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4 years ago

15

Which statement is true? A 10° angle is congruent to a 10° angle. Congruent angles always add up to 90°. A congruent angle is al

ways 90°. none of the above

1 answer:

Ainat [17]4 years ago

7 0

The first statement is correct. Congruent angles have the same angles.

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An electric current, I, in amps, is given by I=cos(wt)+√8sin(wt), where w≠0 is a constant. What are the maximum and minimum valu

exis [7]

Take the derivative with respect to t
$- w \sin(wt) + \sqrt{8} w cos(wt)$
the maximum and minimum values occur when the tangent line is zero so we set the derivative to zero
$0 = -w \sin(wt) + \sqrt{8} w cos(wt)$
divide by w
$0 =- \sin(wt) + \sqrt{8} cos(wt)$
we add sin(wt) to both sides

$\sin(wt)= \sqrt{8} cos(wt)$
divide both sides by cos(wt)
$\frac{sin(wt)}{cos(wt)}= \sqrt{8} \\ \\ arctan(tan(wt))=arctan( \sqrt{8} ) \\ \\ wt=arctan(2 \sqrt{2)}$ OR $\\$ $wt=arctan( { \frac{1}{ \sqrt{2} } )$
(wt)=2(n*pi-arctan(2^0.5))
(wt)=2(n*pi+arctan(2^-0.5))
where n is an integer
the absolute max and min will be

$I=cos(2n \pi -2arctan( \sqrt{2} ))$
since 2npi is just the period of cos
$cos(2arctan( \sqrt{2} ))= \frac{-1}{3} 
$
substituting our second soultion we get
$I=cos(2n \pi +2arctan( \frac{1}{ \sqrt{2} } ))$
since 2npi is the period
$I=cos(2arctan( \frac{1}{ \sqrt{2}} ))= \frac{1}{3}$
so the maximum value = $\frac{1}{3}$
minimum value = $- \frac{1}{3}$

4 0

3 years ago

What is the volume of the right rectangular prism?

ddd [48]

Answer:

i think its 735

Step-by-step explanation:

since the base is a square it should be a whole square which is 7 and the height is 15 and v=whl and multiply all of it 7 times 7 is 49 times 15 is 735.

5 0

3 years ago

In a completely randomized design involving three treatments, the following information is provided:Treatment 1Treatment 2Treatm

Aliun [14]

Answer:

7.25

Step-by-step explanation:

Given :

___________ Sample size __ sample mean

Treatment 1 ____ 5 _______ 4

Treatment 2 ____ 10 ______ 8

Treatment 3 ____ 5 _______ 9

Sample size = (5 + 10 + 5). = 20

Overall mean = ((5*4). + (10*8) + (5*9)) / 20

Overall mean = (20 + 80 + 45) / 20

= 145 / 20

= 7.25

6 0

3 years ago

Please Help !!!

solong [7]

Best Answer: 2 LiCl = 2 Li + Cl2
mass Li = 56.8 mL x 0.534 g/mL=30.3 g
moles Li = 30.3 g / 6.941 g/mol=4.37
the ratio between Li and LiCl is 2 : 2 ( or 1 : 1)

moles LiCl required = 4.37
mass LiCl = 4.37 mol x 42.394 g/mol=185.3 g

Cu + 2 AgNO3 = Cu/NO3)2 + 2 Ag
the ratio between Cu and AgNO3 is 1 : 2
moles AgNO3 required = 4.2 x 2 = 8.4 : but we have only 6.3 moles of AgNO3 so AgNO3 is the limiting reactant
moles Cu reacted = 6.3 / 2 = 3.15
moles Cu in excess = 4.2 - 3.15 =1.05

N2 + 3 H2 = 2 NH3
moles N2 = 42.5 g / 28.0134 g/mol=1.52
the ratio between N2 and H2 is 1 : 3
moles H2 required = 1.52 x 3 =4.56
actual moles H2 = 10.1 g / 2.016 g/mol= 5.00 so H2 is in excess and N2 is the limiting reactant
moles NH3 = 1.52 x 2 = 3.04
mass NH3 = 3.04 x 17.0337 g/mol=51.8 g
moles H2 in excess = 5.00 - 4.56 =0.44
mass H2 in excess = 0.44 mol x 2.016 g/mol=0.887 g

5 0

4 years ago

How can you tell if a function is linear by looking at the graph or the equation

MrMuchimi

Every linear graph is just a straight line, so if there are any curves or unnatural shapes, than you know it is not linear. As for equations, if it can be shaped into y=mx+b where m and b are numbers, then it will be a linear equation.

7 0

3 years ago