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3 years ago

The area of a circle is less than 1 dm². Find the radius of the circle.

Mathematics

1 answer:

KATRIN_1 [288]3 years ago

4 0

Answer:

Step-by-step explanation:

pi r^2 < 1

r^2 < 1/π

r < 1/√π dm

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Verify the identity. <br><br> cos 4x + cos 2x = 2 - 2 sin^2(2x) - 2 sin^2 x

Advocard [28]

So are you trying to simplify one side to get it to look like the other?

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2 years ago

What is the best method to be use in solving quadratic equation x²+16x+63=0?

Strike441 [17]

Answer:

Factorization

Step-by-step explanation:

This can be easily factorized into (x+7)(x+9)=0 which can be solved for the two roots x = -7 and x = -9

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3 years ago

Find the EXACT value of sin(A−B) if cos A = 3/5 where A is in Quadrant IV and cos B = 12/13 where B is in Quadrant IV. Assume al

MissTica

$\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta)$

well, for both angles A and B we're on the IV Quadrant, meaning, the sine is negative, the cosine is positive, likewise, the opposite side is negative and the adjacent side for the angle is positive.

$\bf cos(A)=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\qquad \qquad \stackrel{\textit{getting the opposite side}}{b=\pm\sqrt{5^2-3^2}}\implies b = \pm 4 \\\\\\ \stackrel{IV~Quadrant}{b = -4}\qquad \qquad sin(A)=\cfrac{\stackrel{opposite}{-4}}{\underset{hypotenuse}{5}} \\\\[-0.35em] ~\dotfill\\\\ cos(B)=\cfrac{\stackrel{adjacent}{12}}{\underset{hypotenuse}{13}}\qquad \qquad \stackrel{\textit{getting the opposite side}}{b=\pm\sqrt{13^2-12^2}}\implies b = \pm 5$

$\bf \stackrel{IV~Quadrant}{b = -5}\qquad \qquad sin(B)=\cfrac{\stackrel{opposite}{-5}}{\underset{hypotenuse}{13}} \\\\[-0.35em] ~\dotfill\\\\ sin(A-B)=\cfrac{-4}{5}\cdot \cfrac{12}{13}-\left( \cfrac{3}{5}\cdot \cfrac{-5}{13} \right)\implies sin(A-B)=\cfrac{-48}{65} - \left( \cfrac{-15}{65} \right) \\\\\\ sin(A-B)=\cfrac{-48}{65} + \cfrac{15}{65}\implies sin(A-B)=\cfrac{-33}{65}$

4 0

2 years ago

Solve the triangle for x.

Damm [24]

Answer:

d) 86.2 degrees

x = 86.20°

Attached is the image used in the question;

Step-by-step explanation:

Applying the law of cosine;

Cos C = (a² + b² - c²)/2ab

Where;

Angle C = x

c = 13 ft

b = 9ft

a = 10ft

Substituting into the equation;

Cos x = (10² + 9² - 13²)/(2×10×9)

Cos x = 0.0667

x = cos⁻¹(0.0667)

x = 86.20°

4 0

3 years ago

Write and solve an equation to represent the following situation.

LuckyWell [14K]

Answer:

$6 + 7x = 27$

$x = 3cm$

Step-by-step explanation:

so the question lets us know 3 things:

1) Sarah has a 27 ft pipe

2) she cuts 6 ft off

3) she cuts remaining pipe into 7 equal sections

what we don't know from the question is how big each of those 7 sections were. To form the equation we do this.

Since we know Sarah has 27 ft of pipe that would be our answer of the equation.

Sarah also removed 6 ft and the rest of the pipe she cut up into 7 small sections of equal length. since we don't know the length of the 7 smaller sections we will use the variable X to represent the length. this means that 6ft + 7x (X is the length of the pipes, and we multiply by 7 since there are 7 of them) must equal Sarah's total length of 27ft, therefore meaning our education would be

$6 + 7x = 27$

to solve for how long each pipe was, we need to solve for X by rearranging the equation as shown bellow.

$7x = 27 - 6$

$7x = 21$

$x = \frac{21}{7}$

$x = 3cm$

4 0

2 years ago