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3 years ago

What is the surface area of the figure?

Mathematics

2 answers:

lisov135 [29]3 years ago

7 0

Answer:

The surface area of the figure is $SA=458\ ft^{2}$

Step-by-step explanation:

we know that

The surface area of the figure is equal to

$SA=2B+PH$

where

B is the area of the L-shaped cross section

P is the perimeter of L-shaped cross section

H is the width of the figure

Find the area of the L-shaped cross section

$B=12*7+5*5=109\ ft^{2}$

Find the perimeter P of L-shaped cross section

$P=(12+7+7+5+5+12)=48\ ft$

$H=5\ ft$

substitute

$SA=2(109)+(48)(5)=458\ ft^{2}$

Readme [11.4K]3 years ago

4 0

Answer:

Surface area = 458 square ft

Step-by-step explanation:

From the figure attached with this answer we can see figure.

To find the surface area of the figure

Surface area is sum of area of small rectangles

Surface area = 2(12 * 7 ) + 4(5 * 5) + 2(12 * 5) + 2(7 * 5)

= 2*84 + 4*25 + 2 *60 + 2*35

= 168 + 100 + 120 + 70

= 458

Therefore surface area of given figure = 458 square ft

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Ben and Josh went to the roof of their 40-foot tall high school to throw their math books offthe edge.The initial velocity of Be

Taya2010 [7]

Answer

Josh's textbook reached the ground first

Josh's textbook reached the ground first by a difference of $t=0.6482$

Step-by-step explanation:

Before we proceed let us re write correctly the height equation which in correct form reads:

$h(t)=-16t^2 +v_{o}t+s$ Eqn(1).

Where:

$h(t)$ : is the height range as a function of time

$v_{o}$ : is the initial velocity

$s$ : is the initial heightin feet and is given as 40 feet, thus Eqn(1). becomes:

$h(t)=-16t^2 + v_{o}t + 40$ Eqn(2).

Now let us use the given information and set up our equations for Ben and Josh.

Ben:

We know that $v_{o}=60ft/s$

Thus Eqn. (2) becomes:

$h(t)=-16t^2+60t+40$ Eqn.(3)

Josh:

We know that $v_{o}=48ft/s$

Thus Eqn. (2) becomes:

$h(t)=-16t^2+48t+40$ Eqn. (4).

Now since we want to find whose textbook reaches the ground first and by how many seconds we need to solve each equation (i.e. Eqns. (3) and (4)) at $h(t)=0$ . Now since both are quadratic equations we will solve one showing the full method which can be repeated for the other one.

Thus we have for Ben, Eqn. (3) gives:

$h(t)=0-16t^2+60t+40=0$

Using the quadratic expression to find the roots of the quadratic we have:

$t_{1,2}=\frac{-b+/-\sqrt{b^2-4ac} }{2a} \\t_{1,2}=\frac{-60+/-\sqrt{60^2-4(-16)(40)} }{2(-16)} \\t_{1,2}=\frac{-60+/-\sqrt{6160} }{-32} \\t_{1,2}=\frac{15+/-\sqrt{385} }{8}\\\\t_{1}=4.3276 sec\\t_{2}=-0.5776 sec$

Since time can only be positive we reject the $t_{2}$ solution and we keep that Ben's book took $t=4.3276$ seconds to reach the ground.

Similarly solving for Josh we obtain

$t_{1}=3.6794sec\\t_{2}=-0.6794sec$

Thus again we reject the negative and keep the positive solution, so Josh's book took $t=3.6794$ seconds to reach the ground.

Then we can find the difference between Ben and Josh times as

$t_{Ben}-t_{Josh}= 4.3276 - 3.6794 = 0.6482$

So to answer the original question:

Whose textbook reaches the ground first and by how many seconds?

Josh's textbook reached the ground first
Josh's textbook reached the ground first by a difference of $t=0.6482$

3 0

2 years ago

The value of 12pi over 10pi times 5pi Over 6pi is closest to the whole number (blank). Find the blank

lisov135 [29]

Given:

The expression is

$\dfrac{12\pi}{10\pi}\times \dfrac{5\pi}{6\pi}$

To find:

The value of the given expression closest to the whole number.

Solution:

We have,

$\dfrac{12\pi}{10\pi}\times \dfrac{5\pi}{6\pi}$

Cancel out the common factors from each fraction.

$=\dfrac{6}{5}\times \dfrac{5}{6}$

$=\dfrac{6\times 5}{5\times 6}$

$=\dfrac{30}{30}$

$=1$

Therefore, the value of the given expression is 1.

6 0

2 years ago

The gas tank of Tyrell's truck holds 19.8 gallons. when the tank empty, Tyrrell fills it with gas that costs $3.65 per gallon. a

Tems11 [23]

It is given in the question that

The gas tank of Tyrell's truck holds 19.8 gallons. when the tank empty, Tyrrell fills it with gas that costs $3.65 per gallon.

It means cost of one gallon of gas is $3.65 .

And the tank hold 19.8 gallon . So cost of 19.8 gallon is

$= $3.65*19.8 = $72.27$

Therefore about $72.27 it will cost to fill the tank .

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3 years ago

PLEASE Answer

Burka [1]

A......

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5 0

2 years ago

Please help, will give extra points

adelina 88 [10]

Answer:x=31

angle AOC = 124

angle BOC = 56

Step-by-step explanation:

We first need to solve for x to solve the rest. We would normally solve for x by setting 2 equations equal to each other, in this case however, we know that the two angles are adjacent and in total add up to 180. Therefore we combine like terms of both angles, and set them equal to 180.

So, we do

3x+31+2x-6=180 We will combine like terms

5x+25=180 Now we will do inverse operations

5x=155

x=31

We plug x into angle AOC to solve for it

3(31)+31= 124

180-124=56 or angle BOC because the whole angle is 180, and if we subtract 124 from 180 we get the remainder which is angle BOC

Or if you want,

2(31)-6=56

5 0

3 years ago

Read 2 more answers