monica is standing in a building looking out a window at a tree the tree is 121 feet away from monica monica line of sight to the top of the tree creates a 42 degree angle of depression. what is the height of the tree rounded to the nearest tenth

Answer:

[tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Calculus

Derivatives

Derivative Notation

Antiderivatives - Integrals

Integration Constant C

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle f'(t) = t^4 + 91 - \frac{3}{t}[/tex]

[tex]\displaystyle f(1) = \frac{1}{4}[/tex]

Step 2: Integration

Integrate the derivative to find function.

Our general solution is  [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| + C[/tex].

Step 3: Find Particular Solution

Find Integration Constant C for function using given condition.

∴ Our particular solution to the differential equation is  [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}[/tex].

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Integration

Book: College Calculus 10e

Given :

Cathy lives in a state where speeders are fined $15 for each mile per hour over the speed limit.

Cathy was given a ticket for $105 for speeding on a road where the speed limit is 60 miles per hour.

To Find :

How fast was Cathy driving.

Solution :

Let, speed of Cathy is v miles per hour.

Number of miles per hour over the speed limit, n = v - 60 miles per hour.

It is given that speeders are fined $15 for each mile per hour over the speed limit.

So, total amount of fine for Cathy is :

105 = 15×( v - 60 )

v-60 = 7

v = 67 miles per hour

Therefore, Cathy was driving with speed of 67 miles per hour.

Answer:

yes, it is a right triangle

Step-by-step explanation:

the other two angles are 35 and 55 degrees

Answer:

is NOT a right triangle

Step-by-step explanation:

is a right triangle if it checks the Pythagorean Th.

12² = 10² + 7²

144 = 100+49

144 = 149 False

Answer:

Variance = 9

Standard deviation = 3

Step-by-step explanation:

Step 1

Find the Mean

Means = Sum of values/Number of values

= 0 + 1 + 4 + 4 + 6 + 7 + 7 + 7 + 9/9

= 45/9

= 5

Step 2

The formula for Sample variance

= (x - Mean)²/n - 1

Where

n = number of values = 9

Hence:

Sample variance =

( (0 - 5)² + (1 - 5)²+ (4 - 5)² + (4 - 5)² + (6 - 5)² + (7 - 5)² + (7 - 5)² + (7 - 5)² + (9 - 5)²)/9 - 1

= (-5² + -4²+ -1² + -1² + 1² + 2² + 2² + 2² + 4²) /8

= (25 + 16 + 1 + 1 + 1 + 4 + 4 + 4 + 16)/8

= 72/8

= 9

Sample Standard deviation = √Sample variance

= √9

= 3

Answer:

x =41.18114952

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

We know the hypotenuse and adjacent sides

cos theta = adjacent / hypotenuse

cos x  = 14.3/19

taking the inverse cos of each side

cos^-1 (cos x) = cos ^-1 ( 14.3/19)

x =41.18114952

Answer:

Step-by-step explanation:

take x degree as reference angle

using cos rule

cos x=adjacent/hypotenuse

cos x=14.3/19

cos x=0.75

x=cos 41

x= 41 degree

Answer:

1600

Step-by-step explanation:

1.25x + 1000 = 3000

Subtract 1000 from both sides

1.25x = 2000

Divide both sides by 1.25

x = 1600

Answer:

2.8

Step-by-step explanation:

x2.3, x2.4, 2.8, x2.9, x2.9

Answer:

A) 64 cm²

Step-by-step explanation:

Trapezoid area formula:

[tex]A=\frac{a+b}{2} h[/tex]

Given:

a = 6

b = 10

h = 8

Work:

[tex]A=\frac{a+b}{2} h\\\\A=\frac{6+10}{2} *8\\\\A=\frac{16}{2} *8\\\\A=8*8\\A=64[/tex]

Answer:

2/7

Step-by-step explanation:

All I did was just simplify the fraction 4/14

4/14=2/7

9514 1404 393

Answer:

  correct choice is marked

Step-by-step explanation:

The error is in step 2. The square root cannot be distributed to a sum.

Answer:

48

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

48

the picture 20 words or longer for the answer so this is extra text

Answer:

[tex]2x - 7 = 3x + 5 \\ - x = 12 \\ x = - 12[/tex]

If you just want to check then substitute the value

[tex]2x - 7 = 3x + 5 \\ 2 \times ( - 12) - 7 = 3 \times ( - 12) + 5 \\ - 24 - 7 = - 36 + 5 \\ - 31 = - 31[/tex]

Hope it helps

Answer:

634 steak sandwiches.

Step-by-step explanation:

Let's say X is the number of hot dogs and Y is the number of steak sandwiches.

2.95x + 9,95y = 7343.75

x + y = 985

y = 985 - x

2.95x + 9.95(985-x) = 7343.75

2.95x + 9800.75 - 9.95x = 7343.75

7x = 2457

x = 351

y = 985 - 351

y = 634

Answer:

[tex]circumference = \pi \: d \\ 11.27\pi = \pi \: d \\ d = 11.27 \: ft[/tex]

Answer:

2(15p+1)

Step-by-step explanation:

hope this helps

Answer:

V =65416.666666 cm^3

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

The diameter is 50 so the radius is 1/2 of the diameter

r = 1/2 (50) = 25

V = 4/3 ( pi) (25)^3

V = 4/3 (pi) 15625

V =20833.3333 pi

Using 3.14 for pi

V =65416.666666 cm^3

Answer:

V =65416.666666 cm^3

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

The diameter is 50 so the radius is 1/2 of the diameter

r = 1/2 (50) = 25

V = 4/3 ( pi) (25)^3

V = 4/3 (pi) 15625

V =20833.3333 pi

Using 3.14 for pi

V =65416.666666 cm^3

Answer:

the answer is :.......

x+x+x

Answer:

x+x+x

Step-by-step explanation:

Answer:

The answers is " Option B".

Step-by-step explanation:

[tex]CI=\hat{Y}\pm t_{Critical}\times S_{e}[/tex]

Where,

[tex]\hat{Y}=[/tex] predicted value of lead content when traffic flow is 15.

[tex]\to df=n-1=8-1=7[/tex]

 [tex]95\% \ CI\ is\ (463.5, 596.3) \\\\\hat{Y}=\frac{(463.5+596.3)}{2}\\\\[/tex]

     [tex]=\frac{1059.8}{2}\\\\=529.9[/tex]

Calculating thet-critical value[tex]t_{ \{\frac{\alpha}{2},\ df \}}=-2.365[/tex]

The lower predicted value [tex]=529.9-2.365(Se)[/tex]

[tex]463.5=529.9-2.365(Se)\\\\529.9-463.5=2.365(Se)\\\\66.4=2.365(Se)\\\\Se=\frac{66.4}{2.365} \\\\Se=28.076[/tex]

When [tex]99\%[/tex] of CI use as the expected lead content: [tex]\to 529.9\pm t_{0.005,7}\times 28.076 \\\\=(529.9 \pm 3.499 \times 28.076)\\\\=(529.9 \pm 98.238)\\\\=(529.9-98.238, 529.9+98.238)\\\\=(431.662, 628.138)\\\\=(431.6, 628.1)[/tex]

Answer: 77

Step-by-step explanation:

Answer: It's not equal to 20% discount.

Step-by-step explanation:

Let's assume the cost of a good is $100. Since there's 10% off on every item, the cost of the good will be:

= $100 - (10% × $100)

= $100 - $10

= $90

Since the coupon states that one will receive an additional 10% off, therefore the amount that the person will pay will be:

= $90 - (10% × $90)

= $90 - (0.1 × $90)

= $90 - $9

= $81

If the same good is $100 and there's a 20% discount, the amount that'll be paid will be:

= $100 - (20% × $100)

= $100 - (0.2 × $100)

= $100 - $20

= $80

Therefore, it's not equal to 20% discount.

Answer: The ladder reaches 14.46 feet up of the building.

Step-by-step explanation:

According to Pythagorean theorem,

In a right triangle,

(Hypotenuse)²= (Base)²+(perpendicular)^2

Using given information, we have

[tex](15)^2=(4)^2+(height)^2\\\\225=16+(height)^2\\\\(height)^2=209\\\\ (height)^2=\sqrt{209}\approx14.46\ feet[/tex]

Hence, the ladder reaches 14.46 feet up of the building.

Answer:

C. a = 7

D. c = -3

Step-by-step explanation:

C. 7(2a + 3) + 21 = 100+ 40

   14a + 21 + 21 = 140

   14a = 140 - 21 - 21

    14a = 98

    a = 7

D. 6+ 14 - 12c = 56

    20 - 12c = 56

     -12c = 56 - 20

     -12c = 36

       c = - 3

Answer:

Step-by-step explanation:

c.7(2a+3)+21=100+40

14a+21+21=140

14a+42=140

14a=140-42

a=98/14

a=7

d.6+14-12c=56

20-12c=56

-12c=56-20

c=36/-12

c=-3

9514 1404 393

Answer:

  1/10

Step-by-step explanation:

The value of any digit is found by setting all other digits to zero.

The value of the 2 in 43,290 is 200.

The value of the 2 in 32,865 is 2,000.

200 is 200/2000 = 1/10 times 2000

The value of 2 in 43,290 is 1/10 times the value of 2 in 32865.

Answer:

D.

Step-by-step explanation:

The mean is 11,000

Answer:

13. [tex]x^{3} y^3[/tex] cubic units

14. 43 million; 79 million; 3.6 × [tex]10^7[/tex]

15. 2.68 × [tex]10^5[/tex]

Step-by-step explanation:

[tex]4d = - 16 \\ \\ d = \cancel \frac{ - 16}{4} \\ \\ d = - 4[/tex]

Answer:

The value of d is -4. When you multiply 4 by -4 you get -16. If you want me to elaborate, let me know.

Step-by-step explanation: