please help me with geometry

Answer:

a. 16 slug b. 3.2 ft

Step-by-step explanation:

a. Total mass of the rod

Since the linear density at a point of the rod,λ varies directly as the third power of the measure of the distance of the point form the end, x

So, λ ∝ x³

λ = kx³

Since the linear density λ = 2 slug/ft at then center when x = L/2 where L is the length of the rod,

k = λ/x³ = λ/(L/2)³ = 8λ/L³

substituting the values of the variables into the equation, we have

k = 8λ/L³

k = 8 × 2/4³

k = 16/64

k = 1/4

So, λ = kx³ = x³/4

The mass of a small length element of the rod dx is dm = λdx

So, to find the total mass of the rod M = ∫dm = ∫λdx we integrate from x = 0 to x = L = 4 ft

M = ∫₀⁴dm

= ∫₀⁴λdx

= ∫₀⁴(x³/4)dx

= (1/4)∫₀⁴x³dx

= (1/4)[x⁴/4]₀⁴

= (1/16)[4⁴ - 0⁴]

= (256 - 0)/16

= 256/16

= 16 slug

b. The center of mass of the rod

Let x be the distance of the small mass element dm = λdx from the end of the rod. The moment of this mass element about the end of the rod is xdm =  λxdx = (x³/4)xdx = (x⁴/4)dx.

We integrate this through the length of the rod. That is from x = 0 to x = L = 4 ft

The center of mass of the rod x' = ∫₀⁴(x⁴/4)dx/M where M = mass of rod

= (1/4)∫₀⁴x⁴dx/M

= (1/4)[x⁵/5]₀⁴/M

= (1/20)[x⁵]₀⁴/M

= (1/20)[4⁵ - 0⁵]/M

= (1/20)[1024 - 0]/M

= (1/20)[1024]/M

Since M = 16, we have

x' =  (1/20)[1024]/16

x' = 64/20

x' = 3.2 ft

Answer: 12%

Step-by-step explanation:

95,000-83,600=11,400

(11,400/95000)(100) = 12%

The percentage reduction in the price of the car is 12%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here: Original price of car=95000 and Selling price=83600

Thus the reduction in price= 95000-83600

                                            =11400

Thus percentage reduction in the price of the car is

= 11400/95000 × 100

=12%

Hence, The percentage reduction in the price of the car is 12%

Learn more about percentages here:

https://brainly.com/question/29306119

#SPJ2

Answer:

[tex]- \frac{\pi}{3}[/tex]

Step-by-step explanation:

Given

[tex]y = -3\cos(3x - \pi) + 5[/tex]

Required

The phase

We have:

[tex]y = -3\cos(3x - \pi) + 5[/tex]

Rewrite as:

[tex]y = -3\cos(3(x - \frac{\pi}{3})) + 5[/tex]

A cosine function is represented as:

[tex]y = A\cos(B(x + C)) + D[/tex]

Where:

[tex]C \to[/tex] Phase

By comparison:

[tex]C = - \frac{\pi}{3}[/tex]

Hence, the phase is: [tex]- \frac{\pi}{3}[/tex]

Answer:

I think you can go with:

The margin of error is equal to half the width of the entire confidence interval.

so  try .74 ±   =   [ .724 , .756] as the confidence interval

Step-by-step explanation:

Step-by-step explanation:

the guys is wrong i checked

Answer:

9

Step-by-step explanation:

b = Brandon

4b=b+27

-b   -b

-------------

3b = 27

----   ----

3      3

b = 9

Brandon is 9 years old.

Answer:

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]

Step-by-step explanation:

Given

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]

Required

Simplify

We have:

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]

Open brackets

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²+xy+5x - 2x\²-2xy-10 + xy + y\²[/tex]

Collect like terms

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²- 2x\²+xy-2xy+ xy+5x -10 + y\²[/tex]

[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]

Answer:

Let x = the number of ounces of Solution A

Let y = the number of ounces of Solution B

x + y = 180        y = 180 - x

.60x + .85y = .75(180)

.60x + .85y = 135      Multiply both sides of the equation by 100 to remove the decimal points.

60x + 85y = 13500

60x + 85(180 - x) = 13500

60x + 15300 - 85x = 13500

-25x = -1800

x = 72ounces

y = 180 - 72

y = 108 ounces          

Step-by-step explanation:

Wyzant (ask an expert) solution on their website.

the answer is 1/12

the first rolling a 4 has a 1/6 chance of happening and half of the numbers on the die are odd, so 1/6*1/2=1/12

Answer:

30.03

Step-by-step explanation:

[(33.7)² - (15.3)²]^½

= [1135.69 - 234.09]^½

= [901.6]^½

= 30.02665483

= 30.03 (4sf)

Answer:

5/12

Step-by-step explanation:

Heads: 1/2

Number greater than 1

A dice has 6 sides. 5 are greater than 1

The probability is 5/6

P(heads and a die greater than 1) = 1/2 * 5/6 = 5/12 or a little less than 1/2

Answer:

16[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Answer:

First, find two points on the graph:

Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}} = \frac{8-2}{2-0} =\frac{6}{2}=3[/tex]

16 + (-3) = 16 - 3 = 13

Answer:

the ans is 252................

9514 1404 393

Answer:

Step-by-step explanation:

The expression written is interpreted according to the order of operations as ...

  sin(x) -(1/x) -1

As x approaches 0 from the left, this approaches +∞. As x approaches 0 from the right, this approaches -∞. These values are different, so the limit does not exist.

__

Maybe you intend ...

  sin(x -1)/(x -1)

This can be evaluated directly at x=0 to give sin(-1)/-1 = sin(1). The argument is interpreted to be radians, so sin(1) ≈ 0.84147098...

The limit is about 0.841 at x=0.

Answer:

C. repeating back what the customer says

9514 1404 393

Answer:

  4·10 +4·5 = 6·12 -6·2

Step-by-step explanation:

Each outside factor multiplies each inside term.

  4(10 +5) = 6(12 -2)

  4·10 +4·5 = 6·12 -6·2

Given:

If x, y, and z are positive integers, then

[tex]2^x\times 3^y\times 5^z=54000[/tex]

To find:

The value of [tex]x+y+z[/tex].

Solution:

First we need to find the prime factors of 54000.

[tex]54000=2\times 2\times 2\times 2\times 3\times 3\times 3\times 5\times 5\times 5[/tex]

[tex]54000=2^4\times 3^3\times 5^3[/tex]        ...(i)

We have,

[tex]54000=2^x\times 3^y\times 5^z[/tex]        ...(ii)

On comparing (i) and (ii), we get [tex]x=4,y=3,z=3[/tex].

The sum of [tex]x,y,z[/tex] is:

[tex]x+y+z=4+3+3[/tex]

[tex]x+y+z=10[/tex]

Therefore, the value of [tex]x+y+z[/tex] is 10.

Answer:

$240

Step-by-step explanation:

A year has 12 month in it so lets multiply the 10 by 12 which is $120,Mean a year is $120 so 2years will be $120×2 which is $240

Answer:

x+1/5x

Step-by-step explanation:

Because the eqaution would be x+10%=x+1/10+10%=1/5+x

Then the equation equals x+1/5

Step-by-step explanation:

here's the answer to your question

Answer:

I believe the answer is 4 37/50!

Answer:

3645

Step-by-step explanation:

f(1)=5

f(2)=3*5=15.

f(3)=45, basically it's a geometric sequence with formula an=5*(3)^(n-1). The 7th term is 5*(3)^6=3645

Answer:

dv = surface area * dh

so

dv/dt = surface area * dh/dt

width at surface = 40 + (80-40)(30/40)

= 40 + 30 = 70 cm = 0.70 m

so

surface area = 9 * .7 = 6.3 m^2

so

.3 m^3/min = 6.3 m^2 * dh/dt

and

dh/dt = .047 meters/min or 4.7 cm/min

Step-by-step explanation:

Answer: y = 3x + 6

Step-by-step explanation:

(x-intercept of -2: (-2,0))

(slope = m)

y = mx + b, (-2,0), m = 3

[tex]y=mx+b\\0=3(-2)+b\\0=-6+b\\b=6\\y=3x+6[/tex]

Answer:

z = √3

Step-by-step explanation:

sin (30°) = z / 2√3

z = sin (30°) 2√3

z = √3

Answer:

900

Step-by-step explanation:

Given that :

Enrollment declined by 20% from between September 1991 to September 1994

This means there was a reduction in enrollment ;

Enrollment in September 1994 = 720

Enrollment in September 1991 = x

Hence,

Enrollment in 1994 = (1 - decline rate ) * enrollment in 1991

720 = (1 - 20%) * x

720 = (1 - 0.2) * x

720 = 0.8x

720 / 0.8 = 0.8x/0.8

900 = x

Hence, Enrollment in September 1991 = 900 enrollments

Answer: hello from the question the volume of tank = 6000 gallons while the value in the Torricelli's equation = 5000 hence I resolved your question using the Torricelli's law equation

answer:

1) a) -180  gallons/minute ,

  b)  -160 gallons/minute

  c)  -120 gallons/minute

  d) 0

2) The water is flowing out fastest when t = 5 min

3) The water is flowing out slowest after t = 20 mins

Step-by-step explanation:

Volume of tank = 5000 gallons

Time to drain = 50 minutes

Volume of water remaining after t minutes by Torricelli's law

V = 5000 ( 1 - [tex]\frac{1}{50}t[/tex] )^2 ----- ( 1 )

1) Determine the rate at which water is draining from the tank

First step : differentiate equation 1 using the chain rule to determine the rate at which water is draining from the tank

V' = [tex]-10000[ ( 1 - \frac{1}{50}t ) (\frac{1}{50}) ][/tex]

a) After t = 5minutes

V' = - 10000[ ( 1 - 0.1 ) * ( 0.02 ) ]

   = -180  gallons/minute

b) After t = 10 minutes

V' = - 10000[ ( 1 - 0.2 ) * ( 0.02 ) ]

   = - 160 gallons/minute

c) After t = 20 minutes

V' = - 10000 [ ( 1 - 0.4 ) * ( 0.02 ) ]

   = -120 gallons/minute

d) After t = 50 minutes

V' = - 10000 [ ( 1 - 1 ) * ( 0.02 ) ]

   = 0 gallons/minute

2) The water is flowing out fastest when t = 5 min

3) The water is flowing out slowest after t = 20 mins  because no water flows out after 50 minutes