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3 years ago

PLZ HELP DUE IN 5 MINUTES

Mathematics

1 answer:

Marta_Voda [28]3 years ago

7 0

Answer:

angles 3 and 4 are 125 degrees and angle 2 is 55 degrees

Step-by-step explanation:

just putting my answer here to get points

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If an open box has a square base and a volume of 115 in.3 and is constructed from a tin sheet, find the dimensions of the box, a

Karolina [17]

Let h = height of the box,
x = side length of the base.

Volume of the box is $V=x^{2} h = 115$ .
So $h = \frac{115}{ x^{2} }$

Surface area of a box is S = 2(Width • Length + Length • Height + Height • Width).
So surface area of the box is
$S = 2( x^{2} + hx + hx) \\ = 2 x^{2} + 4hx \\ = 2 x^{2} + 4( \frac{115}{ x^{2} } )x$
$= 2 x^{2} + \frac{460}{x}$
The surface are is supposed to be the minimum. So we'll need to find the first derivative of the surface area function and set it to zero.

$S' = 4x- \frac{460}{ x^{2} } = 0$
$4x = \frac{460}{ x^{2} } \\ 4x^{3} = 460 \\ x^{3} = 115 \\ x = \sqrt[3]{115} = 4.86$
Then $h= \frac{115}{4.86^{2}} = 4.87$
So the box is 4.86 in. wide and 4.87 in. high.

5 0

3 years ago

Read 2 more answers

For questions 13-15, Let Z1=2(cos(pi/5)+i Sin(pi/5)) And Z2=8(cos(7pi/6)+i Sin(7pi/6)). Calculate The Following Keeping Your Ans

weqwewe [10]

Answer:

Step-by-step explanation:

Given the following complex values Z₁=2(cos(π/5)+i Sin(πi/5)) And Z₂=8(cos(7π/6)+i Sin(7π/6)). We are to calculate the following complex numbers;

a) Z₁Z₂ = 2(cos(π/5)+i Sin(πi/5)) * 8(cos(7π/6)+i Sin(7π/6))

Z₁Z₂ = 18 {(cos(π/5)+i Sin(π/5))*(cos(7π/6)+i Sin(7π/6)) }

Z₁Z₂ = 18{cos(π/5)cos(7π/6) + icos(π/5)sin(7π/6)+i Sin(π/5)cos(7π/6)+i²Sin(π/5)Sin(7π/6)) }

since i² = -1

Z₁Z₂ = 18{cos(π/5)cos(7π/6) + icos(π/5)sin(7π/6)+i Sin(π/5)cos(7π/6)-Sin(π/5)Sin(7π/6)) }

Z₁Z₂ = 18{cos(π/5)cos(7π/6) -Sin(π/5)Sin(7π/6) + i(cos(π/5)sin(7π/6)+ Sin(π/5)cos(7π/6)) }

From trigonometry identity, cos(A+B) = cosAcosB - sinAsinB and sin(A+B) = sinAcosB + cosAsinB

The equation becomes

= 18{cos(π/5+7π/6) + isin(π/5+7π/6)) }

= 18{cos((6π+35π)/30) + isin(6π+35π)/30)) }

= 18{cos((41π)/30) + isin(41π)/30)) }

b) z2 value has already been given in polar form and it is equivalent to 8(cos(7pi/6)+i Sin(7pi/6))

c) for z1/z2 = 2(cos(pi/5)+i Sin(pi/5))/8(cos(7pi/6)+i Sin(7pi/6))

let A = pi/5 and B = 7pi/6

z1/z2 = 2(cos(A)+i Sin(A))/8(cos(B)+i Sin(B))

On rationalizing we will have;

= 2(cos(A)+i Sin(A))/8(cos(B)+i Sin(B)) * 8(cos(B)-i Sin(B))/8(cos(B)-i Sin(B))

= 16{cosAcosB-icosAsinB+isinAcosB-sinAsinB}/64{cos²B+sin²B}

= 16{cosAcosB-sinAsinB-i(cosAsinB-sinAcosB)}/64{cos²B+sin²B}

From trigonometry identity; cos²B+sin²B = 1

= 16{cos(A+ B)-i(sin(A+B)}/64

= 16{cos(pi/5+ 7pi/6)-i(sin(pi/5+7pi/6)}/64

= 16{ (cos 41π/30)-isin(41π/30)}/64

Z1/Z2 = (cos 41π/30)-isin(41π/30)/4

8 0

3 years ago

What set of reflections would carry trapezoid ABCD onto itself? (1 point) Trapezoid ABCD is shown. A is at negative 5, 1. B is a

amid [387]

Answer:

y=x, x axis, y=x, y axis

Step-by-step explanation:

If a point A(x, y) is reflected along the y = x line, the new coordinates would be A'(y, x)

If a point A(x, y) is reflected across the x axis, the new coordinates would be A'(x, -y)

If a point A(x, y) is reflected along the y axis, the new coordinates would be A'(-x, y)

Firstly reflect Trapezoid ABCD along the y = x line to give:

A (-5, 1) ⇒ A'(1, -5). B (-4, 3) ⇒ B'(3, -4). C (-2, 3) ⇒C'(3, -2). D (-1, 1) ⇒ D'(1, -1)

Secondly reflect along the x axis to give:

A'(1, -5)⇒ A"(1,5). B'(3, -4)⇒ B"(3,4), C'(3, -2)⇒C"(3, 2), D'(1, -1) ⇒ D"(1, 1)

Thirdly reflect along the y = x line to give:

A"(1,5) ⇒ A"'(5, 1). B"(3,4) ⇒ B"'(4, 3). C"(3, 2) ⇒ C"'(2, 3). D"(1, 1) ⇒ D"'(1, 1)

Lastly reflect along the y axis to give:

A"'(5, 1) ⇒ A""(-5, 1), B"'(4, 3) ⇒ B""(-4, 3), C"'(2, 3) ⇒ C""(-2, 3), D"'(1, 1) ⇒ D""(-1.1)

6 0

4 years ago

Calculator

Ludmilka [50]

Answer:

Step-by-step explanation:

42/21 = x/17

solve to get the answer

2 = x/17

2*17 = x/17 * 17

34 = x

5 0

3 years ago

If a shirt costs $40 and the amount of tax collected was $2 what is the sales tax rate?

scoundrel [369]

Answer:

Step-by-step explanation:

To find the tax, we take the price times the tax rate

2 = 40* rate

Divide each side by 40

2/40 =rate

.05 = rate

Changing to percent form

5% = rate

7 0

3 years ago

Read 2 more answers