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3 years ago

What is the simplified form of the expression square root 1 over 121???

2 answers:

5 0

We are given the expression of square root of one over 121 and is asked to simplify the expression. Simply, to answer this question, we take the square root of each number. square root of 1 is 1 while the square root of 121 is 11. Hence the simplified expression becomes 1/11.

jenyasd209 [6]3 years ago

5 0

Answer:

$\frac{1}{11}$

Step-by-step explanation:

$\sqrt{\frac{1}{121} }$

To simplify the square root we take square root at the top and bottom separately.

$\sqrt{\frac{1}{121} }$

$\frac{\sqrt{1}}{\sqrt{121}}$

square root (1)=1

square root of 121 is 11

So the fraction becomes

$\frac{\sqrt{1}}{\sqrt{121}}$

$\frac{1}{11}$

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Rodney can wash 24 windows in an hour how many windows can he wash in 1/8 of an hour

Viktor [21]

Answer:

Step-by-step explanation:

24x (1/8) = 3

hope this helps

3 0

3 years ago

What is the modulus and argument after (StartRoot 3 EndRoot) (cosine (StartFraction pi Over 18 EndFraction) + I sine (StartFract

fgiga [73]

Answer:

$|z| = 27$ -- Modulus

$\theta = \frac{\pi}{3}$ --- Argument

Step-by-step explanation:

Given

$((\sqrt 3)(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18}))^6$

Required

Determine the modulus and the argument

We have that:

$z = ((\sqrt 3)(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18}))^6$

Expand:

$z = (\sqrt 3)^6(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18})^6$

$z = 27(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18})^6$

A complex equation can be expressed as:

$z = |z| e^{i\theta}$

Where

$|z| = modulus$

$\theta = argument$

Where

$e^{i\theta} = (cos\frac{\pi}{18} + i\ sin\frac{\pi}{18})$

So:

$z = 27(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18})^6$ becomes

$z = 27(e^{i\frac{\pi}{18}})^6$

By comparison:

$e^{i\theta} = (e^{i\frac{\pi}{18}})^6$

This gives:

${i\theta} = i\frac{\pi}{18}}*6$

${i\theta} = i\frac{6\pi}{18}}$

${i\theta} = i\frac{\pi}{3}}$

Divide through by i

$\theta = \frac{\pi}{3}$

Hence, the modulus, z is:

$|z| = 27$

And the argument $\theta$ is

$\theta = \frac{\pi}{3}$

4 0

3 years ago

Write an equation of the perpendicular bisector of the segment with end points M(1,5) and N(7,-1)

vitfil [10]

The perpendicular bisector of the segment passes through the midpoint of this segment. Thus, we will initially find the midpoint P:

$P=\dfrac{(1,5)+(7,-1)}{2}=\dfrac{(8,4)}{2}=(4,2)$

Now, we will calculate the slope of the segment support line (r). After this, we will use the fact that the perpendicular bisector (p) is perpendicular to r:

$m_r=\dfrac{\Delta y}{\Delta x}=\dfrac{5-(-1)}{1-7}=\dfrac{6}{-6}\iff m_r=-1$

$p\perp r\Longrightarrow m_p\cdot m_r=-1\Longrightarrow m_p\cdot(-1)=-1\iff m_p=1$

We can calculate the equation of p by using its slope and its point P:

$y-y_P=m_p(x-x_P)\\\\
y-2=1\cdot(x-4)\\\\
y-2=x-4\\\\
\boxed{p:~~y=x-2}$

4 0

3 years ago

form a polynomial function whose real zeros are -2 with multiplicity 2 and 4 with multiplicity 1 whose degree is 3

NeTakaya

Answer:

$f(x) = {x}^{3} -12x - 16$

Step-by-step explanation:

We want to for a polynomial function whose real zeros are -2 with multiplicity 2 and 4 with multiplicity 1.

If -2 is a zero of a polynomial, then by the factor theorem, x+2 is a factor.

Since -2 has multiplicity 2, (x+2)² is a factor.

Also 4 is a zero which means x-4 is a factor.

We write the polynomial in factored form as:

$f(x) = {(x + 2)}^{2} (x - 4)$

We expand to get:

$f(x) = ({x}^{2} + 4x + 4)(x - 4)$

We expand further to get:

$f(x)=x({x}^{2} + 4x + 4) - 4({x}^{2} + 2x + 4)$

$f(x) = {x}^{3} + 4 {x}^2 + 4x - 4 {x}^{2} + 8x - 16$

$f(x) = {x}^{3} - 12x - 16$

4 0

3 years ago

Kathy has 3/4 of a yard of fabric. She needs 3/10 of a yard for each doll dress she makes. How many doll dresses can she make?

NeTakaya

In order to calculate correctly, it is important that we are able to understand well the given values. We have
3/4 yard fabric = total amount of available fabric
3/10 yard= amount needed to make one doll
Therefore,
number of doll dresses = 3/4 / 3/10 = 2 doll dresses

4 0

4 years ago