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2 years ago

If a+1,2a+1,4a-1 are in A.P, then the value of a is

Mathematics

1 answer:

Digiron [165]2 years ago

6 0

Answer:

a = 2

Step-by-step explanation:

In an AP the difference between consecutive terms is common (equal), thus

t₂ - t₁ = t₃ - t₂ , that is

2a + 1 - (a + 1) = 4a - 1 - (2a + 1) ← distribute and simplify both sides

2a + 1 - a - 1 = 4a - 1 - 2a - 1

a = 2a - 2 ( subtract 2a from both sides )

- a = - 2 ( multiply both sides by - 1 )

a = 2

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a famer has 120 feet of fencing with whcih to enclose two adjacent rectangular pens as shown. what dimeensions should be used th

Nat2105 [25]

The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Let the area be y .

Area = (base) × (height)

Base = 2x

Height = h

Let the area of the rectangular pens be y .

∴ y = 2xh

Perimeter of all the fencing = 4x+3h

∴ 4x+3h = 120

now we solve for h

3h = 120-4x

h = 40 - 4/3 x

Now we will substitute this value in the above first equation:

y = 2xh

or, y = 2x (40 - 4/3 x)

or, y = 80x - 8/3 x²

Now for the maximum area we have to find the first order differentiation of y

now,

dy /dx = 80 - 16/3 x

At dy/dx = 0 we get the value of x for which y is maximum.

80 - 16/3 x = 0

or, - 16/3 x = -80

or, x = 15 feet

Hence height = 40 - 4/3 x = 40 - 20 = 20feet

Maximum area = 2xh = 2×15×40 = 1200 square feet

The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Disclaimer : The missing figure for the question is attached below.

To learn more about area visit:

brainly.com/question/27531272

#SPJ4

6 0

10 months ago

PLEASE HELP ME ASAP!!!

Olenka [21]

Answer:

The answer is D. Surface Tension. :) I am forsure this is correct but please let me know. If I am correct please rate me 5 and thank me and mark me brainlest :)

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Find the output for each input of y = -2x.

VashaNatasha [74]

The 2nd choice down in correct.

4 0

2 years ago

Read 2 more answers

Please Answer

Lapatulllka [165]

Answer:

Part A: C. 4 to 1

Part B: 2

Step-by-step explanation:

What is the ratio of the number of students receiving a C and the number of students receiving an A?

<u>As per table given:</u>

12 students received a C and 3 students received a A

The ratio C/A is:

12/3 = 4/1

The correct answer choice is:

C. 4 to 1

Complete the statement:

For every student receiving a D, ______ students received a B.

<u>As per table given:</u>

4 students received a D and 8 students received a B

<u>The ratio D/B is:</u>

4/8 = 1/2

<u>The statement is:</u>

For every student receiving a D, 2 students received a B.

7 0

2 years ago

Learning the basics 6.23 suppose you select one value from a uniform distribution with a=0and b=10.what is the probability that

IgorC [24]

The area under the graph of the continuous uniform distribution is 1.
a. The probability that the value will be between 5 and 7 is the area between 5 and 7.
$P(5 \ \textless \ x \ \textless \ 7) = \frac{2}{10} = \frac{1}{5}$
b. The probability that the value will be between 2 and 3 is the are between 2 and 3.
$P(2 \ \textless \ x \ \textless \ 3)=\frac{1}{10}$
c. The mean is given by:
$\mu=\frac{a+b}{2}=\frac{0+10}{2}=5$
d. The variance is given by:
$\sigma^2}=\frac{1}{12}(b-a)^{2}=\frac{1}{12}(10)^{2}=8.3333$
The standard deviation is:
$\sqrt{\sigma} = \sqrt{8.3333} =2.887$

5 0

2 years ago