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2 years ago

Which statement is NOT true?

2 answers:

iogann1982 [59]2 years ago

4 0

C."<em>Two lines lie in one plane if and only if the lines are parallel" </em>is a wrong statement.
To lie in the one same plane, the two lines need not be parallel.
So, the answer is option C.

laila [671]2 years ago

4 0

Answer:

A. If two coplanar lines do not intersect, then the lines are parallel. This is true. Two lines are parallel lines if they are coplanar and do not intersect.

B. Two lines lie in one plane and do not intersect if and only if the two lines are parallel. This is true. Only parallel lines lying in a plane do not intersect.

C. Two lines lie in one plane if and only if the lines are parallel. This is false. Two lines in the same 3 d space which do not intersect need not be parallel. They are parallel only if they lie in a common plane. If not, they are called skew lines.

D. If two lines are parallel, then they lie in one plane and do not intersect. Yes this is true.

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Evaluate the iterated integral. $$ \int\limits_0^{2\pi}\int\limits_0^y\int\limits_0^x {\color{red}9} \cos(x+y+z)\,dz\,dx\,dy $$

KengaRu [80]

$\displaystyle\int_{y=0}^{y=2\pi}\int_{x=0}^{x=y}\int_{z=0}^{z=x}\cos(x+y+z)\,\mathrm dz\,\mathrm dx\,\mathrm dy=\int_{y=0}^{y=2\pi}\int_{x=0}^{x=y}\sin(x+y+z)\bigg|_{z=0}^{z=x}\,\mathrm dx\,\mathrm dy$
$\displaystyle=\int_{y=0}^{y=2\pi}\int_{x=0}^{x=y}\sin(2x+y)-\sin(x+y)\,\mathrm dx\,\mathrm dy$
$\displaystyle=\int_{y=0}^{y=2\pi}-\frac12\left(\cos(2x+y)-2\cos(x+y)\right)\bigg|_{x=0}^{x=y}\,\mathrm dx\,\mathrm dy$
$\displaystyle=\int_{y=0}^{y=2\pi}-\frac12\left((\cos3y-2\cos2y)-(\cos y-2\cos y)\right)\bigg|_{x=0}^{x=y}\,\mathrm dy$
$\displaystyle=-\frac12\int_{y=0}^{y=2\pi}(\cos3y-2\cos2y+\cos y)\,\mathrm dy$
$\displaystyle=-\frac12\left(\frac13\sin3y-\sin2y+\sin y\right)\bigg|_{y=0}^{y=2\pi}$
$=0$

4 0

3 years ago

Adam put $100 in a savings account. After 10 years, he had $1649 in the account. What rate of interest did he earn? Use the form

Rina8888 [55]

Answer:

Step-by-step explanation: C. 28%

$A = Pe^{rt}$

$1649 = 100 \cdot e^{10r}\\16.49 = e^{10r}\\\ln{16.49} = 10r\\r = \frac{\ln{16.49}}{10} = 0.28\\$

7 0

2 years ago

Multiply Conjugates Using the Product of Conjugates Pattern

weeeeeb [17]

Answer:

The product is the difference of squares is $\left(xy-9\right)\left(xy+9\right)={{x}^2}{{y}^2}-81$

Step-by-step explanation:

Explanation

The given expression is (x y-9)(x y+9).
We have to multiply the given expression.
Square the first term xy. Square the last term 9 .

$\begin{aligned}&(x y-9)(x y+9)=(x y)^{2}-(9)^{2} \\&(x y-9)(x y+9)=x^{2} y^{2}-81\end{aligned}$

5 0

1 year ago

Two trains, Train A and Train B, simultaneously depart Station A and Station B. Station A and Station B are 252.5 miles apart fr

omeli [17]

-- The trains start moving at the same time.

-- The space between them is initially 252.5 miles.

-- They reduce the distance between them at the rate of (124.7+253.5)=378.2mph.

-- It will take them (252.5 / 378.2) = 0.6676 hour to meet.

That's 40min 3.49sec .

-- After tooting and puffing toward each other for 8 minutes, they still have <em>32min 3.49sec</em> to go before they meet each other. We're all hoping that they're on different tracks.

4 0

2 years ago

Whats the inverse of y=0.07x

dmitriy555 [2]

Answer: y=0

Step-by-step explanation: i think this is right

3 0

2 years ago