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patriot [66]
3 years ago
14

Help please I would really really appreciate it!!!i need someone kind hearted and that cares to help!!!

Mathematics
1 answer:
Free_Kalibri [48]3 years ago
6 0
#5) 7.065 sq. ft.
#6) 36 ft
#7) 200.96 sq. ft.
#8) 176.625 sq. ft.

Explanation
#5) Converting 18 inches to feet, 18/12 = 1.5.  The area of the circle would be given by A=3.14(1.5)² = 3.14(2.25) = 7.065 sq. ft.

#6) The radius is 18 inches, so the diameter is twice that:  18*2 = 36 inches.  Converting this to feet, we have 36/12 = 3 feet.  Each stone is 3 feet across.  Laying 12 of them against each other would give us a total length of 12*3 = 36 feet.

#7) The radius of the entire mirror with frame is 20/2 = 10.  The area of the entire mirror with frame is A=3.14(10²) = 3.14(100) = 314 in².
The area of the mirror without the frame is A=3.14(6²) = 3.14(36) = 113.04 in².

The difference between the two will give the area of the frame:
314-113.04 = 200.96 in²

#8) The area of the circular region is given by A=3.14(7.5²) = 176.625 ft²
You might be interested in
A body of constant mass m is projected vertically upward with an initial velocity v0 in a medium offering a resistance k|v|, whe
bixtya [17]

Answer:

tm = tₐ = -m/k ㏑{ [mg/k] / [v₀ + mg/k] }

Xm = Xₐ = (v₀m)/k - ({m²g}/k²) ㏑(1+{kv₀/mg})

Step-by-step explanation:

Note, I substituted maximum time tm = tₐ and maximum height Xm = Xₐ

We will use linear ordinary differential equation (ODE) to solve this question.

Remember that Force F = ma in 2nd Newton law, where m is mass and a is acceleration

Acceleration a is also the rate of change in velocity per time. i.e a=dv/dt

Therefore F = m(dv/dt) = m (v₂-v₁)/t

There are two forces involved in this situation which are F₁ and F₂, where F₁ is the gravitational force and F₂ is the air resistance force.

Then, F = F₁ + F₂ = m (v₂-v₁)/t

F₁ + F₂ = -mg-kv = m (v₂-v₁)/t

Divide through by m to get

-g-(kv/m) = (v₂-v₁)/t

Let (v₂-v₁)/t be v¹

Therefore, -g-(kv/m) = v¹

-g = v¹ + (k/m)v --------------------------------------------------(i)

Equation (i) is a inhomogenous linear ordinary differential equation (ODE)

Therefore let A(t) = k/m and B(t) = -g --------------------------------(ia)

b = ∫Adt

Since A = k/m, then

b = ∫(k/m)dt

The integral will give us b = kt/m------------------------------------(ii)

The integrating factor will be eᵇ = e ⁽<em>k/m</em>⁾

The general solution of velocity at any given time is

v(t) = e⁻⁽b⁾ [ c + ∫Beᵇdt ] --------------------------------------(iiI)

substitute the values of b, eᵇ, and B into equation (iii)

v(t) = e⁻⁽kt/m⁾ [ c + ∫₋g e⁽kt/m⁾dt ]

Integrating and cancelling the bracket, we get

v(t) = ce⁻⁽kt/m⁾ + (e⁻⁽kt/m⁾ ∫₋g e⁽kt/m⁾dt ])

v(t) = ce⁻⁽kt/m⁾ - e⁻⁽kt/m⁾ ∫g e⁽kt/m⁾dt ]

v(t) = ce⁻⁽kt/m⁾ -mg/k -------------------------------------------------------(iv)

Note that at initial velocity v₀, time t is 0, therefore v₀ = v(t)

v₀ = V(t) = V(0)

substitute t = 0 in equation (iv)

v₀ = ce⁻⁽k0/m⁾ -mg/k

v₀ = c(1) -mg/k = c - mg/k

Therefore c = v₀ + mg/k  ------------------------------------------------(v)

Substitute equation (v) into (iv)

v(t) = [v₀ + mg/k] e⁻⁽kt/m⁾ - mg/k ----------------------------------------(vi)

Now at maximum height Xₐ, the time will be tₐ

Now change V(t) as V(tₐ) and equate it to 0 to get the maximum time tₐ.

v(t) = v(tₐ) = [v₀ + mg/k] e⁻⁽ktₐ/m⁾ - mg/k = 0

to find tₐ from the equation,

[v₀ + mg/k] e⁻⁽ktₐ/m⁾ = mg/k

e⁻⁽ktₐ/m⁾ = {mg/k] / [v₀ + mg/k]

-ktₐ/m = ㏑{ [mg/k] / [v₀ + mg/k] }

-ktₐ = m ㏑{ [mg/k] / [v₀ + mg/k] }

tₐ = -m/k ㏑{ [mg/k] / [v₀ + mg/k] }

Therefore tₐ = -m/k ㏑{ [mg/k] / [v₀ + mg/k] } ----------------------------------(A)

we can also write equ (A) as tₐ = m/k ㏑{ [mg/k] [v₀ + mg/k] } due to the negative sign coming together with the In sign.

Now to find the maximum height Xₐ, the equation must be written in terms of v and x.

This means dv/dt = v(dv/dx) ---------------------------------------(vii)

Remember equation (i) above  -g = v¹ + (k/m)v

Given that dv/dt = v¹

and -g-(kv/m) = v¹

Therefore subt v¹ into equ (vii) above to get

-g-(kv/m) = v(dv/dx)

Divide through by v to get

[-g-(kv/m)] / v = dv / dx -----------------------------------------------(viii)

Expand the LEFT hand size more to get

[-g-(kv/m)] / v = - (k/m) / [1 - { mg/k) / (mg/k + v) } ] ---------------------(ix)

Now substitute equ (ix) in equ (viii)

- (k/m) / [1 - { mg/k) / (mg/k + v) } ] = dv / dx

Cross-multify the equation to get

- (k/m) dx = [1 - { mg/k) / (mg/k + v) } ] dv --------------------------------(x)

Remember that at maximum height, t = 0, then x = 0

t = tₐ and X = Xₐ

Then integrate the left and right side of equation (x) from v₀ to 0 and 0 to Xₐ respectively to get:

-v₀ + (mg/k) ㏑v₀ = - {k/m} Xₐ

Divide through by - {k/m} to get

Xₐ = -v₀ + (mg/k) ㏑v₀ / (- {k/m})

Xₐ = {m/k}v₀ - {m²g}/k² ㏑(1+{kv₀/mg})

Therefore Xₐ = (v₀m)/k - ({m²g}/k²) ㏑(1+{kv₀/mg}) ---------------------------(B)

3 0
3 years ago
What can 45/8 be simplified down to?
Alenkinab [10]
Eight goes into 45, 5 times so it would be 5 and 5/8.
5 0
3 years ago
Use the diagram. AB is a diameter, and AB is perpendicular to CD. The figure is not drawn to scale.
Westkost [7]

Answer:

The measure of arc BD is 147°

Step-by-step explanation:

we know that

If segment AB is perpendicular to segment CD

then

The measure of the inner angle CPA is a right angle (90 degrees)

Remember that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

so

m∠CPA=(1/2)[arc AC+arc BD]

substitute the given values

90°=(1/2)[33°+arc BD]

180°=33°+arc BD

arc BD=180°-33°=147°

7 0
3 years ago
A candy store sells varieties of candy. Out of these 20 varieties,12 varieties contain chocolate. What precent of the total numb
vazorg [7]
12/20=.6

Thus, move the decimal point two places to the right, and the answer is 60%
5 0
3 years ago
In a survey of 603 adults, 98 said that they regularly lie to people conducting surveys. Create a 99% confidence interval for th
marysya [2.9K]

Answer:

The population proportion is estimated to be with 99% confidence within the interval (0.1238, 0.2012).

Step-by-step explanation:

The formula for estimating the population proportion by a confidence interval is given by:

\hat{p}\pm z_{\alpha /2}\times\sqrt{\frac{\hat{p}\times(1-\hat{p})}{n}}

Where:

\hat{p} is the sample's proportion of success, which in this case is the people that regularly lie during surveys,

z_{\alpha /2} is the critical value needed to find the tails of distribution related to the confidence level,

n is the sample's size.

<u>First</u> we compute the \hat{p} value:

\hat{p}=\frac{successes}{n}=\frac{98}{603}=0.1625

<u>Next</u> we find the z-score at any z-distribution table or app (in this case i've used StatKey):

z_{\alpha /2}=2.576

Now we can replace in the formula with the obtained values to compute the confidence interval:

\hat{p}\pm z_{\alpha /2}\times\sqrt{\frac{\hat{p}\times(1-\hat{p})}{n}}=0.1625\pm 2.576\times\sqrt{\frac{0.1625\times(1-0.1625)}{603}}=(0.1238, 0.2012)

5 0
3 years ago
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