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shutvik [7]
2 years ago
9

Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.

Mathematics
1 answer:
makkiz [27]2 years ago
8 0

Answer:

390ft^2\\

Step-by-step explanation:

Ok so we have 2 (congruent) triangles and 3 rectangles.

Your main approach to this problem should be to find the area of each of the faces and adding them up to get to your final answer. Your question makes a point of including the correct unit in your answer. Since this is surface area, the unit would be ft^2

Now let's start:

First, I am going to start with finding the area of the rectangles.

12\cdot11=132\\13\cdot11=143\\5\cdot11=55\\\\55+143+132=330

Alright, next lets move on to the triangles.

They are both the same, if you notice. So find one and double it.

12\cdot5=60\\\frac{60}{2}=30\\30\cdot2=60

now lets add em all

330+60

= 390 and thats your final answer, dont forget to include the unit, ft^2

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Answer:

Answer c

Step-by-step explanation:

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6 0
3 years ago
2. The sum of two numbers is 30. Determine the two numbers if their product is a maximum.
SCORPION-xisa [38]

Answer:

X+y=30

X=30-y

Z=yx

Z=y(30-y)

D/dy

z=30–2y

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Therefore x=15

Step-by-step explanation:

5 0
2 years ago
Use lagrange multipliers to find the shortest distance, d, from the point (4, 0, −5 to the plane x y z = 1
Varvara68 [4.7K]
I assume there are some plus signs that aren't rendering for some reason, so that the plane should be x+y+z=1.

You're minimizing d(x,y,z)=\sqrt{(x-4)^2+y^2+(z+5)^2} subject to the constraint f(x,y,z)=x+y+z=1. Note that d(x,y,z) and d(x,y,z)^2 attain their extrema at the same values of x,y,z, so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.

The Lagrangian is

L(x,y,z,\lambda)=(x-4)^2+y^2+(z+5)^2+\lambda(x+y+z-1)

Take your partial derivatives and set them equal to 0:

\begin{cases}\dfrac{\partial L}{\partial x}=2(x-4)+\lambda=0\\\\\dfrac{\partial L}{\partial y}=2y+\lambda=0\\\\\dfrac{\partial L}{\partial z}=2(z+5)+\lambda=0\\\\\dfrac{\partial L}{\partial\lambda}=x+y+z-1=0\end{cases}\implies\begin{cases}2x+\lambda=8\\2y+\lambda=0\\2z+\lambda=-10\\x+y+z=1\end{cases}

Adding the first three equations together yields

2x+2y+2z+3\lambda=2(x+y+z)+3\lambda=2+3\lambda=-2\implies \lambda=-\dfrac43

and plugging this into the first three equations, you find a critical point at (x,y,z)=\left(\dfrac{14}3,\dfrac23,-\dfrac{13}3\right).

The squared distance is then d\left(\dfrac{14}3,\dfrac23,-\dfrac{13}3\right)^2=\dfrac43, which means the shortest distance must be \sqrt{\dfrac43}=\dfrac2{\sqrt3}.
7 0
3 years ago
Find the unit rate, and then use it to solve the problem.
rusak2 [61]
Rate = 10/2 = 5 trees per hour

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3 0
3 years ago
For a party, the family bought 24 pizzas for $12.50 each and 36 bottles of soda for $1.20 each. How much did the family spend on
xxTIMURxx [149]

Answer:

1) The amount the family spent on pizza is $300

2) The amount the family spent on soda is $43.2

3) The amount the family spent in all is $343.2

Step-by-step explanation:

The number of pizzas bought by the family = 24

The price of each pizza = $12.50

The number of bottles of soda the family bought = 36

The price of each bottles of soda = $1.20

1) The amount the family spent on pizza = 24 × $12.50 = $300

2) The amount the family spent on soda = 36 × $1.20 = $43.2

3) The amount the family spent in all = The amount the family spent on pizza + The amount the family spent on soda

∴ The amount the family spent on soda = $300 +$43.2 = $343.2.

7 0
2 years ago
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