The equation for the volume of a cylinder is v=πr²h the positive value of r, in terms of h and V, is

Answers

Answer 1

Answer:

The positive value of r is $\sqrt{(v)/(\pi h) }$

What is the volume of cylinder ?

The volume of cylinder is basically the density of the cylinder which amount it can carry.

The volume of cylinder is the product of the area of the circular base and height.

If, r be the base radius and h be the height of a cylinder, then the volume of cylinder(v) = $\pi r^(2) h$ cubic unit

How to find the value of r from volume of cylinder formula ?

The volume of cylinder(v) = $\pi r^(2) h$ ,where r=radius, h=height, v=volume of cylinder

∴ $v=\pi r^(2) h$

⇒ $r^(2) =(v)/(\pi h)$

⇒ $r=$ ± $\sqrt{(v)/(\pi h) }$

According to the problem, Only the positive value of r is required.

So, $r=\sqrt{(v)/(\pi h) }$

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The base of a triangle is 3 cm longer than its altitude. The area of the triangle is 35cm^2. Find the altitude. (Hint: use the area of a triangle. 1/2 * base * altitude.)

Answers

The altitude of the triangle whose base is 3 cm longer than its altitude is 7cm.

What is triangle?

Triangle is a plane figure with three straight sides and three angles such that the sum of the angles is 180°.

Given is a triangle whose base is 3cm longer than its altitude. The area of the triangle is 35 cm².

Assume that the altitude of the triangle is 'a' cm.

The area of a tringle is given by -

A [T] = 1/2 x base x height.

Now,

Altitude of triangle = a cm

Base of triangle = (a + 3) cm

Substituting the values in the formula of area, we get -

A [T] = 1/2 x base x height

A [T] = 1/2 x a x (a + 3)

a(a + 3) = 35 x 2

a(a + 3) = 70

a² + 3a - 70 = 0

On solving the above quadratic equation, you will get two values of x -

a = - 10 and a = 7

Altitude cannot be negative. Therefore, the altitude of the triangle is 7 cm.

Therefore, the altitude of the triangle whose base is 3 cm longer than its altitude is 7cm.

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The base is 3+(x), altitude is x so substitute. Now we know the area of a triangle is base X height X 1/2. Substitute again! 1/2 (3+x)(x)=35. Multiply both sides by 2 to cancel out the 1/2. Now you have (x)(x+3)=70 and you have to foil out the left side x^2+3x=70. Subtract 70 on both sides x^2+3x-70=0. Find two numbers that multiply to -70 and add to 3. Solve (x+10)(x-7)=0. the x value is 7. since you can't have negative length values. Substitute 7 into 3+x for the base so you know the base is 10 and the height is 7.

Identify all of the expressions that simplify to −7/8.2 1/2 ÷ -7/20
______________

-1 2/5÷ -1 3/5
_____________
4 ÷ −4 4/7
_____________
−7/10 ÷ 4/5

Show your work pls

Answers

5/2 ÷ 7/10
5/2 x 10/7
50/14; 25/7; Answer: 3 4/7

-7/5 ÷ -8/5
-7/5 x 5/8
-35/40
-(-35/40)
-(-7/8). Answer: 7/8

-7/10 x 5/4
-35/40
-7/8. Answer: -7/8

Hoped this helped

A chord can contain at most how many diameters

Answers

A cord links any two points on a circle.

The greatest distance between two points on a circle is the length of the diameter.

Hence a chord can contain at most one diameter.

Caleb's mother said they will drive 1 /4 hour to get there, and they will drive another 1 /4 hour back. Once they arrive, Caleb's brother will be playing in 3 soccer games. Each soccer game takes 3 4 hour, and there is no break in between games. Calculate how long will they be away from home.

Answers

Answer: They are away for $2(3)/(4)\ hours$ from home.

Step-by-step explanation:

Since we have given that

Time to get there = $(1)/(4)$

Time to get back = $(1)/(4)$

Number of soccer games = 3

Time for each soccer games = $(3)/(4)$

So, total time for 3 games would be

$3* (3)/(4)=(9)/(4)$

So, the time for which they will be away from home is given by

$(1)/(4)+(9)/(4)+\frac{1}4}=(1+9+1)/(4)=(11)/(4)=2(3)/(4)\ hours$

Hence, they are away for $2(3)/(4)\ hours$ from home.

Which of the following terms are like terms?a) 9x and 9y b)12ac^2 and ac^2 c)8xy and 8xz d)ab^2 and x^2y

Answers

Like terms means terms that have the same variable (and with the same exponent).

A) 9x and 9y <-- those are different variables. This is incorrect.

B) 12ac^2 and ac^2 <-- those are the same variables and same exponent. Correct.

C) 8xy and 8xz <-- different variables, incorrect.

D) ab^2 and x^2y <-- different variables, incorrect.

Correct answer is $\fbox {B)}$

Like terms are terms that have the same variables and also have the same exponents on those variables.

Out of all your choices, answer choice B) 12ac^2 and ac^2 fits that definition.

B is your answer.

The population of a city is represented by the function p(t)=33,500(1.014)^t where t represents time in years and corresponds to the year 2000. According to this model, what is the expected population of the city 2015

Answers

Replace t with 15 (2015-2000):

$p(15)=33,500(1.014)^(15)\n \n p(15)=33,500(3,8729)\n \n p(15) \approx 129,742 \ inhabitants$

$p(t) = 33500(1.014)^t\n \n t = (2015 - 2000) = 15\n \n i.e., p(15) = 33500(1.014)^(15) \n \n => p(15) = 33500.38729 \n \n => 1297421500$

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