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3 years ago

Is it true that a plane consists of an infinite set of lines?

Mathematics

1 answer:

svet-max [94.6K]3 years ago

5 0

Its depends on what you are working on

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Let f be the following piecewise-defined function. f(x)equals left brace Start 2 By 1 Matrix 1st Row 1st Column x squared plus

Colt1911 [192]

Answer:

the function is continuous but not differentiable in x=3

Step-by-step explanation:

for f(x) defined as

x²+5 for x≤3

3*x+5 for x>3

then for f to be continuous then

when x→a , lim f(x) = f(a)

thus

from the left

when x→3⁻ , lim f(x) = lim x²+5 = 3²+5 = 14

from the right

when x→3⁺ , lim f(x) = lim 3*x+5 = 3*3+5 = 14

and f(3) = 3²+5 = 14

since both limits converge and are equal to f(3), then the function is continuous in 3

Nevertheless, the function is not differentiable in 3 since the curve is not smooth in f(3) ( it has an sharp change in f(3) ) , then the function is not differentiable in x=3

to prove it , when x=3 and

when h→0⁻ , f'(x=3)= lim [f(x+h)-f(x)] /h = lim [(x+h)²+5 - (x² + 5)]/h = lim [2*x*h+h²] /h = lim [2*x+h] = 2*3+0 = 6

when h→0⁺ , f'(x=3)= lim [f(x+h)-f(x)] /h = lim [3*(x+h)+5 - (3*x + 5)]/h = lim [3*h] /h = lim 3 = 3

since the limits do not converge →the limit does not exist → the derivative does not exist → the function is not differentiable in x=3

4 0

4 years ago

Milena wants to power toy cars and helicopters using batteries. Her goal is to power at least 11 toys with a most 60 batteries .

Anni [7]

Answer:

8 helicopters at most

Step-by-step explanation:

I worked on this problem and that was the answer not 99 like the other.

6 0

3 years ago

A test consists of 10 multiple choice questions, each with five possible answers, one of which is correct. To pass the test a st

Softa [21]

Answer:

0.006369

Step-by-step explanation:

Given that a test consists of 10 multiple choice questions, each with five possible answers, one of which is correct.

By mere guessing p = probability for a right answer = 1/5 =0.20

There are two outcomes and each question is independent of the other.

X no of questions right is Bin (10,0.20)

the probability that the student will pass the test

= prob of getting more than 60%

= $P(X\geq 6)$

=0.006369

8 0

4 years ago

What is the solution (ordered pair) for the following system of equations? 4x + 3y = 9 and 2x - y = 7?

Naddika [18.5K]

Solve for the first vaiable in one of the equation, then substitute the result into the other equation.

Point Form:

(3, -1)

Equation Form:

x = 3

y = -1

8 0

3 years ago

Express each product in the simplest form. 3wx\6x * 3wx\9w

san4es73 [151]

3wx/6x * 3wx/9w = w/2 • x/3 = xw/6

Answer: xw/6

3 0

4 years ago