}}{202}$

5 0

3 years ago

Okay hear this someone came into my shop and stole $100 without my knowledge they came back to the store and spent $70 in items

Tom [10]

............You lost $130......................

4 0

4 years ago

Write the slope-intercept form of the equation of the line

Igoryamba

The slope-intercept form of the equation of the line described is y = 3/4x - 4.

<h3>What is a slope?</h3>

The slope of a line simply refers to the gradient of a line and it's typically used to describe both the ratio, direction and steepness of an equation of a straight line.

<h3>How to calculate the slope of a line?</h3>

Mathematically, the slope of a straight line can be calculated by using this formula;

$Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}$

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + c

Where:

x and y are the points.
m is the slope.
c is the intercept.

The partial equation for the perpendicular line is given by:

y = 3/4x + c

At point (8, 2), we have:

2 = 3/4(8) + c

2 = 6 + c

c = 2 - 6

c = -4.

Therefore, the slope-intercept form of the equation of the line described is y = 3/4x - 4.

Read more on slope-intercept form here: brainly.com/question/1884491

#SPJ1

8 0

2 years ago

3. Marie planted a tree a few years ago and wanted to see how much it had grown. Marie

Andreas93 [3]

Answer:

5.4 m

Step-by-step explanation:

<u>Given </u>

The top of the tree, the point A and the base form a right triangle
Horizontal leg = 8 m
Vertical leg = the height of the tree = x
Angle A = 34° is opposite to the three

<u>Use the ratio to find the value of x:</u>

opposite / adjacent = tan A
x/8 = tan 34°
x = 8 tan 34 degree
x = 5.4 m (rounded)

8 0

3 years ago

PLEASE HELP!! IM TIMED!

Sati [7]

in triangle interior opposite angles is equals to exterior angle, but here it is not that way

Step-by-step explanation:

95+30 cannot be 85 so this the error

4 0

3 years ago

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Find the slope of -8x+5y=0 can anyone help with finding the slope i don't understand