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
Butoxors [25]
3 years ago
5

The area of a trapezoid is 864 cm. It has a height of 24 cm, and the length

Mathematics
1 answer:
Bogdan [553]3 years ago
6 0

Answer:=42 cm

Step-by-step explanation:

Strap=(a+b)*h/2    ( where a and b are trapezoid' s  bases and h is a height)

So   864=(30+b)*24/2

30+b=864*2/24

30+b=864/12

30+b=72

b=72-30

b=42 cm

You might be interested in
Use the pic for more info will mark brainlest
Lelechka [254]

Answe7.5 i think

Step-by-step explanation:

4 0
3 years ago
Find the prime factorization of each number 891
cricket20 [7]

Answer:

The prime factorization of 891 is 9^2*11

Step-by-step explanation:

Divide 891 by 9, 9, and finally, 11. Or use a factorization calculator.

6 0
3 years ago
What is 5 1/2 +2 1/7 due in one hour help please
nika2105 [10]

Answer:

7 9/14

Step-by-step explanation:

1/2=7/14

1/7=2/14

7/14+2/14=9/14

5+2=7

6 0
2 years ago
Read 2 more answers
Lagrange multipliers have a definite meaning in load balancing for electric network problems. Consider the generators that can o
Ivahew [28]

Answer:

The load balance (x_1,x_2,x_3)=(545.5,272.7,181.8) Mw minimizes the total cost

Step-by-step explanation:

<u>Optimizing With Lagrange Multipliers</u>

When a multivariable function f is to be maximized or minimized, the Lagrange multipliers method is a pretty common and easy tool to apply when the restrictions are in the form of equalities.

Consider three generators that can output xi megawatts, with i ranging from 1 to 3. The set of unknown variables is x1, x2, x3.

The cost of each generator is given by the formula

\displaystyle C_i=3x_i+\frac{i}{40}x_i^2

It means the cost for each generator is expanded as

\displaystyle C_1=3x_1+\frac{1}{40}x_1^2

\displaystyle C_2=3x_2+\frac{2}{40}x_2^2

\displaystyle C_3=3x_3+\frac{3}{40}x_3^2

The total cost of production is

\displaystyle C(x_1,x_2,x_3)=3x_1+\frac{1}{40}x_1^2+3x_2+\frac{2}{40}x_2^2+3x_3+\frac{3}{40}x_3^2

Simplifying and rearranging, we have the objective function to minimize:

\displaystyle C(x_1,x_2,x_3)=3(x_1+x_2+x_3)+\frac{1}{40}(x_1^2+2x_2^2+3x_3^2)

The restriction can be modeled as a function g(x)=0:

g: x_1+x_2+x_3=1000

Or

g(x_1,x_2,x_3)= x_1+x_2+x_3-1000

We now construct the auxiliary function

f(x_1,x_2,x_3)=C(x_1,x_2,x_3)-\lambda g(x_1,x_2,x_3)

\displaystyle f(x_1,x_2,x_3)=3(x_1+x_2+x_3)+\frac{1}{40}(x_1^2+2x_2^2+3x_3^2)-\lambda (x_1+x_2+x_3-1000)

We find all the partial derivatives of f and equate them to 0

\displaystyle f_{x1}=3+\frac{2}{40}x_1-\lambda=0

\displaystyle f_{x2}=3+\frac{4}{40}x_2-\lambda=0

\displaystyle f_{x3}=3+\frac{6}{40}x_3-\lambda=0

f_\lambda=x_1+x_2+x_3-1000=0

Solving for \lambda in the three first equations, we have

\displaystyle \lambda=3+\frac{2}{40}x_1

\displaystyle \lambda=3+\frac{4}{40}x_2

\displaystyle \lambda=3+\frac{6}{40}x_3

Equating them, we find:

x_1=3x_3

\displaystyle x_2=\frac{3}{2}x_3

Replacing into the restriction (or the fourth derivative)

x_1+x_2+x_3-1000=0

\displaystyle 3x_3+\frac{3}{2}x_3+x_3-1000=0

\displaystyle \frac{11}{2}x_3=1000

x_3=181.8\ MW

And also

x_1=545.5\ MW

x_2=272.7\ MW

The load balance (x_1,x_2,x_3)=(545.5,272.7,181.8) Mw minimizes the total cost

5 0
3 years ago
What is the length of the dotted line in the diagram below? Leave your answer in simplest radical form.
Pachacha [2.7K]

Answer:

\sqrt{93}

Step-by-step explanation:

8^2+5^2=c^2

64+25=c^2

89=c^2

c=\sqrt{89} <-- this is the length of the rectangle at the bottom

2^2+(\sqrt{89})^2=c^2

4+89=c^2

c=\sqrt{93}  <-- length of dotted line (diagonal)

6 0
3 years ago
Read 2 more answers
Other questions:
  • What is ten + ten • 2
    15·2 answers
  • Thomas made 8700mL of tomato soup. He packed 1.6L of the soup in his kids' lunches. He then froze half of the remaining soup. Ho
    12·1 answer
  • A study of the effect of exposure to color (red or blue) on the ability to solve puzzles used 42 subjects. Half the subjects (21
    6·1 answer
  • The expression below is a sum of cubes.<br> 64x3 + 125<br> O A. True<br> O B. False
    12·2 answers
  • F(x)=2x2 – 3x2 – 12x +3<br> 1 -5,5,1) by (-21,21,3)<br> Relative maxima
    6·1 answer
  • The cost of renting a car is $46/week plus $0.25/mile traveled during that week. An equation to represent the cost would be y =
    9·1 answer
  • 2x+5y=50<br><br> Solve for x and then solve for y
    15·1 answer
  • Damon is 12 3 4 years old. Dwight is 1 1 2 years younger than Damon and Jane is 1 1 5 years younger than Dwight. How old is Jane
    5·1 answer
  • What is the slope of y=0.75x+1 in fraction form <br> Will give brainliest
    7·1 answer
  • Create a real-world situational problem to represent the given equation or inequality.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!