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3 years ago

Evaluate without a calculator: cot -270°

Mathematics

2 answers:

Luden [163]3 years ago

6 0

Answer:

0 is the answer.

Step-by-step explanation:

<h3>#CarryOnLearning</h3>

Nat2105 [25]3 years ago

4 0

Answer:

Step-by-step explanation:

The cotangent function is defined as cot x = adj / opp.

The terminal side of 270 degrees is the lower half of the y-axis. The adj side is zero (0) and the opp side is -1;

Therefore, cot (-270 degrees) = adj / opp = 0/(-1) = 0

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Ghost, Inc., has no debt outstanding and a total market value of $369,600. Earnings before interest and taxes, EBIT, are project

arlik [135]

Answer:

Ghost Inc.

A1.

Earnings Per share (EPS)

EPS in normal projection is $4.61 per share

EPS in an expansion is $5.31 Per share

EPS in a recession is $3.51 Per share

A2.

Changes to EPS in an expansion is +15.18%

Changes to EPS in a recession is -23.86%

B1.

Earnings Per share (EPS)

EPS in normal projection is $7.23 per share

EPS in an expansion is $8.62 Per share

EPS in a recession is $5.01 Per share

B2.

Changes to EPS in an expansion is +19.23%

Changes to EPS in a recession is -30.71%

Step-by-step explanation:

Underlying Information:

Earnings before interest and taxes, EBIT projections = $51,000

Expansionary EBIT projections = $51,000 x (100% + 15%) = $58,650

Recessionary EBIT projections = $51,000 x (100% -24%) = $38,760

Tax Rate = 24%

Market to Book Ratio = 1.0

Stock Price is constant.

Solution to A1.

Scenario 1 (Projected Earnings)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBIT minus tax = $51,000 - ($51,000 x 24%)

= $51,000 - $12240

= $38,760

Outstanding shares in issue = 8,400 ordinary Shares

EPS = $38,760 divided by 8,400 shares = $4.61 Per share

Scenario 2 (Projected Earnings in a strong expansion)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBIT minus tax = $58,650 - ($58,650 x 24%)

= $58,650 - $14,076

= $44,574

Outstanding shares in issue = 8,400 ordinary Shares

EPS = $44,574 divided by 8,400 shares = $5.31 Per share

Scenario 3 (Projected Earnings in a Recession)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBIT minus tax = $38,760 - ($38,760 x 24%)

= $38,760 - $9,302.4

= $29,457.6

Outstanding shares in issue = 8,400 ordinary Shares

EPS = $44,574 divided by 8,400 shares = $3.51 Per share

Solution to A2.

1.Changes to EPS in an expansion = EPS (Expansion) minus EPS (normal projection), all divided by EPS (normal projection)

= (5.31 - 4.61) / 4.61

= +15.18% change during an expansion

2.Changes to EPS in a recession = EPS (Recession) minus EPS (normal projection), all divided by EPS (normal projection)

= (3.51 - 4.61) / 4.61

= -23.86% change during a recession

Underlying Information:

Debt issue = $185,000

Interest on debt issued = 6% = $11,100

Market to Book Ratio = 1.0

Stock Price is constant.

Therefore Share Price = Market Value divided by Outstanding shares in issue = 369,600 / 8400 = $44

This implies our proceeds of $185,000 from debt issue would have repurchased $185,000 divided by $44 = 4,205 ordinary shares

This decision to repurchase its shares indicates the shares outstanding will reduce by 4,205. New outstanding shares will now be 4,195 shares

*Earnings before interest and taxes, EBIT normal projections = $51,000 & Earnings Before Tax (EBT) = $51,000 minus $11,100 (debt interest) = $39,900

*Expansionary EBIT projections = $51,000 x (100% + 15%) = $58,650 & Earnings Before Tax = $58,650 minus $11,100 (debt interest) = $47,550

*Recessionary EBIT projections = $51,000 x (100% -24%) = $38,760 & Earnings Before Tax = $38,760 minus $11,100 (debt interest) = $27,660

Tax Rate = 24%

Solution to B1.

Scenario 1 (Projected Earnings)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBT minus tax = $39,900 - ($39,900 x 24%)

= $39,900 - $9,576

= $30,324

Outstanding shares in issue = 4,195 ordinary Shares

EPS = $30,324 divided by 4,195 shares = $7.23 Per share

Scenario 2 (Projected Earnings in a strong expansion)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBT minus tax = $47,550 - ($47,550 x 24%)

= $47,550 - $11,412

= $36,138

Outstanding shares in issue = 4,195 ordinary Shares

EPS = $36,138 divided by 4,195 shares = $8.62 Per share

Scenario 3 (Projected Earnings in a Recession)

Earnings Per Share (EPS) = Net Income (Earnings after Tax) divided by Outstanding Shares in Issue

Net Income = EBT minus tax = $27,660 - ($27,660 x 24%)

= $27,660 - $6,638.40

= $21,021.60

Outstanding shares in issue = 4,195 ordinary Shares

EPS = $21,021.60 divided by 4,195 shares = $5.01 Per share

Solution to B2.

1.Changes to EPS in an expansion = EPS (Expansion) minus EPS (normal projection), all divided by EPS (normal projection)

= (8.62 - 7.23) / 7.23

= +19.23% change during an expansion

2.Changes to EPS in a recession = EPS (Recession) minus EPS (normal projection), all divided by EPS (normal projection)

= (5.01 - 7.23) / 7.23

= -30.71% change during a recession

6 0

3 years ago

Which transformation have been preformed on a graph of f(x)=x2 to obtained the graph of g(x) =-3(x+1)2-4?

avanturin [10]

Horizontal shift because g(x)=f(x+1) 1 unit left

Vertical shift because g(x)=f(x+1)-4 4 units down

Reflected across x-axis because g(x)=-f(x)

Vertically stretched because g(x)=3(f(x))

Step-by-step explanation:

We need to identify which transformation have been preformed on a graph of f(x)=x2 to obtained the graph of g(x) =-3(x+1)2-4?

Rules for transformation:

Horizontal shift: depends on the value h

if g(x)=f(x+h) then: the graph is shifted left h units

if g(x)=f(x-h) then: the graph is shifted right h units

Vertical Shift: depends on the value k

if g(x)=f(x)+k then: the graph is shifted up k units

if g(x)=f(x)-k then: the graph is shifted down k units

Reflection:

if g(x)=-f(x) then graph is reflected at x-axis

if g(x)=f(-x) then graph is reflected at y-axis

Vertical Stretch:

if g(x)=c.f(x) then graph is vertically stretched.

In the given question:

f(x)= x^2

g(x)=-3(x+1)^2-4

Applying the above rules of transformation:

The graph is:

Horizontal shift because g(x)=f(x+1) 1 unit left

Vertical shift because g(x)=f(x+1)-4 4 units down

Reflected across x-axis because g(x)=-f(x)

Vertically stretched because g(x)=3(f(x))

Keywords: Transformations

Learn more about Transformations at:

#learnwithBrainly

7 0

3 years ago

Kenny likes to count his money by tiling it on his table as shown. The diameter of a quarter is 24.26 mm. Find the area of the t

ElenaW [278]

First we have to assume that each quarter touched each other. Hence the area of the table not covered by the coins (A) is equal to the total area of the table (At) minus the total area of the coins (Ac). Coins are circle, so $A = \pi r^{2}$ and r =24.26mm. The area of one coin is then 1848.98mm^2. Hence the equation is A = At - xAc where x is the number of coins.