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viva [34]
2 years ago
13

Show that b^2 is greater than equal to or less than ac, according as a, b, c are in A.P., G.P.

Mathematics
1 answer:
ValentinkaMS [17]2 years ago
5 0

Answer/Step-by-step explanation  (ac > b² or b² < ac. )

A/c to question, we have to show:-

b² >ac in A.P ........ (1)

b² = ac in G.P .....(2)

b² < ac in H.P. ..... (3)

b = a+c/2 (A.P)

b = √ac ( G.P)

b = 2ac/a+c (H.P)

In A.P :

b² > ac = b² - ac

= (a+c/2)² - ac

= (a²+2ac+c²/4) - ac  = a² + 2ac + c² - 4ac / 4

= a² - 2ac + c² / 4  = ( a - c ) ² / 4 > 0  Hence, b²>ac

In G.P:-

b = √ac

Hence, b² = ac

In H.P :-  b² < ac = ac > b²  = ac - b²  = ac - ( 2ac / a+c)

= ac(a+c) - 2ac / a+c

= a²c + ac² - 2ac / a+c

= ac(2ac - 2) / a+c > 0

Hence, ac > b² or b² < ac.

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A trapezoid has an area of 35 square inches. It has a base of 8 inches and 6
Liula [17]

the height of the trapezoid of 5, i think.

my work:

i used this formula: 2 x a + b / A

so, you plug in what you know.

2 x 8+6 / 35 = 5

5 0
3 years ago
The formula for the volume of a cone is V=1/3 pi r2h the radius r of the cone may be expressed as
Naily [24]

r = √(3V/πh)

multiply both sides by 3 to eliminate the fraction

πr²h = 3V ( divide both sides by πh )

r² = 3V/ πh ( take the square root of both sides )

r = √(3V/πh)


3 0
3 years ago
Read 2 more answers
Iris weighed 5 large watermelons from her garden. Here are the weights in pounds. 17,11,21,24,22 what is the mean weight
Rufina [12.5K]

Answer:

Mean weight = 19 pounds

Step-by-step explanation:

From the question given above, the following data were obtained:

17, 11, 21, 24, 22

Number of data (n) = 5

Mean weight =?

The mean of a set of data is the value obtained by adding all the data together and dividing the result obtained by the total number of data. Thus, the mean can be obtained as follow:

Summation of data = 17+ 11 + 21 + 24 + 22

= 95

Number of data = 5

Mean = Summation of data / Number of data

Mean = 95 / 5

Mean weight = 19 pounds

Therefore, the mean weight of the data is 19 pounds

5 0
3 years ago
Plz help I will do anything
Basile [38]

There's no need to get into an ethical morass over math homework.


111.


M is 20% less than N means

M is 100-20=80% of N

M=0.80 N

M/N = 0.8 = 4/5


Ratio: 4/5


112.


When we know <em>a, </em>the average, and <em>n, </em>how many numbers there are, we know the sum <em>s</em>, because <em>a=s/n </em>so <em>s=na.</em>


So the sum of our six numbers is 6(3.5)=21 so the sum of the seven numbers is 21+4.2=25.2 so the average is 25.2/7 = 3.6


Answer: 3.6


113.


|2p + 4 | < 3


At p=-2 the absolute value is zero. As p gets more negative the absolute value argument (inside part) gets negative and the absolute value gets bigger, more positive. Eventually the inside will be exactly -3, when


2p +4 = -3


2p = -7


p = -7/2 = -3 1/2


So p=-4 will make the inequality false, and p=-3 is the smallest integer that makes the inequality true.


Answer: -3



114.


The distance from the origin is given by the Pythagorean Theorem and this one is a 3/4/5 right triangle:


d = \sqrt{(-.3)^2 + (-.4)^2}=.5


Answer: .5 or 1/2


4 0
3 years ago
What is the solution to 5a-15+9a=3a+29
pogonyaev

5a-15+9a=3a+29

We simplify the equation to the form, which is simple to understand

5a-15+9a=3a+29

We move all terms containing a to the left and all other terms to the right.

+5a+9a-3a=+29+15

We simplify left and right side of the equation.

+11a=+44

We divide both sides of the equation by 11 to get a.

a=4

3 0
3 years ago
Read 2 more answers
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