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horrorfan [7]
3 years ago
8

At a baseball game, 3 drinks and 4 hotdogs cost $15.00. At the same game, 3 drinks and 1 hotdog cost $10.50. Find the cost for a

drink.
Mathematics
1 answer:
Serhud [2]3 years ago
8 0

Answer:

$3

Step-by-step explanation:

Given data

Let the cost of drinks be x

and the cost of hotdogs be y

so

3x+4y=15-------1

also

3x+y= 10.5------2

solve 1 and 2

 3x+4y=15

-3x+y= 10.5

     3y= 4.5

divide both sides by 3

y= 4.5/3

y= $1.5

Put y= 1.5 in 1

3x+4(1.5)=15

3x+6= 15

3x=15-6

3x= 9

x= 9/3

x= $3

Hence the cost of a drink is $3

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Write the equation of the line that passes through 7, 0 and is parallel to y = -3x + 4​
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y = - 3x + 21

Step-by-step explanation:

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y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 4 ← is in slope- intercept form

with slope m = - 3

Parallel lines have equal slopes , then

y = - 3x + c ← is the partial equation

To find c substitute (7, 0 ) into the partial equation

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8 0
2 years ago
Using differential calculus, maximize the volume of a box made of cardboard (top is open) as shown in Figure A. 15, subject to t
lana [24]

The maximum volume of the box is 40√(10/27) cu in.

Here we see that volume is to be maximized

The surface area of the box is 40 sq in

Since the top lid is open, the surface area will be

lb + 2lh + 2bh = 40

Now, the length is equal to the breadth.

Let them be x in

Hence,

x² + 2xh + 2xh = 40

or, 4xh = 40 - x²

or, h = 10/x - x/4

Let f(x) = volume of the box

= lbh

Hence,

f(x) = x²(10/x - x/4)

= 10x - x³/4

differentiating with respect to x and equating it to 0 gives us

f'(x) = 10 - 3x²/4 = 0

or, 3x²/4 = 10

or, x² = 40/3

Hence x will be equal to 2√(10/3)

Now to check whether this value of x will give us the max volume, we will find

f"(2√(10/3))

f"(x) = -3x/2

hence,

f"(2√(10/3)) = -3√(10/3)

Since the above value is negative, volume is maximum for x = 2√(10/3)

Hence volume

= 10 X 2√(10/3)  -  [2√(10/3)]³/4

= 2√(10/3) [10 - 10/3]

= 2√(10/3) X 20/3

= 40√(10/27) cu in

To learn more about Maximization visit

brainly.com/question/14682292

#SPJ4

Complete Question

(Image Attached)

3 0
1 year ago
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