Question:
Exodus Limousine Company has $1,000 par value bonds outstanding at 15 percent interest. The bonds will mature in 30 years. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. Compute the current price of the bonds if the percent yield to maturity is 10%
Note the tutor added 10% as the yield
Answer:
Price of bond= $1,471.35
Explanation:
The value of the bond is the present value (PV) of the future cash receipts expected from the bond. The value is equal to present values of interest payment plus the redemption value (RV) discounted at the yield rate
Value of Bond = PV of interest + PV of RV
The value of bond Exodus Limousine Company can be worked out as follows:
Step 1
PV of interest payments
PV = A × (1+r)^(-n)/r
A-annul interest payment:
= 15% × 1,000 = 150
r-Annual yield = 10%
n-Maturity period = 30
PV of interest payment:
=150× (1- (1+0.1)^(-30)/0.1= 1,414.037
Step 2
PV of Redemption Value
= 1000 × (1.1)^(-30) = 57.308
Step 3
Price of bond
=1,414.037 + 57.308 = 1,471.345
Price of bond= $1,471.345
Which of the following statements are true?
A. Different companies will use different charts of accounts based on individual company need.
B. The chart of accounts contains the balance of all the accounts in the ledger.
C. The general ledger contains all of the accounts that a company uses, along with detail of the balances in those accounts.
D. The general ledger and the chart of accounts can be ordered in any sequence because they are not formal financial systems.
Answer:
TRUE: A. Different companies will use different charts of accounts based on individual company need.
C. The general ledger contains all of the accounts that a company uses, along with detail of the balances in those accounts.
Explanation:
A. Different companies will use different charts of accounts based on individual company need.
A chart of accounts is the combination of all the accounts of an organization in an organized and structured model whose objective is to establish a codification so that there is a standardization of the company's financial information to assist the work of the accounting sector.
Therefore, each company will have a model chart of accounts referring to its activities and processes.
C. The general ledger contains all of the accounts that a company uses, along with detail of the balances in those accounts.
The general ledger can be defined as the set of all accounts held in the organization in detail.
Through the information in the accounts, the organization is able to correctly separate each one by type and carry out the organizational financial statement.
Cooperton Mining just announced it will cut its dividend from $4.01 to $2.57 per share and use the extra funds to expand. Prior to the announcement, Cooperton's dividends were expected to grow at a 3.4% rate, and its share price was $50.07. With the planned expansion, Cooperton's dividends are expected to grow at a 4.7% rate. What share price would you expect after the announcement? (Assume that the new expansion does not change Cooperton's risk.) Is the expansion a good investment?
Answer:
$34.35
The price has fallen from $50.07 to $34.35 which means that Expansion will not be a good option.
Explanation:
Computation for the share price to expect after the announcement
Using this formula
Ke = [ D1 / P0 ] +g
Where,
D1 =$4.01
P0 = $50.07
g =3.4%
Let plug in the formula
Ke = [ D1 / P0 ] +g
Ke= [ $4.01 / $50.07] + 0.034
Ke= 0.0800+ 0.034
Ke= 0.1140
Second step is to find the Price after Expansion using this formula
P0 = D1 / [ Ke - g ]
Where,
D1=$2.57
Ke=0.1140
g=4.7%
Let plug in the formula
P0= $ 2.57 / [ 0.1140 - 0.047 ]
P0=$2.57/0.067
P0=$ 34.35
Based on this calculation, we can see that the price has fallen from $50.07 to $34.35 which means that Expansion will not be a good option.
Therefore the share price that you would expect after the announcement will be $34.35
Larry Nelson holds 1,000 shares of General Electric's (GE) common stock. The annual stockholder meeting is being held soon, but as a minor shareholder, Larry doesn't plan to attend. Larry did not sell his shares but gave his voting rights to the management group running General Electric (GE). Larry must have signed a ________ that gives the management group control over his shares.
Larry also holds 2,000 shares of common stock in a company that only has 20,000 shares outstanding. The company's stock currently is valued at $47.00 per share. The company needs to raise new capital to invest in production. The company is looking to issue 5,000 new shares at a price of $37.60 per share. Larry worries about the value of his investment.
Larry's current investment in the company is_______. If the company issues new shares and Larry makes no additional purchase, Larry's investment will be worth_______.
This scenario is an example of_______. Larry could be protected if the firm's corporate charter includes a ________ provision.
If Larry exercises the provisions in the corporate charter to protect his stake, his investment value in the firm will become________.
Answer:
Larry must have signed a PROXY AGREEMENT that gives the management group control over his shares.
A proxy agreement is generally used for stockholders voting procedures, they basically grant another person the right to vote on behalf of another stockholder.
Larry's current investment in the company is $94,000.
= 2,000 stocks x $47 = $94,000
If the company issues new shares and Larry makes no additional purchase, Larry's investment will be worth $90,240.
company's new market value = (20,000 x $47) + (5,000 x $37.60) = $1,128,000
new stock price = $1,128,000 / 25,000 stocks = $45.12
= $45.12 x 2,000 = $90,240
This scenario is an example of STOCK DILUTION.
The stock price will lower because the increase in the company's value is less than proportional to the increase in the number of stocks.
Larry could be protected if the firm's corporate charter includes a PREEMPTIVE provision.
Preemptive rights give current stockholders the right to purchase more stocks (in case the company issues more stocks) before any outside investors.
If Larry exercises the provisions in the corporate charter to protect his stake, his investment value in the firm will become $112,800.
= [(5,000 / 10) x $37.60] + $94,000 = $18,800 + $94,000 = $112,800
Suppose that on Valentine's Day, the demand for both roses and greeting cards increases by the same percentage amount. However, the price of roses increases by more than the price of greeting cards. Based on this information, you can conclude that the supply of Valentine's card:_______.
Answer:
The correct answer is: the supply of the greeting cards is less elastic than the one of the roses.
Explanation:
To begin with, the elasticity show how much the price and the quantity are related by indicating the variation that happens to one of them when the other changes. Therefore that the supply of the greeting cards is less sensitive to price because when the quantity demanded increased the price did not change as much as the roses due to the fact that the sellers were not encourage as much as the sellers of the roses to produce more and therefore to increase the price of the cards. So to sum up, when the price changed the sellers were not encourage to increase the production of the cards as much as the production of the roses because of its elasticity.
Answer:
the supply of the greeting cards is less elastic than the one of the roses.
Explanation:
All of the following are normally found in a corporation's stockholders' equity section, exceptAll of the following are normally found in a corporation's stockholders' equity section, except a. Paid-in-capital in excess of par b. Unearned Rent c. Retained Earnings d. Common Stock
Answer:
b. Unearned Rent
Explanation:
Shareholders Equity is the residual amount of Assets after deducting the Liabilities.
The Unearned Rent is a Liability and is not found in the Shareholders Equity Section.
Liabilities are Present obligations of an entity that arise as a result of past events, the settlement of which will result in out flow of economic benefits from the entity.
A growing population encourages economic growth as it creates a larger workforce. Suppose a surge in immigration increases a country's total population and its overall economic output increases. As a result, the country's real GDP increases from $304,000 to $316,500. What is the percent change in real GDP
Answer:
4.11%
Explanation:
the percentage change in real GDP = [(new real GDP - old real GDP) / old real GDP] x 100 = [($316,500 - $304,000) / $304,000] x 100 = 4.11%
Generally a surge in immigration will result in both higher nominal and real GDP, but what should be more important is how real GDP per capita changes. If real GDP per capita increases, then the inflow was positive and made the economy grow for better. If real GDP per capita decreases, even if total real GDP increases, then the economy is not doing better.
Nathan works for a major automobile manufacturing company. His company is being sued by hundreds of customers who have been injured when the steering wheel airbags exploded upon a low-impact collision. The customers are demanding monetary damages. This lawsuit is based on
Answer:
Product liability, is the right answer.
Explanation:
The liability of a manufacturer or seller for handing over a defective commodity into the hands of the consumers is known as the product liability. The responsibility for handing over the defective product that causes injuries lies with the retailers of the product who are a part of the distribution chain. The law requires that the good sold to the consumer meets the ordinary expectations of the consumer. If the consumer's ordinary expectations aren't met due to an unexpected defect or danger, the consumer may ask for monetary damages.
"An analysis of yield curves of U.S. Government and lower medium quality corporate bonds shows the yield spread to be widening over the last 4 months. This is an indication that investors expect the economy to:"
Explanation:
recession
Answer:
To be going into recessionary situation over the coming time period. The widening spread indicates that the yield on lower grade corporate bond are higher than normal relative to yield bonds issued by government. This situation is happening due to investors investing highly in government bonds leading to increase in yields.
Aladdin Jets is attempting to build an airplane that is made by welding the skin (outside layer) of the plane. The technique is much less expensive than an alternative riveting technology. The firm is also using a new type of jet engine with superior efficiency. The new entrant is entering a market that is realizing a substantial increase in competition. Which of the following would be strategies that the firm is attempting?
a. Cost reduction
b. Product differentiation
c. reduction in competitive intensity
d. a and b
e. all of the above.
Answer: Option D( a and b)
Explanation:
From the question, we are informed that Aladdin Jets wants to build an airplane that is made by welding the skin of the plane and that the technique is much less expensive than an alternative riveting technology.
We are further informed that the firm is also using a new type of jet engine with superior efficiency. The above analysis shows that the firm is using a product differentiation strategy and also reducing costs. While the company is trying out new things, it's also trying to minimize cost.
Kindzi Co. has preferred stock outstanding that is expected to pay an annual dividend of $4.18 every year in perpetuity. If the required return is 4.19 percent, what is the current stock price?
Answer:
The current price of the stock is $99.76
Explanation:
The price of a stock which pays a constant dividend throughout for an indefinite period of time can be calculated using the present value of perpetuity formula. The stock qualifies as a perpetuity as it pays a constant cash flow after equal intervals of time and for indefinite time period.
The formula for the present value of perpetuity is,
Present Value = Cash Flow or Dividend / r
Where,
r is the discount ratePresent value = 4.18 / 0.0419
Present value = $99.76
So, the current price of the stock is $99.76
Beatrice invests $1,320 in an account that pays 4 percent simple interest. How much more could she have earned over a 5-year period if the interest had been compounded annually
Answer:
How much more earned is $21.98
Explanation:
Calculation of the amount earned when investment in paying on simple interest
Interest = Amount * Interest rate * No of years
Interest = 1320 * 4% * 5
Interest = $264
Total amount = Interest + Amount invested
Total amount = $1320 + 264
Total amount = $1,584
Therefore, the total amount earned when earning on simple interest of 4% is $1,584
Calculation of the amount earned when investment interest in paying compounded annually
Pv= 1320
n= 5
i= 4%
Fv= ?
Fv= P(1+i)^-n
Fv= 1320(1+0.04)^5
Fv= 1320(1.04)^5
Fv= 1320(1.216652)
Fv= $1605.98
Therefore, the total amount earned when earning on interest compounded annually is $1,605.98
Calculation of how much more earned
Amount earned = Amount earned as per compounded interest - Amount earned as per simple interest
Amount earned = $1,605.98 - $1,584
Amount earned = $21.98
Therefore, how much more earned is $21.98
If a small electric automobile manufacturer is able to gain the social return generated by its electric motor, its demand for financial capital would Group of answer choices
Answer: shift to the left
Explanation:
When a small electric automobile manufacturer is able to gain the social return generated by its electric motor, then its demand for financial capital will shift to the left.
This means that since the financial capital shift to the left, there will be a reduction in the demand for financial capital.
holdy Inc's bonds currently sell for $1,275. They pay a $120 annual coupon and have a 20-year maturity, but they can be called in 5 years at $1,120. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. What is the difference between the bond's YTM and its YTC?
Answer:
Yield to maturity (YTM) is 1.91% higher than yield to call (YTC).
Explanation:
YTM = {coupon + [(face value - market value)/n]} / [(face value + market value)/2]
YTM = {$120 + [($1,000 - $1,275)/20]} / [($1,000 + $1,275)/2] = $106.25 / $1,137.50 = 9.34%
YTC = {coupon + [(call price - market value)/n]} / [(call price + market value)/2]
YTC = {$120 + [($1,120 - $1,275)/5]} / [($1,120 + $1,275)/2] = $89 / $1,197.50 = 7.43%
9.34% - 7.43% = 1.91%
A university bookstore buys mechanical pencils from a wholesaler. The wholesaler offers discount for large order quantity per shipment according to the following price schedule:
Order Quantity Price Per Unit
1 to 200 $4.00
201 to 1,000 $3.60
1,001 to 2,000 $3.40
2,001 and greater $3.25
The bookstore expects an annual demand of 2,500 units. It costs $10 to place an order, and the annual cost of holding a unit in stock is 30% of the unit’s procurement price. Determine the best order quantity.
Answer:
226 units
Explanation:
Formula : [tex]\sqrt{\frac{2 * Annual Demand * Ordering Cost}{Holding Cost}[/tex]
[tex]\sqrt{\frac{2*2500*10}{0.3*3.25} }[/tex] = 226
The economic order quantity is the minimum amount of inventory that a seller must keep to demand and lower the holding cost. The reorder point is the inventory management system in which a certain level of inventory is set as a trigger for reordering the stock. Ordering cost is determined by the number of order placed.
Mayan Company had net income of $132,000. The weighted-average common shares outstanding were 80,000. The company has no preferred stock. The company sold 3,000 shares before the end of the year. There were no other stock transactions. The company's earnings per share is:
Answer:
EPS = $1.71 per unit
Explanation:
Earnings per share is the total earnings attributable to ordinary shareholders divided by the number of units of common stock .
It represents profit per unit of stock unit held by common stock holder investor. The higher the more profitable and the better.
Earnings per share = Earnings attributable to ordinary shareholders / units of common stock
Earnings attributable to ordinary shareholders= Net income after tax - preference dividend
Net income = 132,000
Preference dividend = Nil
Number of shares at the end of the year = Number of shares at the beginning - number of shares at the end
Number of shares at the end of the year = 80,000 - 3000 = 77,000 units
Earnings = = 132,000 - 0 = 132,000
Earnings per shares(EPS) = $132,000 / 77,000 units = $1.71 per unit
EPS = $1.71 per unit
The petty cash fund has a current balance of $ 350, which is the established fund balance. Based on activity in the fund, it is determined that the balance needs to be changed to $ 550. Which journal entry is needed to make this change?
A. No journal entry is needed because this change only involves cash.
B. Debit the Petty Cash account and credit the Cash account for $200.
C. Debit the Cash account and credit the Petty Cash account for $200.
D. Debit the Petty Cash account and credit the Cash account for $550.
Answer:
i think the answer is B. Debit the Petty Cash account and credit the Cash account for $200.
Explanation:
The goal of collaborative planning, forecasting, and replenishment (CPFR) is to improve operational efficiency and manage inventory.
a. True
b. False
Answer:
Option "a" = true.
Explanation:
"The goal of collaborative planning, forecasting, and replenishment (CPFR) is to improve operational efficiency and manage inventory"
The statement given above is right or CORRECT and TRUE(option a).
The concept of "Collaborative Planning, Forecasting and Replenishment" was first brought into limelight in the year 1995. Collaborative Planning, Forecasting & Replenishment make sure that a terminology or say a concept in commerce which is know as "Integration of supply chain" is improving greatly.
The collaborative planning, forecasting, and replenishment (CPFR) helps to improve operational efficiency by reducing costs such as that of logistics, transportation and many more.
In order to achieve the target for the nominal interest rate established by the monetary policy rule, the central bank adjusts:
Answer: C. the money supply.
Explanation:
The Money Supply in an economy can be adjusted to influence interest rates due to the indirect relationship that exists between them. This means that when there is a high money supply, interest rates are lower and vice versa.
The Central Bank controls how much money is in the economy by using Open Market operations that buy or sell government securities as well as reserve requirements on banks.
Creating own dividend policy. Carmen owns shares of Wiseguy Entertainment. Wiseguy has just declared a per share dividend on a stock selling at $. What must Carmen do if she wants no cash dividends at this time, worth of dividends, or $ worth of dividends? Show her wealth in paper and cash under each scenario. Assume a world of no taxes. First, if Carmen does not want an annual "dividend income" from his stock holdings, what must she do to get this level of income? (Select the best response.)
Answer:
Hello your question has some missing figures here is the complete question with the missing figures
Creating own dividend policy. Carmen owns shares of Wiseguy Entertainment. Wiseguy has just declared a $0.30 per share dividend on a stock selling at $24.3. What must Carmen do if she wants no cash dividends at this time, $82000 worth of dividends, or $107000 worth of dividends? Show her wealth in paper and cash under each scenario. Assume a world of no taxes. First, if Carmen does not want an annual "dividend income" from his stock holdings, what must she do to get this level of income? (Select the best response.)
Answer: Wealth in cash = $107000 , wealth in paper = $8160000
since her annual dividend received = ($102000) Carmen needs to purchase 4250 more shares of stock to get to this level of income
Explanation:
Given data
shares held = 340000
dividend = $0.3
stock price = $24.3
Stock price - dividend = $24 ( dividend price )
A) what Carmen must do if she doesn't want cash dividends
Based on shares held the annual dividend of Carmen = 340000 * 0.3 = $102000
If Carmen doesn't want the cash dividend she can use it to purchase more shares for Wiseguy entertainment which will be = dividend received / dividend price = 102000 / 24 = 4250 shares
when the Annual dividend required is $82000
she can buy shares worth = $20000 ( 102000 - 82000 )
= 20000 / 24 = 833.33
when the Annual dividend required is $107000
Carmen can sell shares worth = $5000 ( 107000 - 102000 )
= 5000 / 24 = 208.33
therefore wealth in cash would be
= $107000
wealth in paper would be
= dividend price * number of shares held
= $24 * 340000 = $8160000
Stan Slickum has a used car that can be bought for $8 comma 500 cash or for a $1 comma 000 down payment and $770 per month for 12 months. What is the effective annual interest rate on the monthly payment plan?
Answer:
48.8%
Explanation:
We can use the rate formula to determine the monthly rate as follows:
=rate(nper,pmt,-pv,fv)
nper is the number of monthly payments which is 12
pmt is the amount of monthly payment which is $770
pv is the cash price of the minus downpayment i.e $8500-$1000=$7500
fv is the balance after all payments have been made i.e $0
=rate(12,770,-7500,0)=3.37%
effective monthly rate=(1+3.37% )^12-1=48.8%
You have $256,000 to invest in a stock portfolio. Your choices are Stock H, with an expected return of 14.1 percent, and Stock L, with an expected return of 10.7 percent. If your goal is to create a portfolio with an expected return of 12.3 percent, how much money will you invest in Stock H and in Stock L
Answer: Investment in H = .4706($256,000)
Investment in H = $120,470.59
Investment in L = .5294($256,000)
Investment in L = $135,529.41
Explanation:
Investment in Stock H
Investment in Stock L
Here, the expected return of the portfolio and the expected return of the assets in the portfolio have been given and we're to calculate the dollar amount of each asset in the portfolio. So, we need to find the weight of each asset in the portfolio. Since the total weight of the assets in the portfolio must equal 1 (or 100%), we can find the weight of each asset as:
E[Rp] = .1230 = .141xH + .107(1 - xH)
xH = .4706
xL = 1 - xH
xL = 1 - .4706
xL = .5294
So, the dollar investment in each asset is the weight of the asset times the value of the portfolio, so the dollar investment in each asset must be:
Investment in H = .4706($256,000)
Investment in H = $120,470.59
Investment in L = .5294($256,000)
Investment in L = $135,529.41
Which of these would most likely be funded through a Community Facilities District?
Answer:
what ones there's only the question not the answers
Teller Co. is planning to sell 900 boxes of ceramic tile, with production estimated at 870 boxes during May. Each box of tile requires 44 pounds of clay mix and a quarter hour of direct labor. Clay mix costs $0.40 per pound and employees of the company are paid $12.00 per hour. Manufacturing overhead is applied at a rate of 110% of direct labor costs. Teller has 3,900 pounds of clay mix in beginning inventory and wants to have 4,500 pounds in ending inventory.
Required:
What is the total amount to be budgeted for manufacturing overhead for the month?
Answer:
Budgeted overhead= $2,877.6
Explanation:
Giving the following information:
Direct labor required:
Production= 870 units
Direct labor hours= 870*0.25= 218 hours
Direct labor cost= $12 an hour
Manufacturing overhead is applied at a rate of 110% of direct labor costs.
To calculate the allocated overhead for the period, we need to use the following formula:
Allocated MOH= Estimated manufacturing overhead rate* Actual amount of allocation base
Direct labor cost= 218*12= $2,616
Allocated MOH= 1.1*2,616= $2,877.6
An online-only bank currently offers a 7-year CD (certificate of deposit) paying simple interest rate of 4% per quarter. If you want to get $4,240 from this CD 7 years later, how much do you have to purchase today?
Answer:
The answer is $1,413.94
Explanation:
Number of periods(N) = 28 periods (7 years x 4 quarters)
Interest rate(I/Y) = 4% per quarter. Therefore, interest rate per year is 16% per year(4% x 4 quarters)
Future value(FV) = $4,240
Present Value (PV) = ?
Let's use a financial calculator:
N = 28; I/Y = 4, FV = 4,240; CPT PV= -1,413.94
Therefore, the present value is $1,413.94
_______________ of well-to-do individuals often put their own money into small new companies at an early stage of development, in exchange for owning some portion of the firm. Group of answer choices
Answer: C. A Network
Explanation:
One of the ways of raising capital is through the use of Angel Investors. These are usually well off individuals with excess cash for investment who look for companies to invest in at an early stage because they are trying to gain a positive return when the companies become successful.
To make their funds more substantial and their services easier to reach, Angel investors form networks to enable them achieve their mission of putting their own money into small new companies at an early stage of development, in exchange for owning some portion of the firm.
Suppose you are Coca-Cola and you are competing with Pepsi-Cola. Both of you would make more money if you advertised less - but you find yourself in a repeated prisoner's dilemma where you both are deciding to advertise. How would you prefer to deal with your competitor
Available Options Are:
A. Be nice and don't advertise first.
B. If your competitor advertises do not escalate the situation, but do match their move
C. Wait to respond to your competitors actions.
D. Make sure your actions are clear to your competitor.
E. All of the above except 'c'.
Answer:
Option C. Wait to respond to your competitors actions.
Explanation:
The best way to respond to our customer would be by to wait to respond to Pesi-cola's actions. By doing so, we have option to take best advantage out of the position. Furthermore, it is in the best interest of both competitors to increase the revenue by not sepending huge amounts on advertising products. And this is only possible if both Coca-cola and Pepsi-cola not investing in marketing products. So the only option here that gicves this option is Statement C.
It can also help to design better strategy to take advantage of the competitor's strategy.
Scenario: Home Monopolist) A monopolist faces a demand curve given by P = 60 2Q and has total costs given by TC = Q2. Its marginal revenue is MR = 60 4Q and its marginal cost is MC = 2Q. Compared with the no-trade equilibrium, consumer surplus ___________ when the monopolist engages in free trade.
Answer:
2Q
Explanation:
Economy equilibrium is where MC = MR.
Marginal cost equals marginal return when the supply and demand is linear. Consumer surplus is the additional amount that a consumer is willing to pay for the goods and services. Here MC = 2Q and MR = 60 + 4Q. Here consumer is paying 2Q additional in the equation of marginal return.
Based on predicted production of 28,000 units, a company anticipates $574,000 of fixed costs and $511,000 of variable costs. The flexible budget amounts of fixed and variable costs for 26,000 units are
Answer:
$574,000 fixed costs and $474,500 variable cost
Explanation:
According to the predicted production of 28,000 units, a company has a fixed cost of $574,000
The variable costs is $511,000
Therefore the flexible budget amount for the fixed and variable costs when 26,000 units are produced can be calculated as follows
The fixed costs still remains constant at $574,000
Variable cost = 511,000/28,000×26,000
= 18.25×26,000
= $474,500
Hence the fixed cost is $574,000 and the variable cost is $474,500
Which of the following determine(s) the level of real interest rates? I) The supply of savings by households and business firms II) The demand for investment funds III) The government's net supply and/or demand for funds
Answer:
I II & III - All of the above.
Explanation:
Real interest rate is an interest rate that shows actual cost of funds to a borrower having taken into consideration the effects of inflation while also reflecting actual gain to the lender. It shows how purchasing power has value on interest paid on a loan.
With regards to the above, determinants of real interest rates are; the supply of savings by household and business firms, the demand for investment funds and the government's net supply/and or demand for funds.
Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with a diameter of 30 meters.
Answer:
dv= 989100cm^3
Explanation:
The volume of a sphere can be calculated using below formula
Volume of a sphere = 4/3 π r^3
Therefore, for a hemisphere, V= 2/3 pi r^3
V=(4/3)πr³
V= 2/3πr³
dV/dr=4πr²
Then we need to pproximate dV/dr with
ΔV/Δr then we have
Volume of hemispherical some is one half of the the volume of a sphere where dr is change in radius, dv is change in volume
dV/dr=2πr²
Take the derivative of V with respect to r then we have
dV=2πr²dr
where
Radius = diameter/2
Our diameter is 30cm then
r=30m/2 = 15cm
Then we convert to cm we have
r= 1500cm
dv= 2×π ×(1500)^2 × 0.07
dv= 989100cm^3
the amount of paint in cubic centimeters needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with a diameter of 30 meters is
989100cm^3
Using a linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with a diameter of 30 meters will be: 989,601.69 cubic centimeters
Volume of a sphere = 4/3 πr^3
Hemisphere:
V= 2/3 πr^3
dV = 2πr^2 dr
Where:
dr=0.07cm
r=(1/2)×30m=1500cm
Let plug in the formula
dV = 2×π×(1500^2)×(.07)
dV=989,601.69 cubic centimeters
Inconclusion using a linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with a diameter of 30 meters will be: 989,601.69 cubic centimeters
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