1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nitella [24]
2 years ago
12

A box has the shape of a rectangular prism with height 30 cm. If the height is increased by 0.9 ​cm, by how much does the surfac

e area of the box​ increase?
Use pencil and paper. Show your work. Then show a second way to solve the problem. Explain which way you like better and why.
Mathematics
1 answer:
crimeas [40]2 years ago
4 0

Answer:

The corresponding increase in surface area of the rectangular prism for an increase of 0.9 cm in height is given by

ΔS = [1.8 (L + B)] cm

where L = length of the rectangular prism

B = Breadth of the rectangular prism

Step-by-step explanation:

A rectangular prism is essentially a cuboid.

The surface area of the cuboid is given as

S = 2[LB + LH + BH]

where

L = length of the rectangular prism

B = Breadth of the rectangular prism

H = Height of the rectangular prism

S = 2LB + 2LH + 2BH

Derivative explains that, for small changes in the two quantities,

(∂S/∂H) = (ΔS/ΔH)

ΔS = ΔH × (∂S/∂H)

S = 2LB + 2LH + 2BH

(∂S/∂H) = 2L + 2B = 2(L + B)

ΔH = 0.9 cm

ΔS = ΔH × (∂S/∂H)

ΔS = 0.9 × 2(L + B) = 1.8 (L + B)

A rectangular prism is essentially a cuboid.

The surface area of the cuboid is given as

S = 2[LB + LH + BH]

where

L = length of the rectangular prism

B = Breadth of the rectangular prism

H = Height of the rectangular prism

S = 2LB + 2LH + 2BH

If the height of the rectangular prism increases by 0.9 cm

S(new) = (2×L×B) + 2L(H + 0.9) + 2B(H + 0.9)

S(new) = 2LB + 2LH + 1.8L + 2BH + 1.8B

S(new) = 2LB + 2LH + 2BH + 1.8L + 1.8B

The old surface area, S = 2LB + 2LH + 2BH

Hence, the change or increase in surface area is S(new) - S

[2LB + 2LH + 2BH + 1.8L + 1.8B] - [2LB + 2LH + 2BH] = 1.8L + 1.8B = 1.8 (L + B)

Still the same increase in surface area as obtained by the first method.

Hope this Helps!!!

You might be interested in
HELP PLEASEEEEEE NO LINKS PLEASE 20PTS!!!!
nevsk [136]

Answer:

x = 5

Step-by-step explanation:

3x + 11 = 26

3x = 15

x = 5

5 0
3 years ago
Use symmetry to graph the inverse of the function.
Olin [163]
<h2>Answer:</h2>

a. is the correct option

<h2>Step-by-step explanation:</h2>

The graph of a function f and its inverse function f^{-1} are related to each other. The relationship between these two graphs can be explained by taking a point (a,b) that is on the graph of f, then point (b,a) must lie on the graph f^{-1} and vice versa meaning that the graph of f^{-1} is a reflection of f in the line y=x. The only graph that meet this requirement is the option a. For instance, the point (0,5) is on the graph of f while the point (5,0) is on the graph of f^{-1} as indicated below.

5 0
3 years ago
Item 7<br> Find the sum.<br> 3(2−0.9h)+(−1.3h−4) =
m_a_m_a [10]

Answer:

= 2(1 - 2h)

Step-by-step explanation:

Given that:

=3(2−0.9h)+(−1.3h−4)

Simplifying:

=(6 - 2.7h) + (-1.3h - 4)

Removing brackets

=6 - 2.7h -1.3h - 4

Adding like terms (h terms and constants)

= 2 - 4h

We can take 2 common as:

= 2(1 - 2h)       Required sum

I hope it will help you!

7 0
3 years ago
Read 2 more answers
What is 62 take away 38 =​
Allushta [10]

Answer:

the answer is 24

Step-by-step explanation:

68-38 = 24

3 0
3 years ago
Read 2 more answers
Will give brainlliest :&gt;
Goshia [24]

Answer:

48 degrees

Step-by-step explanation:

<u>1) Solve for x</u>

Complementary angles add up to 90 degrees. Therefore, m<A + m<B is equal to 90:

A+B=90\\(2x+20)+(3x)=90

Open up the parentheses

2x+20+3x=90\\5x+20=90

Subtract 20 from both sides

5x+20-20=90-20\\5x=70

Divide both sides by 5

\frac{5x}{5} =\frac{70}{5} \\x=14

Therefore, x is equal to 14.

<u>2) Determine angle A</u>

A=2x+20

Substitute x with 14

A=2(14)+20\\A=28+20\\A=48

Therefore, the measure of angle A in degrees is 48 degrees.

I hope this helps!

3 0
2 years ago
Other questions:
  • Summerschool help part 2
    13·1 answer
  • PLEASE HELP ASAP!!!!
    11·1 answer
  • The revenue, cost, and profit functions for a line of cell phone cases is shown. Identify the location on the profit function wh
    14·2 answers
  • Line AB has a slope of -3 with point A at (2,4) and Point B at (x,-2). What is the value of the x-coordinate of Point B?
    9·1 answer
  • Write 0.2 as a fraction in simplest form.<br> 0.2=0
    8·1 answer
  • Please help, its so simple
    7·2 answers
  • Urgent please ans this​
    14·1 answer
  • Please help with this its confusing somehow :(​
    9·1 answer
  • The area of a planned garden can be modeled by the equation A= -4w2 + 64w,
    13·2 answers
  • What fraction is greter than 3 - 5
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!