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3 years ago

Find the point on the curve y = √ 2 x + 4 which is closest to the point ( 3 , 0 ) .

1 answer:

8 0

Here you'll need differential calculus.

The distance between (3,0) and (x, sqrt(2)*x + 4) is given by the distance formula:

distance: sqrt [ (3+x)^2 + (sqrt(2)*x + 4)^2 ]

Differentiate this, and then set the resulting derivative = to 0. Solve for x. Test your results to ensure that the distance d is actually the SMALLEST, given the root(s) x that you've found.

Write the coordinates of this point on the curve as ( x, f(x) ).

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To rent a certain meeting room, a college charges a reservation fee of $19 and an additional fee of $4 per hour. The chemistry c

prisoha [69]

Answer:

t = 5

Step-by-step explanation:

$19 + 4t = 39$
$4t = 20$ Subtract 19 from 39
$\frac{4t}{4} = \frac{20}{4}$ Divide by 4
$t = 5$

6 0

3 years ago

Which equation is written in slope-intercept form?

dlinn [17]

Answer:

y=3x+2

Step-by-step explanation:

slope intercept form

y=mx+b

y=y coordinate

m=slope

x=x coordinate

b= y-intercept

5 0

3 years ago

In a class if 20 students, 60% are girls. How many Students are girls?

seropon [69]

12 students are girls and 8 are boys.

6 0

3 years ago

25 points, look at the picture.

attashe74 [19]

Answer:

1080

Step-by-step explanation:

PEMDAS says multiply and divide from left to right

9*5*6*3÷3*4*6÷6

45*6*3÷3*4*6÷6

270*3÷3*4*6÷6

810÷3*4*6÷6

270*4*6÷6

1080*6÷6

6480÷6

1080

6 0

3 years ago

Darin can purchase tile at a store for 0.79 per tile and rent a tile saw for $24. At another store, he can borrow the tile saw f

ankoles [38]

Let us denote the number of tiles by $T$ .

In the first store, if Darin bought $T$ tiles, he would need to spend:
                        $0.79\times T+24$ (measured in $)

In the second store, if Darin bought $T$ tiles, he would need to spend:
                        $1.19\times T$ (measured in $)

For the cost to be the same at both stores, it means (measured in $)
                                           $1.19T=0.79T+24$

Moving $0.79T$ over to the left hand side and changing signs:
                                            $1.19T-0.79T=24$
                                            $0.4T=24$
                                            $T= \frac{24}{0.4}$
                                            $T=60$ tiles

Let's check. If he buys 60 tiles in the first store, he spends:
      $0.79×60 + $24 = $47.40 + $24 = $71.40

If he buys 60 tiles in the second store, he spends:
                               $1.19×60 = $71.40

∴ Darin needs to buy 60 tiles for the cost to be the same at both stores.

7 0

3 years ago