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zmey [24]
3 years ago
11

HELP ASAP! I WILL MARK BRIANLIST! THANK YOU (:

Mathematics
1 answer:
bonufazy [111]3 years ago
6 0
The answer is 3 just took the test
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Let f be the function defined as follows:
katen-ka-za [31]

With f defined by

f(x)=\begin{cases}|x-1|+2&\text{for }x

in order for it to be continuous at x=c, we require

\displaystyle\lim_{x\to c^-}f(x)=\lim_{x\to c^+}f(x)=f(c)

(i) If a=2 and b=3, then f(1)=2(1)^2+3(1)=5 and

\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1}|x-1|+2=2

\displaystyle\lim_{x\to1^+}f(x)=\lim_{x\to1}2x^2+3x=5

The limits don't match, so f is not continuous at x=1 under these conditions.

(ii) To establish continuity at x=1, we'd need the limit as x\to1 from the right to be equal to the limit from the left, or

\displaystyle\lim_{x\to1}ax^2+bx=\lim_{x\to1}|x-1|+2\iff a+b=2

(iii) We have f(2)=0 and

\displaystyle\lim_{x\to2^-}f(x)=\lim_{x\to2}ax^2+bx=4a+2b

\displaystyle\lim_{x\to2^+}f(x)=\lim_{x\to2}5x-10=0

For f to be continuous at x=2, then, we'd need to have

4a+2b=0

(iv) Taking both requirements from parts (ii) and (iii), we solve for a,b:

\begin{cases}a+b=2\\4a+2b=0\end{cases}\implies a=-2,b=4

I've attached a plot that confirms this is correct.

7 0
3 years ago
What is the cost of buying 10 tickets if 4 tickets cost 122 dollars?
Hitman42 [59]

Answer:

$305

Step-by-step explanation:

4 tickets = $122     <-- divide by 4

1 ticket = $30.5       <-- multiply by 10

10 tickets = $305

8 0
2 years ago
Read 2 more answers
Urgent math question, 10 points for a solve.
aalyn [17]

Answer:

cot (X) = 5/12

Step-by-step explanation:

tan (X) = opp/adj so cot (X) is adj/opp

6 0
2 years ago
5x^2-7x=4x^2-10 solve
Luda [366]

Answer:

x = 0, x = - 3

Step-by-step explanation:

Given

5x² - 7x = 4x² - 10 ← subtract 4x² - 10x from both sides

x² + 3x = 0 ← in standard form

Factor out x from each term

x(x + 3) = 0

Equate each factor to zero and solve for x

x = 0

x + 3 = 0 ⇒ x = - 3

5 0
3 years ago
Dayson is covering a package in the shape of a rectangular prism with wrapping paper. The package is 50 centimeters by 20 centim
goblinko [34]
<span>Dayson has 1 m2 of wrapping paper, which is 10000 cm2:
 1 m = 100 cm
 1 m^2 = (100 cm)^2 
 </span>1 m^2 = 10000 cm^2
 <span>The package has a surface area of cm2:
 A = 2*(50*20) + </span>2*(50*18) + 2*(18*20)
 A = <span> <span>4520 cm^2
 </span></span>The area of the package is less than the area of the wrapping paper (4520 cm^2 < 10000 cm^2<span>). So, Dayson cover the package with the wrapping paper.</span>
3 0
3 years ago
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