A boat sails directly toward a 250-m skyscraper that stands on the
edge of a harbor. The angular size of the building is the angle
formed by lines from the top and bottom of the building to the
observer (see figure). Complete parts (a) and (b) below.
Answers
a) The value of [tex]\theta[/tex] as a function of "x" is [tex]\theta = tan^{-1}\frac{250}{x}[/tex]
b) The rate of change of the angle with respect to x is -0.000308rad/m
Find the complete question and diagram attached
Form the right-angled triangle shown:
Adjacent side = x
Opposite side = 250m
angle of elevation = [tex]\theta[/tex]
Using the SOH CAH TOA identity
[tex]tan\theta = \frac{opposite}{hypotenuse} \\tan \theta = \frac{250}{x} \\\theta = tan^{-1}\frac{250}{x}[/tex]
Hence the value of [tex]\theta[/tex] as a function of "x" is [tex]\theta = tan^{-1}\frac{250}{x}[/tex]
b) If x = 450m
[tex]\theta = tan^{-1}\frac{250}{x}\\tan \theta = \frac{250}{x}\\[/tex]
Differentiate both sides with respect to "x"
[tex]sec^2 \theta \frac{d\theta}{dx} = \frac{-250}{x^2} \\ \frac{d\theta}{dx} = \frac{1}{sec^2\theta} \times \frac{-250}{x^2}[/tex]
Substitute x = 450m and [tex]\theta = 60^0[/tex] into the resulting expression to have:
[tex]\frac{d\theta}{dx} = \frac{1}{sec^260^0} \times \frac{-250}{450^2}\\\frac{d\theta}{dx} = (cos60)^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} = 0.5^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} =-0.000308[/tex]
Hence the rate of change of the angle with respect to x is -0.000308rad/m
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Related Questions
20000 divided by 2 x 56 x 7898 - 100
First to Answer gets brainliest!!!
NO LINKS PLEASE!!!!
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Answer:
0.0226122585576093
Graph the line with slope 1 passing through the point (-3, 1).
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Answer:
[tex]y = x + 4[/tex]
Step-by-step explanation:
[tex]1 = 1(- 3 )+ b \\ 1 = - 3 + b \\ b = 4 \: \: \: \: y - intercept[/tex]
a data set has these values: 8,10,10,12,12,12,14,14,16.The histogram of the distribution is shown. Which statement does not describe the data set shown?
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Answer:
it has a range of 17
Step-by-step explanation:
I just took it
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Step-by-step explanation:
Circumference (C):
[tex]C = 2\pi r = 2\pi(5\:\text{ft}) = 31.4\:\text{ft}[/tex]
Area (A):
[tex]A = \pi r^2 = \pi(5\:\text{ft})^2 = 78.5\:\text{ft}^2[/tex]
convert 1040 weeks to months with solution
Answers
Answer:
1040 x 0.229984 = 239.18336
months = 239
Write an equation that represents the line.
Use exact numbers.
Answers
Answer:
y = 1.5x + 3
Step-by-step explanation:
Take the two points marked by the blue dots.
(0,3), (2,6)
Start with (0,3). The zero makes the other number with it = to the y intercept.
So far what you know is
General equation: y = mx + b
b = 3
Partial equation: y = mx + 3
Givens
To get m, you need both points.
y2 = 6
y1 = 3
x2 = 2
x1 = 0
Equation
m = (y2 - y1) / (x2 - x1)
m = (6 - 3) / (2 - 0)
m = 3 / 2
Entire equation
y = 3/2 x + 3
or
y = 1,5x + 3
C: infinitely many solutions, help solve fast pls
Answers
because you end up with the same teem on both sides so it is infinitely many
Mr. Candy needs to purchase large bags of Snickers to sell in the school store. A bag of Snickers contains 72 Snicker bars. A bag of Snickers cost $23. How much should Mr. Candy sell the Snicker bars to make a profit of $49?
Answers
Answer:
70 cents each snickers bar
Step-by-step explanation:
Given f(x)=3x(to the scnd power)−5x−2. What is the value of f(−2/3)? 1 8/3 3 10/3
Answers
Given:
[tex]f(x)=3x^2-5x-2[/tex]; find f(-2/3)
Answer:
[tex]f(-\frac{2}{3} )=\frac{8}{3}[/tex]
Step-by-step explanation:
1. Insert [tex]-\frac{2}{3} \\[/tex] as X; [tex]f(-\frac{2}{3}) = 3 (-\frac{2}{3} )^2 - 5 (-\frac{2}{3}) - 2[/tex]
2. Solve equation; [tex]f(-\frac{2}{3} )=\frac{8}{3}[/tex]
Select True or False for each statement pls.
Answers
Statement 1: False
Statement 2: True
Statement 3: True
from a piece 20m long ,100 pieces each 7.5cm are cut off how much remain
Answers
Answer:100*7.5=750cm=7.5 m
left rope=20-7.5=12.5m
Step-by-step explanation:
Pa Brainliest Kung Pwede.
Answer:
12.5 metres
Step-by-step explanation:
→ Multiply the pieces by the length
100 × 7.5 = 750 cm
→ Convert to metres
750 cm = 7.5 metres
→ Minus from original length
20 - 7.5 = 12.5 metres
NO LINKS OR ASSESSMENT!!!!
Answers
Answer:
See below and attachedStep-by-step explanation:
1. There are infinite number of lines going from only one point (2, 5)
No definite solution for line A.2. This is a proportional relationship, since line passes through the origin. The slope is -3.
The line B is:
y = -3x3. Points (-3, -2) and (3, 10)
The slope:
m = (10 + 2)/(3 + 3) = 2The y - intercept:
10 = 2*3 + b ⇒ b = 4The line C is:
y = 2x + 44. The rate of change is m = 2.5
The y- intercept:
1 = 2*2.5 + b ⇒ - 4The line D is:
y = 2.5x - 45. Line E has a slope of 4, no sufficient info to conclude.
y = 4x + b, with any value of b6. Line F has m = -3/4 and passes through (8, -1).
The y -intercept is:
-1 = 8(-3/4) + b ⇒ b = 5The line F is:
y = -3/4x + 57. G is not a linear relationship as the function increases exponentially with common ratio of 3.
Write an equation of the line in slope-intercept form. JY 1 (3, 3) (0, 2) 2 4
y=
Answers
Correct answer: y = [tex]\frac{1}{3}[/tex]x + 2
To find out the slope, you would need to remember this slope formula: [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]. We can use the two points provided on the graph to figure out the slope. We can label (3, 3) as [tex]x_{1}[/tex] and [tex]y_{1}[/tex], and (0, 2) as [tex]x_{2}[/tex] and [tex]y_{2}[/tex]. Now we can plug these numbers into the slope formula to find out the slope:
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] → [tex]\frac{2-3}{0-3}[/tex] → [tex]\frac{-1}{-3}[/tex] → [tex]\frac{1}{3}[/tex]
To find out the y-intercept, just substitute (3, 3) into the slope-intercept formula ( y = mx + b ) with the slope that is substituted for 'm' that we already solved earlier.
y = mx + b
(3) = [tex]\frac{1}{3}[/tex](3) + b
3 = 1 + b
2 = b
You can also prove this true by looking at the graph provided. The line intersects at the y-axis at 2.
Now we know that m = [tex]\frac{1}{3}[/tex] and b = 2, we can substitute it into the slope-intercept formula. Thus, the answer is y = [tex]\frac{1}{3}[/tex]x + 2.
Hope this helps you! Let me know if you have any more questions related to this problem.
Let p and q Represent the following statement
Answers
Answer:
symbolic representation :negation q (~q)
plz mark me brinest
Data was recorded for the temperature, in degrees Celsius, of a cup of coffee over a 30-minute period. Given the regression equation, , what is the predicted temperature after 3 minutes?
33.45 oC
62.24 oC
65.17 oC
66.69 oC
Answers
Answer:
62.24
Step-by-step explanation:
The predicted temperature after 3 minutes will be 62.24 °C. Then the correct option is B.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
A cup of coffee's temperature was measured over a 30-minute period in degrees Celsius.
Let T be the temperature and t be the time. Then the regression equation is given as,
ln T = 4.20 - 0.023 t
Then predicted temperature after 3 minutes is given as,
ln T = 4.20 - 0.023 x 3
ln T = 4.20 - 0.069
ln T = 4.131
T = 62.24 °C
The predicted temperature after 3 minutes will be 62.24 °C. Then the correct option is B.
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Completely Factor the following equations.
a) 3x^3 + 15x^2 + 18x
Answers
3x^3 + 15x^2 + 18x
3(x^3+5x^2+6x)
Find one factor
3x(x^2+5x+6)
Factor by grouping
3x(x+2)(x+3)
Solution
3x(x+2)(x+3)
What is the value of 7x (3 + x/4) when x = −8?
Answers
Answer:
Third option
Step-by-step explanation:
[tex]7x (3 + \frac{x}{4}) = -56 * (3 + -\frac{8}{4}) = -56 * (3 - 2) = -56 * 1 = -56[/tex]
Peter Piper picked 3 pecks of pickled peppers in 2.5
hours. How many pecks of pickled peppers does
Peter pick in 15 hours?
Answers
double the peppers from 3 to 6 and add another 2.5 to 2.5 and you get 5. multiply the 6 peppers and 5 hours by 3 and you get 18 peppers in 15 hours. picture of math is attached
A new blu-ray player costs $80.99 in the store. What would your total cost be if the sales tax is 5.5%? Round your answer to the nearest cent, if necessary.
Answers
Answer:
445.445
Step-by-step explanation:
because I did it and I got it right
Answer: 85.44
Step-by-step explanation: 80.99*0.055
Consider the equation below. The value of x in terms of h is . The value of x when h = 4 is .
Answers
The value of x when h = 4 is 4.
The given equation is : 4(x − 3) = h. We need to find the value of x in terms of h and the value of x when h = 4.So, we will solve this equation by following the steps given below:
Step 1: Distribute 4 by x and 4 by -3. It gives us:4x - 12 = h
Step 2: Add 12 to both sides of the equation. We get:4x - 12 + 12 = h + 124x = h + 12
Step 3: Divide both sides of the equation by 4. We get:x = (h + 12) / 4
Therefore, the value of x in terms of h is x = (h + 12) / 4.
Now, we need to find the value of x when h = 4. We will put h = 4 in the above equation and get the value of x.x = (4 + 12) / 4 = 16 / 4 = 4.
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Calculate A woman is walking at a rate of 0.5
m/s. Her mass is 62 kg. Calculate the woman's
kinetic energy in joules.
Answers
Answer:
7.75J
Step-by-step explanation:
kinectic energy formula = 1/2mv²
m mass
v velocity
1/2 x 62 x 0.5² = 7.75
A woman is walking at a rate of 0.5m/s. Her mass is 62 kg. The woman's kinetic energy in joules:
K.E. = 7.75 kgm²/s²
What is Kinetic Energy?
The energy an object has as a result of motion is known as kinetic energy in physics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity. The body holds onto the kinetic energy it acquired during its acceleration until its speed changes.
Given,
Mass = 62kg
Velocity = 0.5m/s
The formula for Kinetic Energy is :
K.E. = 1/2 m v².
K.E. = 1/2 (62)(0.5)²
K.E. = 1/2 (62)(0.25)
K.E. = 1/2 (15.5)
K.E. = 15.5/2
K.E. = 7.75 kgm²/s²
or
K.E. = 7.75 joules
Hence, he woman's kinetic energy in joules, K.E. = 7.75 kgm²/s²
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there are 270 sixth grade students and 45 chaperones going on a field trip. how many students will be with each chaperone if the groups are divided equally.
Answers
Answer:
6
Step-by-step explanation:
270 divided by 45
=6
Question Choice Worth 2 points)
(02.06Derek has a bird that weighs 4 pounds. Use the double fine diagram below to help you determine approximately how many kilograms this bird weighs
3 5 7
Pounds
1 2 3
Kilograms
15 klograms
O2 xilogram
5 kilograms
7 kilograms
Answers
is 78.50 is the same as 78.5
Answers
Answer:
yes, 78.50 is the same as 78.5Step-by-step explanation:
You can consider 78.50 as 78.5, cause we basically remove the 0 from it. The whole point is, they are both the same.
Hello there!
Yes, 78.50 is the same as 78.5 because you can remove the 0 and the numbers will be identical.
Hope this helps!
~Just a joyful teen
[tex]SilentNature\\(GraceRosalia)[/tex]
what does this mean??
Answers
Answer:
"do you mock people's mental states?"
Find last year's salary if, after a 4% pay raise, this year's salary is $33,800.
Answers
Answer:
1352
Step-by-step explanation:
4% of 33,800 is 1352 last years salary was 32448
Write a quadratic function whose zeros are -12 and -2.
Answers
Answer:
(x+12) (x+2)
x(x+12)+2(x+12)
x^2+12x+2x+24
x^2+14x+24
Step-by-step explanation:
Answer:
f(x) = x² + 14x + 24
Step-by-step explanation:
Given the zeros of -12 and -2, then it means that:
x + 12 = 0 and x + 2 = 0
As a proof, if you isolate x, you'll end up with the given values:
x + 12 - 12 = 0 - 12
x = -12
x + 2 - 2 = 0 - 2
x = -2
In terms of using these values into the quadratic function:
(x + 12) (x + 2)
Perform the FOIL method in order to find the quadratic function:
(x + 12) (x + 2)
f(x) = x² + 2x + 12x + 24
f(x) = x² + 14x + 24 ⇒ This is the quadratic function, given the zeros as x = -12, and x = -2.
A loan used for buying a home is called a mortgage. The Fortunato family is borrowing $430,000 to buy a home. They are taking out a 30-year mortgage at a rate of 3.55%. a. Compute the monthly payment to the nearest cent. fill in the blank 1 b. Find the total of all of the monthly payments for 30 years. fill in the blank 2 c. What is the total interest? fill in the blank 3 d. Which is greater, the interest or the original cost of the home?
Answers
Using compound interest, it is found that:
a) The monthly payments are of $3,401.49.
b) The total of all monthly payments for 30 years is of $1,224,536.
c) The total interest is of $794,536.
d) The total interest is greater.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.For the parameters, we have that:
The Fortunato family is borrowing $430,000 to buy a home, hence P = 430000.30-year mortgage, hence t = 30.Rate of 3.55%, hence r = 0.0355.Yearly compounding, hence n = 1.For practicality, first we are going to solve item b.
Item b:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(30) = 430000\left(1 + \frac{0.0355}{1}\right)^{30}[/tex]
[tex]A(30) = 1224536[/tex]
The total of all monthly payments for 30 years is of $1,224,536.
Item a:
$1,224,536 is paid in 30 x 12 = 360 months, hence:
1224536/360 = $3,401.49.
The monthly payments are of $3,401.49.
Item c:
The interest is the total subtracted from the principal, hence:
1224536 - 430000 = $794,536.
The total interest is of $794,536.
Item d:
Loan of $430,000, interest of $794,536, hence the total interest is greater.
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Find g(x) for each x value in the table
Answers
Answer:
-2 = -2/7
-1= -1/7
0=0
1= 1/7
2= 2/7
Step-by-step explanation:
it gives you a function of 1/7 so you multiply it by x and u get the g(x) also know as Y
When converted to a household measurement, 9 kilograms is approximately equal to a
Answers
Answer:
D) 19.8 lbs
Explanation:
1kg in household measurement is equal to 35.274 ounces. 35.274*9=317.466 ounces.
1kg is also equal to 2.205 lbs. 9*2.205=19.8416
9 kg is also equal to 9000 grams, but grams are not a part of the household measurement system
a) 9000 grams. b) 9000 ounces. c) 19.8 ounces. d) 19.8 pounds.
This leaves us with 19.8 lbs