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3 years ago

Write a formula that relates the are A of a triangle to to the lengths of its base b and height h

Mathematics

2 answers:

Lena [83]3 years ago

6 0

The area of a triangle is the base multiplied by the height divide by two.
so A = (b x h) / 2

dimaraw [331]3 years ago

6 0

A=1/2(bh) is the formula

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nasty-shy [4]

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Step-by-step explanation:

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2 years ago

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Find the area of a plane figure bounded by lines

natulia [17]

Answer: 4.5

Step-by-step explanation:

First, find the points of intersection by solving the system.

y = x² + 2x + 4

y = x + 6

Solve by substitution:

x² + 2x + 4 = x + 6 ⇒ x² + x - 2 = 0 ⇒ (x + 2)(x - 1) = 0 ⇒ x = -2, x = 1

Now, integrate from x = -2 to x = 1

$\int\limits^1_2 {(x+6)-(x^{2}+2x+4) } \,$ the bottom of the integral is -2

= $\int\limits^1_2 {x+6-x^{2}-2x-4 } \,$

= $\int\limits^1_2 {-x^{2}-x+2 } \,$

= $\frac{-x^{3}}{3} - \frac{x^{2}}{2}+2x\int\limits^1_2 {} \,$

= $(\frac{-1^{3}}{3} - \frac{1^{2}}{2}+2(1)) - (\frac{-(-2)^{3}}{3} - \frac{(-2)^{2}}{2}+2(-2))$

= $(\frac{-1}{3} - \frac{1}{2} +2) - (\frac{8}{3} -\frac{4}{2} -4)$

= $\frac{-9}{3} + \frac{3}{2} +6$

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3 years ago

Help what’s the rule

solong [7]

Doubling or quadruple

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3 years ago

You are constructing a cardboard box from a piece of cardboard with the dimensions 2 m by 4 m. You then cut equal-size squares f

postnew [5]

Answer:

Dimensions:

l =3,15 m

w=1,15 m

x= 0,42 m (height)

V(max) = 1,52 m³

Step-by-step explanation:

The cardboard is L = 4 m and W = 2 m

Let call x the length of the square to cut in each corner, then, volume of open box is:

For the side L is L - 2*x l = 4 - 2*x

For the side W is W - 2*x w= 2 - 2*x

The height is x

Volume of the open box, as function of x is:

V(x) = ( 4 -2x) * ( 2 - 2x) *x ⇒ V(x) = ( 8 - 8x -4x + 4x²) *x

V(x) = ( 8 -12x + 4x² )*x V(x) = 8x - 12x² + 4x³

V(x) = 8x - 12x² + 4x³

Taking derivatives on both sides of the equation

V´(x) = 8 - 24x + 12x²

V´(x) = 0 8 - 24x + 12x² = 0 reordering 12x² - 24x + 8 = 0

or 3x² - 6x + 2 = 0

A second degree equation. Solving for x

x₁,₂ = ( 6 ± √36 - 24 ) /6

x₁,₂ = ( 6 ± 3.46) /6

x₁ = 6 + 3,46 /6 x₁ = 1.58 we dismiss such solution because 1,58 * 2 = 3,15 and is bigger than 2 one of the side of the cardboard

x₂ =( 6 - 3,46 ) / 6

x₂ = 0,42 m

Dimensions of the open box

l = 4 - 2*x l = 4 - 0,85 l = 3,15 m

w = 2 -2*x w = 2 - 0,85 w = 1,15 m

x = 0,42 m

V(max) =3,15*1,15*0,42

V(max) = 1,52 m³

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3 years ago