All categories

3 years ago

Please help me I’m so lost

Mathematics

1 answer:

Finger [1]3 years ago

3 0

Answer:

40.6 units

Step-by-step explanation:

Arc length is given by the formula ...

s = rθ

where θ is the measure of the central angle in radians.

There are 2π radians in a circle (360°), so π radians in 180°. That can be used to convert the central angle ADB to radians for use in the formula.

∠ADB = 360° -194° = 166°

∠ADB = 166° = (166/180)π radians = 83π/90 radians

Then the arc length AB is ...

length AB = (14)(83π/90) ≈ 40.561 units

The length of arc AB is about 40.6 units.

You might be interested in

What fraction is equal to 2/5??? (answer fast pls ill give you a shoutout)

telo118 [61]

Answer:

4/10

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Does the order in which the two transformations in a composite transformation affect the final

kap26 [50]

The order in which the two transformations in a composite transformation affect the final answer

<h3>How to determine the composite transformation?</h3>

To determine if order matters or not, I will use the following example and illustration.

Let the coordinate of point A be:

A = (2, 5)

Perform the following transformations:

Translate by (x, y + 1)
Dilate by a scale factor of 2

First order: Translation before dilation

The translation by (x, y + 1) would give:

A' = (2, 5 + 1)

A' = (2,6)

The dilation by a scale factor of 2 would give

A" = 2 * (2,6)

A" = (4,12)

Second order: Dilation before translation

The dilation by a scale factor of 2 would give

A' = 2 * (2,5)

A' = (4,10)

The translation by (x, y + 1) would give:

A'' = (4, 10 + 1)

A'' = (4,11)

See that the final coordinates in both orders are not the same.

Hence, the order in which the two transformations in a composite transformation affect the final answer

Read more about transformation at:

brainly.com/question/1548871

#SPJ1

6 0

2 years ago

Select the expression that is equivalent to (picture)

seraphim [82]

The answer to this question is x^(rt + s) since (x^r)^t becomes x^(rt) by the exponent power of a power property. Then multiplying powers of the same base results in the exponents being summed.

6 0

3 years ago

The graphs of the polar curves r = 4 and r = 3 + 2cosθ are shown in the figure above. The curves intersect at θ = π/3 and θ = 5π

Gennadij [26K]

(a)

$\displaystyle \frac{1}{2} \cdot \int_{\frac{\pi}{3}}^{\frac{5\pi}{3}} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

or, via symmetry

$\displaystyle\frac{1}{2} \cdot 2 \int_{\frac{\pi}{3}}^{\pi} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

____________

(b)

By the chain rule:

$\displaystyle \frac{dy}{dx} = \frac{ dy/ d\theta}{ dx/ d\theta}$

For polar coordinates, x = rcosθ and y = rsinθ. Since
<span>r = 3 + 2cosθ, it follows that

$x = (3 + 2\cos\theta) \cos \theta \\ 
y = (3 + 2\cos\theta) \sin \theta$

Differentiating with respect to theta

$\begin{aligned}
\displaystyle \frac{dy}{dx} &= \frac{ dy/ d\theta}{ dx/ d\theta} \\
&= \frac{(3 + 2\cos\theta)(\cos\theta) + (-2\sin\theta)(\sin\theta)}{(3 + 2\cos\theta)(-\sin\theta) + (-2\sin\theta)(\cos\theta)} \\ \\
\left.\frac{dy}{dx}\right_{\theta = \frac{\pi}{2}}
&= 2/3
\end{aligned}$

2/3 is the slope

____________

(c)

"</span><span>distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3

A</span>ngle θ and r are related via <span>r = 3 + 2cosθ, so implicitly differentiating with respect to time

</span><span /> $\displaystyle\frac{dr}{dt} = -2\sin\theta \frac{d\theta}{dt} \quad \stackrel{\theta = \pi/3}{\implies} \quad 3 = -2\left( \frac{\sqrt{3}}{2}}\right) \frac{d\theta}{dt} \implies \\ \\ \frac{d\theta}{dt} = -\sqrt{3} \text{ radians per second}$

5 0

3 years ago

Find the product of 400 and 9.460730473 times 10/15

azamat

Answer:

272.973820315

Step-by-step explanation:

5 0

3 years ago