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stich3 [128]
3 years ago
11

The quotient of three times a number and 8 is no more than 13

Mathematics
1 answer:
RideAnS [48]3 years ago
8 0

Answer:

3n/8 ≤ 13

Step-by-step explanation:

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A tangent line and its normal line have a point of tangency to the function f(x) at (x,y). If the slop of the normal line is m=(
alekssr [168]

Answer:

\displaystyle \\\left(\frac{49}{900},\frac{3761}{900}\right) or approximately (0.544, 4.179)

Step-by-step explanation:

A function and its tangent lines intersect when their slopes are the same. Find the x-coordinate when the slope of f(x) is equal to 8/7 by taking the derivative of f(x):

\displaystyle\\f(x)=\sqrt{x}-x+4\\f'(x)=\frac{1}{2}\cdot\frac{1}{\sqrt{x}}-1=\frac{1}{2\sqrt{x}}-1

Set f'(x) equal to 8/7 and solve for x:

\displaystyle \\\frac{1}{2\sqrt{x}}-1=\frac{8}{7},\\x=\frac{49}{900}

Therefore, f(x) will intersect at a point of tangency with a line of slope 8/7 at x=49/900. Plug in x=49/900 into f(x) to get the y-coordinate:

\displaystyle\\y=\sqrt{x}-x+4 \vert_{x=49/900}=\frac{3761}{900}

⇒Answer: (49/900, 3761/900) or approximately (0.544, 4.179)

5 0
2 years ago
a sports tournament has 8 teams. each team has n players. using n, write an expression for the total numbers of players in the t
erastova [34]

Answer:

8n.

Step-by-step explanation:

You would be multiplying the amount of teams by the number of members to find the total members, hence 8 times n.

5 0
3 years ago
The number of calories in a piece of pie is 20 less than three times the number of calories in a scoop of ice cream. The pie and
sergejj [24]

Answer:

130 calories in the ice cream and 500 calories in the pie.

Step-by-step explanation:

Let the amount of calories in the scoop of ice cream be x. the amount of calories in the piece of pie be 3x-20. we know that x+3x-20=500.

4x-20=500

If we add twenty to both sides, we end up with:

4x=520

Divide both sides by four, and you get x=130.

there are 130 calories in the scoop of ice cream and 130*4-20=500 calories in the pie.

5 0
3 years ago
Helpme<br><br><br> Given f(x) = 3x - 1, find f(2).<br> 1<br> 2<br> 5<br> 4
dimulka [17.4K]

Answer:

5

Step-by-step explanation:

f(x)=3x-1

f(2)=3×2-1

f(2)=6-1

f(2)=5

7 0
2 years ago
2) Brian purchased pens for 75 cents each and pencils for 40 cents each he
svet-max [94.6K]

Step-by-step explanation:

Name the total of pens purchased as x and the pencils as y... Make two equations and solve them. I also search for the pencils purchased in addition

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3 years ago
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