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Aleksandr [31]
3 years ago
13

I want to make sure i got this right. PLS HELP ASAP I NEED IT CALC 1 one question

Mathematics
1 answer:
IrinaK [193]3 years ago
6 0
\bf f(x)=
\begin{cases}
x^3&x\le 1\\
mx+b&x\ \textgreater \ 1
\end{cases}

now, a function may well be continuous, but it may not be differentiable.

graph wise, differentiability means, a smooth curve, with no abrupt spikes or drops or cuts.

so for this piece-wise to be differentiable, the subfunctions must meet at junctions smoothly, with no abrupt changes, so mx + b, must blend in with x³ smoothly.

now, that can only occur if mx + b has the same slope as x³ at that point where they meet.  The point where they meet is at x = 1, well, let's check what is the slope of x³ at x = 1.

\bf \cfrac{d}{dx}[x^3]\implies \left.  3x^2\cfrac{}{}\right|_{x=1}\implies 3(1)^2\implies 3

therefore "m" for mx+b, must be 3 then.

now, what's the value of x³ at x = 1?  well is just (1)³, which is 1.

so for 3x + b, when x = 1, it must also equals 1 as well, that way it meets x³, thus

3x + b

3(1) + b = 1

b = -2

check the graph below.

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Answer:

?= 4/3

Step-by-step explanation:

?×1/4=1/3

?/4=1/3

?=1/3×4

?=4/3

3 0
3 years ago
ABC is similar to LMN. Also, side AB measures 5 cm, side AC measures 7 cm, and
Arturiano [62]

49cm Would be your answer, sorry for the late reply

3 0
3 years ago
✎﹏Question~
Varvara68 [4.7K]

Answer:

Sol: In this question, firstly we have to make the first bracket as a complete square of the second bracket. This we can by adding 2.x.1/x which is equivalent to 2. Then the equation becomes:

6(x2 + 1/x2 +2) – 5(x + 1/x) = 50 { 38 + 6*2)

⇒ 6(x2 + 1/x2 +2) – 5(x + 1/x) – 50 = 0

Now put x + 1/x = y

⇒ 6y2 -5y -50 = 0

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As x is positive therefore, x + 1/x =10/3

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7 0
2 years ago
A culture started with 4,000 bacteria. After 5 hours, it grew to 4,800 bacteria. Predict how many bacteria will be present after
eimsori [14]
First we need to find k ( rate of growth)
The formula is
A=p e^kt
A future bacteria 4800
P current bacteria 4000
E constant
K rate of growth?
T time 5 hours
Plug in the formula
4800=4000 e^5k
Solve for k
4800/4000=e^5k
Take the log for both sides
Log (4800/4000)=5k×log (e)
5k=log (4800/4000)÷log (e)
K=(log(4,800÷4,000)÷log(e))÷5
k=0.03646

Now use the formula again to find how bacteria will be present after 15 Hours
A=p e^kt
A ?
P 4000
K 0.03646
E constant
T 15 hours
Plug in the formula
A=4,000×e^(0.03646×15)
A=6,911.55 round your answer to get 6912 bacteria will be present after 15 Hours

Hope it helps!
4 0
3 years ago
Read 2 more answers
Three prime numbers which add up to 25
dolphi86 [110]

Answer:

7 + 11 + 11

Step-by-step explanation:

7 + 11 = 18

18 + 7 = 25

8 0
3 years ago
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