See attached for a sketch of some of the cross sections.
Each cross section has area equal to the square of the side length, which in turn is the vertical distance between the curve y = √(x + 1) and the x-axis (i.e. the distance between them that is parallel to the y-axis). This distance will be √(x + 1).
If the thickness of each cross section is ∆x, then the volume of each cross section is
∆V = (√(x + 1))² ∆x = (x + 1) ∆x
As we let ∆x approach 0 and take infinitely many such cross sections, the total volume of the solid is given by the definite integral,

Decimal form: 4.05, 0.5
Exact form: 9/2, 1/2
Answer:
(-5.77, 6.46)
Step-by-step explanation:
15x + 9y = 45 ----------- i
9x + 8y = 12----------------ii
Multiply equation i by 9 the coefficient of x in equ ii
And equation ii by 15 the coefficient of x in equ I
9 x 15x + 9y = 45 ----------- i
15 x 9x + 8y = 12----------------ii
135x+81y = 405
135x+120y= 180
Subtract equation ii from I
135x-135x+81y-(+120y)= 405-180
-39y=225
y = 225/-39 = -5.77
Insert the value of y in equ i
15x + 9y = 45
15x+9(-5.77) = 45
15x-51.92=45
15x = 45+51.92
15x= 96.92
x = 96.92/15= 6.46
(x,y) = (-5.77, 6.46)
x = 6.92/15
<u>Answer:</u>
- The cost of 1 dozen doughnut is $6 and the cost of a dozen croissant is $10.
<u>Step-by-step explanation:</u>
<u>We know that:</u>
- D = Cost of a dozen doughnut
- C = Cost of a dozen croissant
- 10D + 7C = 130
- 6D + 4C = 76
<u>Work:</u>
6D + 4C = 76
7(6D + 4C = 76)
42D + 28C = 532
- 40D - 42D = 520 - 532
- => -2D = -12
- => 2D = 12
- => D = 6
<u>Now, let's substitute the value of D into the first equation.</u>
- 10D + 7C = 130
- => 10(6) + 7C = 130
- => 60 + 7C = 130
- => 7C = 70
- => C = 10
Hence,<u> the cost of 1 dozen doughnut is $6 and the cost of a dozen croissant is $10.</u>
Hoped this helped.

Answer:
519.6
Step-by-step explanation:
A hexagon has a total of 720 for it's interior angles so each angle is 120 and in the triangle, each of them is 60, making it an equilateral triangle. You can use 30 60 90 triangles to find the height which is 5√3.
(5√3)*10=50√3
The area of the triangle times 6 is 300√3 which is approximately 519.6