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3 years ago

The picture shows a feeding trough that is shaped like a right prism.

Mathematics

1 answer:

ollegr [7]3 years ago

5 0

A)We have been given →

Hieght of trough = 5m

length of trough = 6m

Breadth of trough = 4m

so , As the top is opened for feeding animals.

Area of base = length× Breadth

= (6×4) m²
= 24 m²

Area of Front and back face = Hieght × length

= (5×6) m²
= 30m²

Area of side faces = hieght × Breadth

= (5×4) m²
= 20 m²
____________________________________

B)Total Surface area of trough will be given by formula - 2(lb+bh+hl)

= 2{(6×4)+(4×5)+(5×6)}

= 2{24+20+30}

= 2×74

= 148 m²

As we have been told top is open , so we will deduct top from Total surface Area to obtain Surface area →

(148-24) m²

(Area of top will be same as base area , that is 24m² as we have solved in A)

= 124m²

Answer→ Surface area of trough is 124m²
___________________________________

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Evaluate the surface integral. S xz ds, s is the part of the plane 2x 2y z = 4 that lies in the first octant

maksim [4K]

The value of the given surface integral is 4.

The given plane intercepts the coordinate axes at (2, 0, 0), (0, 2, 0), and (4, 0, 0). These point are the coordinates of a triangular region that we can parameterize using.

$S(u,v)=(1-u)((1-u)(2,0,0)+u(0,2,0)+u(4,0,0)\\S(u,v)=(2(1-u)(1-v),2u(1-v),4v)$

<h3>What is the surface integral?</h3>

A surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analog of the line integral. Given a surface, one may integrate a scalar field over the surface or a vector field.

with 0≤u≤1 and 0≤v≤1. Then the surface element ds is equivalent to

$ds=\||\:\left(s_u\times \:\:S_v\right)||dudv=12\left(1-v\right)dudv$

The surface integral is then

$\int \:\int \:_Sxzds=12\int _0^1\:\int _0^1\:\left(2\left(1-u\right)\left(1-v\right),2u\left(1-v\right),4v\right)dvdu=4$

Therefore the value of the given surface integral is 4.

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2 years ago

In Jamie's class, 1/5 of the students are boys. What percent of the students in Jamie’s class are boys?

Cloud [144]

Answer:

The percentage of boys students in Jamie's class is 20 %

Step-by-step explanation:

Given as :

The total number of boys in the Jamie's class = $\frac{1}{5}$ of the total student

Let the total number of student's in the class = x

So, The number of boys = $\frac{1}{5}$ × x

I.e The number of boys = $\dfrac{x}{5}$

So , in percentage the number of boys students in class = $\dfrac{\textrm Total number of boy student}{\textrm Total number of students}$ × 100

OR, % boys students = $\dfrac{\dfrac{x}{5}}{x}$ × 100

or, % boys students = $\frac{100}{5}$

∴ % boys students = 20

Hence The percentage of boys students in Jamie's class is 20 % . Answer

7 0

3 years ago

Read 2 more answers

Irene knows there are 2 cups in 1 pint. She writes the equation c=2p to find the number of cups, c, in any number of pints, p. U

Natasha2012 [34]

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as there are no options to select from.

However, a general explanation is as follows.

Given

$2\ cups = 1\ pint$

Required

Is $c = 2p$ a correct expression?

Let

$c = cups$

$p = pint$

So:

$2\ cups = 1\ pint$

becomes

$2 * c = 1 * p$

$2c = p$

Divide both sides by 2

$c =\frac{1}{2}p$

Hence:

$c = 2p$ is incorrect

4 0

3 years ago

Hiking up a mountain, you notice that the air temperature drops 10 degrees every 1000 meters increase in elevation. Write a mult

Elina [12.6K]

decrease in temperature if you hike up the mountain 3000 meters is $-30$ ° .

<u>Step-by-step explanation:</u>

Here we have , Hiking up a mountain, you notice that the air temperature drops 10 degrees every 1000 meters increase in elevation . We need to find Write a multiplication expression to represent the decrease in temperature if you hike up the mountain 3000 meters. Let's find out:

For every 1000 meters rise in elevation , there is decrease in 10° of temperature . So , For rise in n meters in elevation , there is decrease in n×10° of temperature i.e

Decrease in temperature = (n/1000)×(-10) i.e.

⇒ (n/1000)×(-10)

⇒ $\frac{n}{1000}(-10)$

At n = 3000 meters:

⇒ $\frac{3000}{1000}(-10)$

⇒ $3}(-10)$

⇒ $-30$ °

Therefore , decrease in temperature if you hike up the mountain 3000 meters is $-30$ ° .

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3 years ago

Given JM=27, ml=16, jl=46, nk=15, KLM= 48, JkM=78, MJL=22, find each missing value.

Llana [10]

Answer:

KL = 27

JK = 16

MK = 30

NL = 23

m∠JKL = 132°

m∠KLJ = 22°

m∠KMJ = 54°

m∠KJL = 26°

Step-by-step explanation:

The given parameters of the quadrilateral JKLM are;

JM = 27, ML = 16, JL = 46, NK = 15, KLM = 48, JKM = 78, MJL = 22

Taking the sides as parallel, we have that quadrilateral JKLM is a parallelogram

Therefore;

KL = JM = 27

JK = ML = 16

m∠KLJ = m∠MJL = 22°

MN = NK = 15

MK = MN + NK = 15 + 15 = 30

NL = JL/2 = 46/2 = 23

m∠KJM = m∠KLM = 48°

m∠KJL = m∠KLM - m∠MJL = 48° - 22° = 26°

m∠KML = m∠JKM = 78°

m∠MKL = 180° - m∠KML - m∠KLM = 180° - 78° - 48° = 54°

m∠MKL = 54°

m∠JKL = m∠JKM + m∠MKL = 78° + 54° = 132°

m∠KMJ = m∠MKL = 54°

3 0

2 years ago