What are the solutions for the equation 2cos0+1=0 ?

Define f(0,0) in a way that extends f to be continuous at the origin. f(x, y) = ln ( 19x^2 - x^2y^2 + 19 y^2/ x^2 + y^2) Let f (

kirill115 [55]

Answer:

f(0,0)=ln19

Step-by-step explanation:

$f(x,y)=ln(\frac{19x^2-x^2y^2+19y^2}{x^2+y^2})$ is given as continuous function, so there exist $lim_{(x,y)\rightarrow(0,0)}f(x,y)$ and it is equal to f(0,0).

Put x=rcosA annd y=rsinA

$f(r,A)=ln(\frac{19r^2cos^2A-r^2cos^2A*r^2sin^2A+19r^2sin^2A}{r^cos^2A+r^2sin^2A})=ln(\frac{19r^2(cos^2A+sin^2A)-r^4cos^2Asin^a}{r^2(cos^2A+sin^2A)})$

we know that $cos^2A+sin^2A=1$ , so we have that

$f(r,A))=ln(\frac{19r^2-r^4cos^2Asin^a}{r^2})=ln(19-r^2cos^2Asin^2A)$

$lim_{(x,y)\rightarrow(0,0)}f(x,y)=lim_{r\rightarrow0}f(r,A)=ln19$

So f(0,0)=ln19.

8 0

2 years ago

There are 8 runners in a race. What is the probability that Abby, Becca, and Carmen place first, second, and third in any order?

Mkey [24]

$|\Omega|=8!\\
|A|=3!\cdot5!\\\\
P(A)=\dfrac{3!5!}{8!}=\dfrac{2\cdot3}{6\cdot7\cdot8}=\dfrac{1}{56}\approx1,8\%$

3 0

2 years ago

Read 2 more answers

What are the differences among an experiment, a study, and a survey? Complete the explanation of the differences by selecting th

artcher [175]

Answer:

The full question is

What are the differences among an experiment, a study, and a survey?

1. In an observational study, randomization of subjects ______

A. occurs

B. does not occur

We understand randomization as a random process of assigning experimental subjects to treatment groups. Through this process, we have more control about variables which are not related to the experiment.

In an observational study, the researcher doesn't change anything, he or she studies the events as they are, without using any randomization process.

Therefore, the right answer here is B. 

2. A survey _______

A. poses no interference on subjects

B. makes inferences about a population

A survey poses no interference on subjects, actually if it does, then that survey is not reliable. An important charactersitic of a survey is that it must be objective, that way it will be reliable enough to use it in the research.

Therefore, the right answer is A.

3. In an experiment, ___________ to discern differences in a response variable.

A. treatment is imposed

B. inferences are made

C. randomization does not occur

Experiments are characterized by having certain "stimulus" at least in one group of subjects, that way researches compare data sets to prove their hypothesis.

Therefore, the right answer here is A.

8 0

2 years ago

It takes 45 minutes to drive to the nearest bowling alley taking city streets going

Savatey [412]

Answer:

21 minutes

Step-by-step explanation:

Given the following :

Taking CITY STREET:

Time taken to drive to nearest bowling alley = 45 minutes = 45/60 = 0.75 hours

Speed of travel = 30 miles per hour

Taking FREEWAY:

speed of travel = 65miles per hour

If the distance to bowling alley is the same along both routes, The time taken along FREEWAY will be :

.

Distance to bowling alley taking city center :

Speed = distance / time

30 mph = distance / 0.75 hour

Distance = 30 × 0. 75 = 22.5 miles

Since distance is the same :

Time taken along FREEWAY :

Time taken = distance / speed

Time taken = 22.5 / 65 = 0.3461538 hour

Converting to minutes :

0.3461538 × 60 = 20.769 minutes

= 21 minutes ( to the nearest minute)

7 0

2 years ago

A heap of grain is shaped as a cone ADCF with height 5 m and base radius 2 m, as shown on the diagram. A and C are points on the

hoa [83]

Answer:

The angle between [A_F] and the base of the cone = 68.2°

The area of the base of the cone ≈ 12.57 m²

Step-by-step explanation:

The given parameters are;

The height of the cone = 5 m

The base radius of the cone = 2 m

The angle which the A $\hat O$ C = 120°

Therefore, we have;

The angle between [A_F] and the base of the cone = The angle between [CF] and the base of the cone

The angle between [CF] and the base of the cone = tan⁻¹(5/2) = tan⁻¹(2.5) ≈ 68.2°

∴ The angle between [A_F] and the base of the cone = The angle between [CF] and the base of the cone = 68.2°

The angle between [A_F] and the base of the cone = 68.2°

The area of the base of the cone = π × r² = π × 2² = 4·π ≈ 12.57

The area of the base of the cone ≈ 12.57 m².

8 0

2 years ago