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2 years ago

What is the surface area of the figure shown?

Mathematics

1 answer:

Shalnov [3]2 years ago

5 0

Answer:

The surface area of the figure = 962 ft²

Step-by-step explanation:

The rectangle dimensions and its area given below

Dimensions Number Area

12 x 7 2 12 x 7 x 2 = 168

16 x 7 1 16 x 7 = 112

12 x (16 + 5) 1 12 x 21 = 252

16 x 12 1 16 x 12 = 192

16 x 13 1 16 x 13 = 208

Triangle dimensions

Dimensions Number Area

b = 12 & h = 5 2 bh/2 = (12*5)/2 = 30

To find total area

Total area = 168 + 112 + 252 + 192 + 208 + 30 = 962 ft²

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irinina [24]

Than answer you looking for is I think B

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2 years ago

C. Make n subject of the formula S= n/2 [2a + (n - 1)d] please provide your working out

yKpoI14uk [10]

Answer:

$n=\frac{4as -2ds}{(1-2ds)}$

Step-by-step explanation:

$S= \frac{n}{2 [2a + (n - 1)d]}$

Simplifying the fraction by multiplying d into the (n-1) term,

$s=\frac{n}{2 [2a + (n - 1)d] } = \frac{n}{2[2a + dn - d] }$

Simplifying the fraction by multiplying 2 throughout,

$s= \frac{n}{4a + 2dn-2d}$

Multiply $(4a + 2dn-2d)$ on both sides

$(4a + 2dn-2d)s= \frac{n}{4a + 2dn-2d} (4a + 2dn-2d)$

Cancel the $(4a + 2dn-2d)$ on the right hand side

$(4a + 2dn-2d)s= n$

Multiply s to the terms,

$4as + 2dns-2ds= n$

Move $2dns$ to the right hand side by subtracting $2dns$ on both sides $4as + 2dns-2ds-2dns= n-2dns$

$4as -2ds= n-2dns$

On the right hand side of the equation, take out $n$

$4as -2ds= n(1-2ds)$

Divide Left hand side by $(1-2ds)$ ,

$n=\frac{4as -2ds}{(1-2ds)}$

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3 years ago

A cereal company wants to change the shape of its cereal box in order to attract the attention of shoppers. The original cereal

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The new box will both hold more cereal and require more material to make.

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3 years ago

Consider the initial value problem yâ€²+2y=4t,y(0)=8.

Xelga [282]

Answer:

Please read the complete procedure below:

Step-by-step explanation:

You have the following initial value problem:

$y'+2y=4t\\\\y(0)=8$

a) The algebraic equation obtain by using the Laplace transform is:

$L[y']+2L[y]=4L[t]\\\\L[y']=sY(s)-y(0)\ \ \ \ (1)\\\\L[t]=\frac{1}{s^2}\ \ \ \ \ (2)\\\\$

next, you replace (1) and (2):

$sY(s)-y(0)+2Y(s)=\frac{4}{s^2}\\\\sY(s)+2Y(s)-8=\frac{4}{s^2}$ (this is the algebraic equation)

$sY(s)+2Y(s)-8=\frac{4}{s^2}\\\\Y(s)[s+2]=\frac{4}{s^2}+8\\\\Y(s)=\frac{4+8s^2}{s^2(s+2)}$ (this is the solution for Y(s))

$y(t)=L^{-1}Y(s)=L^{-1}[\frac{4}{s^2(s+2)}+\frac{8}{s+2}]\\\\=L^{-1}[\frac{4}{s^2(s+2)}]+L^{-1}[\frac{8}{s+2}]\\\\=L^{-1}[\frac{4}{s^2(s+2)}]+8e^{-2t}$

To find the inverse Laplace transform of the first term you use partial fractions:

$\frac{4}{s^2(s+2)}=\frac{-s+2}{s^2}+\frac{1}{s+2}\\\\=(\frac{-1}{s}+\frac{2}{s^2})+\frac{1}{s+2}$

Thus, you have:

$y(t)=L^{-1}[\frac{4}{s^2(s+2)}]+8e^{-2t}\\\\y(t)=L^{-1}[\frac{-1}{s}+\frac{2}{s^2}]+L^{-1}[\frac{1}{s+2}]+8e^{-2t}\\\\y(t)=-1+2t+e^{-2t}+8e^{-2t}=-1+2t+9e^{-2t}$

(this is the solution to the differential equation)

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3 years ago

Suppose that you flip a coin 13 times. what is the probability that you achieve at least 5 tails?

mixer [17]

Probability of flipping either a head or a tail = 1/2

probability of flipping 6 tails in a row (1/2)*6

probability of flipping at least 1 head = 1 - (1/2)*6 = 63/64

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3 years ago