Find the measure of each angle I’ll mark the brainiest :)

A cylinder has diameter of 4ft and a height of 9ft. Explain whether halving the diameter has the same effect on the surface area

elena55 [62]

Answer:

See Below

Step-by-step explanation:

The surface area of cylinder is given by the formula:

$SA=2\pi r^2 + 2\pi r h$

Where

r is radius ( diameter is 4, so radius is 4/2 = 2)

h is height ( h = 9)

Lets find original surface are:

$SA=2\pi r^2 + 2\pi r h\\SA=2\pi (2)^2 + 2\pi (2) (9)\\SA=8\pi +36\pi\\SA=44\pi$

<u>Halving diameter:</u>

diameter would be 4/2 = 2, so radius would be 2/2 = 1

So, SA would be:

$SA=2\pi r^2 + 2\pi r h\\SA=2\pi (1)^2 + 2\pi (1) (9)\\SA=2\pi +18\pi\\SA=20\pi$

<u>Halving height:</u>

Height is 9, halving would make it 9/2 = 4.5

Now, calculating new SA:

$SA=2\pi r^2 + 2\pi r h\\SA=2\pi (2)^2 + 2\pi (2) (4.5)\\SA=8\pi + 18\pi\\SA= 26\pi$

Original SA is $44\pi$ ,

Halving diameter makes it $20\pi$

Halving height makes it $26\pi$

So, halving diameter does not have same effect as halving height.

5 0

3 years ago

Write each expression as an equivalent expression with a single logarithm. Assume xx, yy, and zz are positive real

Alekssandra [29.7K]

Answer:

$\ln(\frac{xx + yy}{zz})^{\frac{1}{2}}$

Step-by-step explanation:

Given:

1/2(ln(xx + yy) − ln(zz))

Now,

From the properties of log function,

1) n × ln(x) = ln(xⁿ)

and,

2) ln(A) - ln(B) = $\ln\frac{A}{B}$

applying the properties in the given equation

we get the above equation as:

$\frac{1}{2}(\ln\frac{xx + yy}{zz})$

( using the property 2 we get (ln(xx + yy) − ln(zz) = $\ln\frac{xx + yy}{zz}$

or

⇒ $\ln(\frac{xx + yy}{zz})^{\frac{1}{2}}$ ( using the property 1 i.e n × ln(x) = ln(xⁿ) )

expression as an equivalent expression with a single logarithm is $\ln(\frac{xx + yy}{zz})^{\frac{1}{2}}$

3 0

4 years ago

Which investor has made a short term investment in this senario. Thomas sofia and aaron work together and they've each recently

jeka57 [31]

Answer:

Sofia bought some Treasury bonds that mature in nine months.

Step-by-step explanation:

it matures in only 9 months

3 0

4 years ago

Question 9 of 10 Which of these groups of values plugged into the TVM Solver of a graphing calculator will return the same value

hodyreva [135]

The TVM solver is a tool found in graphing calculators, that solve Time Value of Money problems.

The group of values that will return the same value as the given expression is;

D. N = 24; I% = 3.6; PV =; PMT = -415; FV = 0; P/Y = 12; C/Y = 12; PMT :END

<h3>What is Present Value?</h3>

Present value (PV) formula finds application in finance to calculate the present day value of an amount that is received at a future date.

In the TVM solver, we have;

I = The annual percentage rate

N = n × t

t = The number of years

PV = Present value

PMT = Payment

P/Y = Number of payments per year = n

C/Y = Number of compounding periods per year = n

The formula for monthly payment is presented as follows;

$P = \frac{M[(1+r/n)^{nt} - 1]}{(r/n)(1+r/n)^{nt}}$

M = $\frac{P.(r/n)(1+ r/n)^{nt} }{(1+ r/n)^{nt} - 1}$

Therefore, we get;

Where;

M = PMT = -415

P = PV

r = I

P/Y = n = 12

Therefore;

0.003 = I/12

I = 0.003 X 12 = 3.6%

N = n X t = 24

The value of the equation is the present value, PV = ?

When payment are made based on the PV, we have FV = 0

The group of values the same value as the expression

P = $\frac{(415)[(1+0.003)^{24}-1]}{(0.003)(1+0.003)^{24}}$

when plugged into the TVM solver of a calculator is;

D. N = 24; I% = 3.6; PV =; PMT = -415; FV = 0; P/Y = 12; C/Y = 12; PMT :END

Learn more about Present Value Solver from:

brainly.com/question/1759639

#SPJ1

7 0

2 years ago

Find the volume of the triangular prism described below.

Luda [366]

The volume of the prism 121.6 cube in.

Step-by-step explanation:

Given,

The base is right angle triangle whose two sides are equal.

So,

Base (b) = 8 in

Another side of right angle triangle (l) = 8 in

Height (h) of the prism = 3.8 in

To find the volume of the prism.

Formula:

V = $\frac{1}{2}$ bhl

Now,

V = $\frac{1}{2}$ ×8×8×3.8 cube in

= 121.6 cube in.

8 0

3 years ago