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3 years ago

If the circumference of a circle measures 8π cm, what is the area of the circle in terms of π?

Mathematics

1 answer:

Anna11 [10]3 years ago

6 0

Answer:16TT

Step-by-step explanation:

If the circumference of the circle is represented by 8TT

Know the formula of circumference

C=2TTr meaning the r will be 4

2*TT*4= 8TT

Therefore the area will be

A=TTr^2

If the radius is 4

TT4^2

TT*4*4=

16TT

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3 years ago

Find the angle between u =the square root of 5i-8j and v =the square root of 5i+j.

fenix001 [56]

Answer:

The angle between vector $\vec{u} = 5\, \vec{i} - 8\, \vec{j}$ and $\vec{v} = 5\, \vec{i} + \, \vec{j}$ is approximately $1.21$ radians, which is equivalent to approximately $69.3^\circ$ .

Step-by-step explanation:

The angle between two vectors can be found from the ratio between:

their dot products, and
the product of their lengths.

To be precise, if $\theta$ denotes the angle between $\vec{u}$ and $\vec{v}$ (assume that $0^\circ \le \theta < 180^\circ$ or equivalently $0 \le \theta < \pi$ ,) then:

$\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ .

<h3>Dot product of the two vectors</h3>

The first component of $\vec{u}$ is $5$ and the first component of $\vec{v}$ is also

The second component of $\vec{u}$ is $(-8)$ while the second component of $\vec{v}$ is $1$ . The product of these two second components is $(-8) \times 1= (-8)$ .

The dot product of $\vec{u}$ and $\vec{v}$ will thus be:

$\begin{aligned} \vec{u} \cdot \vec{v} = 5 \times 5 + (-8) \times1 = 17 \end{aligned}$ .

<h3>Lengths of the two vectors</h3>

Apply the Pythagorean Theorem to both $\vec{u}$ and $\vec{v}$ :

$\| u \| = \sqrt{5^2 + (-8)^2} = \sqrt{89}$ .
$\| v \| = \sqrt{5^2 + 1^2} = \sqrt{26}$ .

<h3>Angle between the two vectors</h3>

Let $\theta$ represent the angle between $\vec{u}$ and $\vec{v}$ . Apply the formula $\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ to find the cosine of this angle:

$\begin{aligned} \cos(\theta)&= \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|} = \frac{17}{\sqrt{89}\cdot \sqrt{26}}\end{aligned}$ .

Since $\theta$ is the angle between two vectors, its value should be between $0\; \rm radians$ and $\pi \; \rm radians$ ( $0^\circ$ and $180^\circ$ .) That is: $0 \le \theta < \pi$ and $0^\circ \le \theta < 180^\circ$ . Apply the arccosine function (the inverse of the cosine function) to find the value of $\theta$ :

$\displaystyle \cos^{-1}\left(\frac{17}{\sqrt{89}\cdot \sqrt{26}}\right) \approx 1.21 \;\rm radians \approx 69.3^\circ$ .

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2 years ago

What are the x intercepts

Oksi-84 [34.3K]

Answer

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Step-by-step explanation:x is the connection of the y intercept in a equation dealing with a graph or coordinates.

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3 years ago

Helen bought notebooks and pencils for school. The number of pencils she bought is given by 6(n-3) , where n is the number of no

pychu [463]

So the number of pencils bought can be represented by an equation: $P=6(n-3)$ , where n is the number of notebooks bought. Since Helen bought 5 notebooks, simply plug 5 into n: $P=6(5-3)=6(2)=12$ . So Helen bought 12 pencils.

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3 years ago

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AnnyKZ [126]

Answer:

2 and 3

Step-by-step explanation:

The pair of angles that is complementary are:

2 and 3

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3 years ago

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