A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, this length is bent up at an angle θ. The area A of the opening may be expressed as the function: A(θ) = 16 sin θ ⋅ (cos θ + 1). If θ = 60°, what is the area of the opening?

Answer:

(1,5) and(4,1).

Step-by-step explanation:

Given :

Brand Calcium Iron Vitamins

A                5 4 7

B                4 6 4

Let x be the quantity of brand A

Let y be the quantity of brand B

Steve needs to take at least 24 milligrams of calcium, 15 milligrams of iron, and 16 milligrams of vitamins.

So, equation becomes:

Now plot the given inequalities on the graph

Refer the attached graph

Thus the points lies in the feasible region are (1,5) and(4,1).

Answer:

C. 6*9^3 + 1*9^2 + 1*9^1 + 5*9^0

Step-by-step explanation:

In base 9, each digit to the left represents a power of 9.

The rightmost digit represents 9^0, the next digit to the left represents 9^1, the next digit to the left represents 9^2, and the 4th digit represents 9^3.

Answer: C. 6*9^3 + 1*9^2 + 1*9^1 + 5*9^0

∫ e^(3x)*(cosh(2x)dx

= ∫ [e^(3x)*(e^(2x)+e^(-2x))/2]dx

= ∫ [(e^(5x)+e^x)/2]dx

=e^(5x)/10+e^x/2+C

=(1/10)(e^(5x)+5e^x)+C

Answer:

30 years then.

Step-by-step explanation:

Let the present age of Ria be x and Abby be y, and of Sweta be z.

Then, according to the question,

• x + y = 48 ..1

Today, Abby is 4 yrs older than Sweta,i.e.,

• y = 4+z.(2)

Also, ratio of present ages of Ria:Sweta

• x:z = 4:7
• x/z = 4/7
• 4z = 7x..(3)

Putting the value of y from eqn (2) to eqn 1,

• x + 4 + z = 48
• x + z = 44( eqn : 4)

From eqn (3),

• 4z = 7x
• x = 4z/7(eqn:5)

Putting the value of x in eqn (4),

• 4z/7 + z = 44
• 11z/7 = 44
• z = 4*7 = 28

From eqn 5, putting the value of z in it,

• x = 4*28/7
• x = 4*4 = 16

Putting the value of x in eqn 1,

• x+y = 48
• y = 48 -16 =32

We have to find the age of Abby two years ago, i.e. 32-2 = 30 years old then back.