Find the minimum value of<br> C = 6x + 7y

The width of a rectangle is 7 inches less than its length. The area of the rectangle is 120 square inches. Solve for the dimensi

kramer

width= 8

Length= 15

(8x15= 120 and 8 is 7 less than 15)

8 0

3 years ago

Please just help with these questions!

devlian [24]

5/7= -----------

0.714285

Convert the fraction to a decimal by dividing the numerator by the denominator.

6/10= 0.6

Convert the fraction to a decimal by dividing the numerator by the denominator.

16/20= 0.8

Convert the fraction to a decimal by dividing the numerator by the denominator.

9/10= 0.9

Convert the fraction to a decimal by dividing the numerator by the denominator.

3 0

3 years ago

The number y of deer in a county after x years can be modeled by y=0.75x^2 + 10.5x + 1300. When were there about 2000 deer? Roun

Lemur [1.5K]

Answer:

24 years

Step-by-step explanation:

We are told that the model of number of deers is;

y = 0.75x² + 10.5x + 1300

Where;

y represents number of deers

x represents number of years

Now, we want to find how many years it will take to get to 2000 deers.

Thus;

2000 = 0.75x² + 10.5x + 1300

0.75x² + 10.5x + 1300 - 2000 = 0

0.75x² + 10.5x - 700 = 0

Using quadratic formula, we have;

x = [-b ± √(b² - 4ac)]/2a

x = [-10.5 ± √(10.5²- (4*0.75*-700)]/(2*0.75)

x = [-10.5 ± √(110.25 + 2100)]/(1.5)

x = [-10.5 ± √2210.25]/(1.5)

x ≈ -38 or 24

Number of years can't be negative, so we will take the positive value.

So, x = 24 years

3 0

3 years ago

A cone-shaped paper drinking cup is to be made to hold 27 cm of water. Find the height h and radius r of the cup that will use t

andreyandreev [35.5K]

Answer:

r = 2.632 cm
h = 3.722 cm

Step-by-step explanation:

The formula for the volume of a cone of radius r and height h is ...

V = (1/3)πr²h

Then r² can be found in terms of h and V as ...

r² = 3V/(πh)

The lateral surface area of the cone is ...

A = (1/2)(2πr)√(r² +h²) = πr√(r² +h²)

The square of the area is ...

T = A² = π²r²(r² +h²)

Substituting for r² using the expression above, we have ...

T = π²(3V/(πh))((3V/(πh) +h²) = 9V²/h² +3πVh

We want to find the minimum, which we can do by setting the derivative to zero.

dT/dh = -18V²/h³ +3πV

This will be zero when ...

3πV = 18V²/h³

h³ = 6V/π . . . . . multiply by h³/(3πV)

For V = 27 cm³, the value of h that minimizes paper area is ...

h = 3∛(6/π) ≈ 3.7221029

The corresponding value of r is ...

r = √(3V/(πh)) = 9/√(π·h) ≈ 2.6319242

The optimal radius is 2.632 cm; the optimal height is 3.722 cm.

_____

The second derivative test applied to T finds that T is always concave upward, so the value we found is a minimum.

__

Interestingly, the ratio of h to r is √2.

8 0

3 years ago

PLEASE HELP! THIS IS DUE TOMORROW! Much appreciated.

denis23 [38]

Answer:

Step-by-step explanation:

1a) angle x and angle y are corresponding angles. Both angles lie on the same side of the transversal. Since the lines are parallel, the angles are equal.

1b) angle x and angle y are interior angles on the same side of the transversal. Since the lines are parallel, the angles are equal supplementary.

1c) angle x and angle y are corresponding angles. Both angles lie on the same side of the transversal. Since the lines are parallel, the angles are equal.

1d) angle x and angle y are alternate interior angles. They are between the parallel lines and alternate sides of the transversal. Since the lines are parallel, the angles are equal.

3 0

4 years ago

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Find the minimum value of C = 6x + 7y