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2 years ago

What is the proof the formula for cos(A+B)=cosAcosB-sinAsinB?

1 answer:

8 0

Given data, cos(A - B) = cosAcosB + sinAsinB
let, A=60' and B=30' ( here the ' sign bears degree) 
L.H.S = cos(A - B) 
=cos (60'-30) ( using value of A and B ) 
=cos30' 
= sqrt3/2 
R.H.S= cosAcosB + sinAsinB 
=cos60' cos30' + sin60' sin30' 
= 1/2* sqrt3/2+ sqrt3/2*1/2 
= sqrt3/4 + sqrt3/4 
=2 sqrt3/4 
= sqrt3/2 
so L.H.S =R.H.S or cos(A - B) = cosAcosB + sinAsinB

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Find FL if H is the circumcenter of EFG,

Zanzabum

The artistic crop isn't helpful; it cuts off some vertex names.

The circumcenter H is the meet of the perpendicular bisectors of the sides, helpfully drawn. We have right triangle ELH, right angle L, so

EH² = HL² + EL²

EL = √(EH² - HL²) = √(5.06²-2.74²) ≈ 4.2539393507665339

Since HL is a perpendicular bisector of EF, we get congruent segments FL=EL.

Answer: 4.25

8 0

2 years ago

A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like

mixas84 [53]

Answer:

a) $\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) $\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) the steady state mass of the drug is 2000 mg

d) t ≅ 153.51 minutes

Step-by-step explanation:

From the given information;

At time t= 0

an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500

The inflow rate is 0.06 L/min.

Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant.

The objective of the question is to calculate the following :

a) Write an initial value problem that models the mass of the drug in the blood for t ≥ 0.

From above information given :

$Rate _{(in)}= 500 \ mg/L \times 0.06 \ L/min = 30 mg/min$

$Rate _{(out)}=\dfrac{x}{4} \ mg/L \times 0.06 \ L/min = 0.015x \ mg/min$

Therefore;

$\dfrac{dx}{dt} = Rate_{(in)} - Rate_{(out)}$

with respect to x(0) = 0

$\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.

$\dfrac{dx}{dt} = -0.015(x - 2000)$

$\dfrac{dx}{(x - 2000)} = -0.015 \times dt$

By Using Integration Method:

$ln(x - 2000) = -0.015t + C$

$x -2000 = Ce^{(-0.015t)$

$x = 2000 + Ce^{(-0.015t)}$

However; if x(0) = 0 ;

Then

C = -2000

Therefore

$\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) What is the steady-state mass of the drug in the blood?

the steady-state mass of the drug in the blood when t = infinity

$\mathbf{x = 2000 - 2000e^{-0.015 \times \infty }}$

x = 2000 - 0

x = 2000

Thus; the steady state mass of the drug is 2000 mg

d) After how many minutes does the drug mass reach 90% of its stead-state level?

After 90% of its steady state level; the mas of the drug is 90% × 2000

= 0.9 × 2000

= 1800

Hence;

$\mathbf{1800 = 2000 - 2000e^{(-0.015t)}}$

$0.1 = e^{(-0.015t)$

$ln(0.1) = -0.015t$

$t = -\dfrac{In(0.1)}{0.015}$

t = 153.5056729

t ≅ 153.51 minutes

4 0

2 years ago

Arti is mixing some orange paint for the class mural.

vitfil [10]

Answer:

Step-by-step explanation:

6 0

2 years ago

Suppose 50 percent of the customers at Pizza Palooza order a square pizza, 70 percent order a soft drink, and 35 percent order b

Firdavs [7]

Answer:

Ordering a soft drink is independent of ordering a square pizza.

Step-by-step explanation:

20% more customers order a soft drink than pizza, therefore they cannot be intertwined.

Given: P(A)=0.5 & P(B)=.7

P(A∩B) = P(A) × P(B)

= 0.5 × .7

= 0.35

P(A∪B) = P(A) + P(B) - P(A∩B)

= 0.5 + .7 - 0.35

= 0.85

P(AΔB) = P(A) + P(B) - 2P(A∩B)

= 0.5 + .7 - 2×0.35

= 0.5

P(A') = 1 - P(A)

= 1 - 0.5

= 0.5

P(B') = 1 - P(B)

= 1 - .7

= 0.3

P((A∪B)') = 1 - P(A∪B)

= 1 - 0.85

= 0.15

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2 years ago

The table gives the probabilities that new cars of different models will have brake failure. The car model that is least likely

melamori03 [73]

All the information we have are the probabilities, and what we need is the lowest number: so let's choose the smallest probability among the numbers: 0.0065%, B 0.0037%,C 0.0108%,D 0.0029%, E 0.0145%. The smallest of the numbers is 0.0029% -it starts with two 00s and the number that follows, 2, is smaller than all there others - so the smallest probability is in option D - and the model would be the corresponding model (but we're missing some information here)

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2 years ago

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