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2 years ago

7

While crossing the Atlantic, sailors spot two mermaids 120° apart on each end of an island that is 6 miles away. How far apart a

re the mermaids around the outer edge of the island to the nearest tenth of a mile?
A. 12.6 miles
B. 3.1 miles
C. 7.2 miles
D. 20.2 miles

1 answer:

Ann [662]2 years ago

3 0

First thing to do is to remember, that the circumference of the full circle is 2(6)pi--12pi. you only want about 120 of it so (120/360)=1/3, so you add it into the thing earlier to get, 12pi(1/3)=4pi =12.566... which you can round into 12.6. This is answer choice A.

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EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

Valentin [98]

If there is such a scalar function <em>f</em>, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to <em>x</em> :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to <em>y</em> :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to <em>y</em> :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to <em>z</em> :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

7 0

2 years ago

In △ABC, m∠A=15 °, a=10 , and b=11 . Find c to the nearest tenth.

pshichka [43]

Answer:

The answer is:

$\bold{c\approx 20.2\ units}$

Step-by-step explanation:

Given:

In △ABC:

m∠A=15°

a=10 and

b=11

To find:

c = ?

Solution:

We can use cosine rule here to find the value of third side c.

Formula for cosine rule:

$cos A = \dfrac{b^{2}+c^{2}-a^{2}}{2bc}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

Putting all the values.

$cos 15^\circ = \dfrac{11^{2}+c^{2}-10^{2}}{2\times 11 \times c}\\\Rightarrow 0.96 = \dfrac{121+c^{2}-100}{22c}\\\Rightarrow 0.96 \times 22c= 121+c^{2}-100\\\Rightarrow 21.25 c= 21+c^{2}\\\Rightarrow c^{2}-21.25c+21=0\\\\\text{solving the quadratic equation:}\\\\c = \dfrac{21.25+\sqrt{21.25^2-4 \times 1 \times 21}}{2}\\c = \dfrac{21.25+\sqrt{367.56}}{2}\\c = \dfrac{21.25+19.17}{2}\\c \approx 20.2\ units$

The answer is:

$\bold{c\approx 20.2\ units}$

4 0

2 years ago

Which equation is the inverse of y = 2x2 – 8?

Marrrta [24]

The inverse of the the function above is y = $\sqrt{\frac{x+8}{2}}$

In order to find the inverse of any function, you need to switch the x and y values. Once you've done that, you need to solve for the new y value. The resulting equation will be your inverse. The work for this one is below.

y = 2x^2 - 8 ----> Switch the terms

x = 2y^2 - 8 ----> Add 8 to both sides.

x + 8 = 2y^2 ----> Divide both sides by 2.

$\frac{x+8}{2}$ = y^2 ----> Now take the square root of both sides.

$\sqrt{\frac{x+8}{2}}$ = y

What's left is your inverse. You can change the order so that it is in a more acceptable form.

y = $\sqrt{\frac{x+8}{2}}$

6 0

2 years ago

If mAC 178°, and mBC= 42°, what is m∠BDC? 110° 65° 68° 136°

Viktor [21]

<span>m∠BDC = 1/2(178 - 42)
</span><span>m∠BDC = 1/2(136)
</span><span>m∠BDC = 68

answer
</span><span>68° </span>

4 0

2 years ago

Read 2 more answers

Suppose that a process is currently operating at a 3.5-sigma quality level, and it is planned to use improvement projects to mov

jenyasd209 [6]

Answer:

$11,373 PPM$

Step-by-step explanation:

The following formula is used to compute the Proportion of error-free units given the sigma level in Excel.

<em> The proportion of error-free units = NORMSDIST(Sigma Level - 1.5) </em>

Suppose that a process is currently operating at a 3.5-sigma quality level.

The proportion of error-free units for this process is

NORMSDIST(3.5 - 1.5) = 0.977250

Therefore, the rejection rate is equal to

$1 - 0.977250 = 0.022750$

or 22750 PPM.

Now, consider a 6-sigma level process.

The proportion of error-free units equals

NORMSDIST(6.0 - 1.5) = 0.9999966

and the rejection rate is

$1 - 0.9999966 = 3.4 PPM$

Hence, reduction is PPM required per year , that is

$\dfrac{22750 - 3.4}{2} = 11,373 PPM$

reduction per year

7 0

2 years ago