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3 years ago

If cos x cos (pi/7)+sin x sin(pi/7)=-(sqrt 2)/2,then x can equal

1 answer:

3 0

Main formula cos (a - b) =cosacosb + sina sinb
arccos(-x) = pi -arccosx

cos x cos (pi/7)+sin x sin(pi/7) = cos(x-pi/7)

so cos(x-pi/7) = -(sqrt 2)/2, x -pi/7 = arc cos[-(sqrt 2)/2 ]= pi - arc cos[(sqrt 2)/2 ]

arc cos[(sqrt 2)/2 ] = Pi/4 + 2kpi, and then x -pi/7 = pi - pi/4 +2kpi,
implies x= -pi/7 + pi - pi/4 = -pi/7 + 3pi/4 = -19pi/28 + 2kpi

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Solve 3x^2= 147 x= X=

marin [14]

Answer:

$3 {x}^{2} = 147 \\ or \: x^{2} = \frac{147}{3} \\ or \: x = \sqrt{49} \\ x = 7$

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2 years ago

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The Varners live on a corner lot. Often children cut across their lot to scar walking distance. The diagram to the right represe

icang [17]

About 12.56 units.
Solve for x by plugging in values into Pythagorean theorem.
$a^{2} +b^{2} = c^{2}$
$x^{2} +(x+12)^{2} = 34^{2}$
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$2x^{2} + 24x+144 = 1156$
Subtract 144 from both sides
$2x^{2} + 24x = 1012$
divide both sides by 2
$x^{2} + 12x = 506$
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$x^{2} + 12x + 36 = 506 +36 . = (x+6)^2 = 542$
take the square root of both sides.
$x+6 = 23.28$
subtract by 6 to get about 17.28 for x.
Plug in values for x to get distance traveled on outside of the yard.
17.28 + (17.28 +12) = 46.56
subtract 34 from the length to get the difference in travel. 46.56-34=12.56

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3 years ago

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3 years ago

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Solve the inequality t/4 >7 And 2c/3 +1>7

Maru [420]

Answer: c > 12

Step-by-step explanation:tep 1 :

Simplify —

Equation at the end of step 1 :

((2 • —) - 1) - 7 > 0

Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 3 as the denominator :

1 1 • 3

1 = — = —————

1 3

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2c - (3) 2c - 3

———————— = ——————

3 3

Equation at the end of step 2 :

(2c - 3)

———————— - 7 > 0

Step 3 :

Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 3 as the denominator :

7 7 • 3

7 = — = —————

1 3

Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions

(2c-3) - (7 • 3) 2c - 24

———————————————— = ———————

3 3

Step 4 :

Pulling out like terms :

4.1 Pull out like factors :

2c - 24 = 2 • (c - 12)

Equation at the end of step 4 :

2 • (c - 12)

———————————— > 0

Step 5 :

5.1 Multiply both sides by 3

5.2 Divide both sides by 2

Solve Basic Inequality :

5.3 Add 12 to both sides

c > 12

Inequality Plot :

5.4 Inequality plot for

0.667 X - 8.000 > 0

One solution was found :

c > 12

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3 years ago

If y = 9 inches, z = 14 inches, h = 5 inches, and w = 4 inches, what is the area of the object?

vekshin1

Answer:

126

Step-by-step explanation:

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1 year ago