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4 years ago

Find an equation of the tangent line to the curve at the given point. y = √ (x) , (16, 4)

Mathematics

1 answer:

asambeis [7]4 years ago

8 0

Answer: y=1/8*x+2

Step-by-step explanation:

The equation of any tangent line is y=a*x+b (1)

To the equation of the tangent line we have to find the coefficients a and b and the to substitute them to equation (1).

As we know a=y'(x0) ( where x0=16)

So y'(x)= (√ (x) )' = 1/(2*√x)

a=y'(x0)= 1/(2*√16)=1/(2*4)=1/8

So lets substitute a in equation (1):

y=1/8 *x+b

Now we have to find b

We know that the point (16, 4) belongs to the tangent line.

That means

4=1/8*16+b => 4=2+b => b=2

SO the equation of the tangent line is y=1/8*x+2

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A factory makes 4250 bars of chocolate. There were three kinds of chocolate bars - creamy, milky and

mariarad [96]

Answer:

2525

Step-by-step explanation:

1. Draw a block diagram to illustrate the different types of chocolate bars. (In this diagram, the creamy chocolate bars are shown as orange blocks, the milky chocolate bars as blue blocks and the white chocolate bars as red blocks.)

2. Since the number of creamy chocolate bars was 5 times the number of milky chocolate bars, we can replace one orange block (creamy) with 5 blue blocks (milky).

Since the number of white chocolate bars was 715 more than the number of milky chocolate bars, we replace one red block with one blue block + 715.

3. Looking at the block diagram, find the number of milky chocolate bars (blue block)

4250 – 715 = 3535

7 blue blocks = 3535

1 blue block = 3535 ÷ 7 = 505

The number of milky chocolate bars made was 505.

4. Calculate the number of creamy chocolate bars.

The number of creamy chocolate bars was 5 times the number of milky chocolate bars = 5 × 505 = 2525

8 0

4 years ago

When point A( 3, 1) is translated 2 units to the right and 6 units up the coordinates of point A'

9966 [12]

Answer:

A' = (5,7)

Step-by-step explanation:

So, we start with the original point A at (3,1), that means x = 3 and y = 1.

We move it 2 units to the right... so we're moving along the X-axis... and we're moving to the right.. so we're increasing the value of x. That means starting with x = 3, we go 2 more units... we then get to x = 5.

In the same way, we move 6 units up... so we move along the Y-axis. We go up, so we also increase the value of y. Starting with y = 1, we move up by 6 units... so we are now at y = 7.

A' point is then at (5,7).

3 0

3 years ago

Gretchen made a paper cone to hold a gift for a friend. The paper cone was

AVprozaik [17]

Answer: 803.84 --> 803.8

Step-by-step explanation:

4^4=16x3.14=50.24*16=803.84

6 0

3 years ago

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RideAnS [48]

Nanakjanajisnanwj ajnwjwhwbjejs

4 0

2 years ago

Can someone help me please

svet-max [94.6K]

9514 1404 393

Answer:

see attached

Step-by-step explanation:

Translation 12 units down puts each point 12 units lower on the graph than the position where it is currently shown. Segment RS is now shown on the line y=9. It will be translated straight down so it appears on the line y = 9-12 = -3.

Similarly, T has a y-coordinate of 2. Translated down 12, it will have a y-coordinate of y = 2-12 = -10.

The x-coordinates of all of the points remain the same.

The translation is shown in the attachment.

3 0

3 years ago