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Illusion [34]
3 years ago
9

What is the least positive integer

Mathematics
1 answer:
OlgaM077 [116]3 years ago
7 0
What is the least positive integer  of what?
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Find a3-digit quotient with a 4 in the one's place
Ostrovityanka [42]
A 3 digit quotient with a 4 in the one's place should be easy. 12 x 12 = 144
8 0
3 years ago
Find the local maxima of f ( x ) = 2 x 3 − 30 x 2 + 126 x + 2
PSYCHO15rus [73]

\text{Consider the function}\\
\\
f(x)=2x^3-30x^2+126x+2\\
\\
\text{To find the local maxima, first we find the critical points.}\\
\text{for critical points set the first derivative 0 and solve for x.}\\
\text{so using power rule of derivatives, we have}\\
\\
f'(x)=2(3x^2)-30(2x)+126(1)+0

\Rightarrow f'(x)=6x^2-60x+126\\
\\
\text{now for critical points, we set }f'(x)=0\\
\\
\Rightarrow 6x^2-60x+126=0\\
\\
\Rightarrow 6(x^2-10x+21)=0\\
\\
\Rightarrow x^2-10x+21=0\\
\\
\Rightarrow x^2-7x-3x+21=0\\
\\
\Rightarrow x(x-7)-3(x-7)=0\\
\\
\Rightarrow (x-3)(x-7)=0

\Rightarrow x-3=0, \ \ \ \ \ \ \ \ \text{ and } \ \ \ \ \ x-7=0\\
\\
\Rightarrow x=3, \ \ \ \ \ \ \ \ \text{ and } \ \ \ \ \ x=7\\
\\
\text{now to check for maximum minimum, we do second derivative test.}\\
\\
f''(x)=12x-60\\
\\
\text{at x=3, second derivative is}\\
\\
f''(3)=12(3)-60=-24

f''(7)=12(7)-60=24>0, \text{ so local minimum occur at x=7.}\\
\\
\text{hence the local maximum value of the function is}\\
\\
f(3)=2(3)^3-30(3)^2+126(3)+2=164

Hence the local maxima of  f is: 164

8 0
4 years ago
mrs.gretta is teaching a 5th grade class. She is standing 12 meters in front of ethan. isabella is sitting to ethans right. if i
Mrrafil [7]

Answer:

Ethan and Isabella are 9 meters apart.

Step-by-step explanation:

1. We can solve this using the Pythagorean Theorem, a²+b²=c².

2. Mrs. Gretta is standing 12 meters in front of Ethan, so a=12.

3. Isabella is sitting to Ethan's right, but we don't know how far away, so b=x.

4. Mrs. Gretta is 15 meters from Isabella, so c=15.

5. Plugging these variables into the equation, we get 12²+x²=15² which equals 144+x²=225.

6. We can move 144 to the other side to get x²=81, then square the 81 to get x=9.

7. Therefore, the answer is 9. Ethan and Isabella are 9 meters apart.

6 0
3 years ago
Express the set using INTERVAL NOTATION -3&lt;=x&lt;10<br> Please help if you can
SVETLANKA909090 [29]
So x is from -3 to 10, including -3, but not including 10

so that would be the interval
[-3,10)
remember, the brackets [] are inclusive meaning ≤ and ≥
parenthasees () are not inclusive maning < and >


[-3,10)
7 0
3 years ago
Find an equation of the line that passes through the points (5,- 4) and (2,-2).
Andru [333]

Answer:

y=-2/3x - 2/3

Step-by-step explanation:

4 0
3 years ago
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