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3 years ago

A circle with radius 4 has a sector with central angle of 8/5pi radians.

Mathematics

1 answer:

Olin [163]3 years ago

8 0

Answer:

(64/5)π units²

Step-by-step explanation:

The area of this sector would be:

Given central angle

------------------------------ *(area of whole circle)

2π rad

In this case, the area of the sector is:

(8/5) π rad

------------------------------ * π(4 units)^2

2π rad

and this reduces to:

(4/5) * π*16 units² or (64/5)π units²

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almond37 [142]

Radio Barn : 200 + .15 x x = the weekly sales

Woofer: 300 + .10x

set them equal to find when they are them same

200 + .15x = 300 + .10x

subtract .10x from both sides

200 +.15x -.10x = 300 + .10x-.10x

200 +.05x = 300

subtract 200 from each side

200+.05x -200 = 300-200

.05x = 100

divide each side by .05

.05x/.05 = 100/.05

x =2000

The 2 jobs pay the same when the weekly sales are 2000 dollars

2. {x - 5 = -y}

{2y - 10 = -2x}

x-5 = -y

add 5 to each side

x = -y+5

multiply each side by -2

-2x = 2y -10

the 2 equations are the same, it has an infinite number of solutions

The system is dependent since the 2 equations are the same line

3. {2x = y - 7}

{4x - 2y - 14 = 0}

2x = y-7

subtract y-7 from each side

2x - (y-7) = 0

2x -y+7 =0

multiply by 2

4x -2y +14 =0

subtract the two equations

4x -2y +14 =0

4x - 2y - 14 = 0

---------------------------

28 = 0

since this cannot happen the lines will never cross ( parallel lines)

the system is inconsistent

5 0

3 years ago

How do you interpret algebraic expressions in terms of context

Zepler [3.9K]

By Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity.

5 0

3 years ago

Represent each of these relations on {1, 2, 3, 4} with a matrix (with the elements of this set listed in increasing order). a) {

Irina-Kira [14]

Answer:

for a a) {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}

$\left[\begin{array}{cccc}0&1&1&1\\0&0&1&1\\0&0&0&1\\0&0&0&0\end{array}\right]$

for b

b) {(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)}

$\left[\begin{array}{cccc}1&0&0&1\\0&1&0&0\\0&0&1&0\\1&0&0&0\end{array}\right]$

for c) {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}

$\left[\begin{array}{cccc}0&1&1&1\\1&0&1&1\\1&1&0&1\\1&1&1&0\end{array}\right]$

for d d) {(2, 4), (3, 1), (3, 2), (3, 4)}

$\left[\begin{array}{cccc}0&0&0&0\\0&0&0&1\\1&1&0&1\\0&0&0&0\end{array}\right]$

Step-by-step explanation:

in matrix, arrays are placed in rows , which represents the horizontal sides from left to right, while arrays in the column are placed vertically from top to bottom. Here, we placed the arrays in a 4x4 matrix

for a a) {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}

$\left[\begin{array}{cccc}0&1&1&1\\0&0&1&1\\0&0&0&1\\0&0&0&0\end{array}\right]$

for b

b) {(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)}

$\left[\begin{array}{cccc}1&0&0&1\\0&1&0&0\\0&0&1&0\\1&0&0&0\end{array}\right]$

for c) {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}

$\left[\begin{array}{cccc}0&1&1&1\\1&0&1&1\\1&1&0&1\\1&1&1&0\end{array}\right]$

for d d) {(2, 4), (3, 1), (3, 2), (3, 4)}

$\left[\begin{array}{cccc}0&0&0&0\\0&0&0&1\\1&1&0&1\\0&0&0&0\end{array}\right]$

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4 years ago

Howard Slater age 44 an actor expected his income to the coin future years he decides to take out a 20-year payment life policy

SpyIntel [72]

Answer:

Individuals end to continue paying the premiums of the automobile insurance as a habit. However, serious thoughts and putting in element of strategizing helps to reduce the premium in most cases. At times, there is a sudden like on the part of the insurer even for a flawless driver.

A good look up and research of the insurance websites can be of real help in comparing whether a better deal is offered by the other insurance companies, or whether a certain change in the policy or small adjustments of the term would give benefit to the customer.

In case a speeding ticket is received, or an accident is mentioned in the driving history, it is maintained there in for a period of three to five years. Thus, the premium increases substantially. A change of insurer is advised in such situations, where a major search for an insurer, who does not pay that much importance to these details, is to be carried on.

Again, having a teenager driver in the family calls for a caution as the insurance premium increases drastically in such occasion. Having clean driving record of the parents, or kids commuting to far away schools without cars help in such situation.

5 0

4 years ago

Sec s = 1.6948

Anastaziya [24]

That'd be true only if the value of "s" is the exact same one for both
namely if sec(s) = cos(s)
then solving for "s"
thus

$\bf sec(s)=cos(s)\qquad but\implies sec(\theta)=\cfrac{1}{cos(\theta)}
\\\\\\
thus\cfrac{1}{cos(s)}=cos(s)\implies 1=cos^2(s)\implies \pm \sqrt{1}=cos(s)
\\\\\\
\pm 1=cos(s)\impliedby \textit{now taking }cos^{-1}\textit{ to both sides}
\\\\\\
cos^{-1}(\pm 1)=cos^{-1}[cos(s)]\implies cos^{-1}(\pm 1)=\measuredangle s$

5 0

3 years ago