A scuba diver spots a shipwreck at an angle of depression of 26°. The
angle of elevation from the scuba diver up to his boat is 53°. If the
shipwreck is located directly below his boat, and the horizontal distance
between the scuba diver and the shipwreck is 120 feet, find the vertical
distance between the shipwreck and the boat. pls pls pls help
Answers
Answer:
79 degrees
Verticle between wreak and boat
The vertical distance between the shipwreck and the boat is 89.76 feet.
We have a scuba diver who spots a shipwreck at an angle of depression of 26°. The angle of elevation from the scuba diver up to his boat is 53°. The shipwreck is located directly below his boat, and the horizontal distance between the scuba diver and the shipwreck is 120 feet.
We have to determine the vertical distance between the shipwreck and the boat.
Define Angle of Elevation and Angle of Depression.If a person stands and looks up at an object, the angle of elevation is the angle between the horizontal line of sight and the object. If a person stands and looks down at an object, the angle of depression is the angle between the horizontal line of sight and the object.
According to question, we have -
Angle of elevation (A) = 26 degrees
Angle of depression (D) = 53 degrees
Horizontal distance between the scuba diver and the shipwreck = 120 feet.
Refer the image to understand the solution.
In Δ OAC -
OA = 120 x tan(53)
In Δ OBC -
OB = 120 x tan(26)
Now, the distance between shipwreck and the boat is x.
x = OA + OB
x = 120 x tan(53) + 120 x tan(26)
x = 120 [tan(53) + tan(26)]
x = 120 x 0.748
x = 89.76
Hence, the vertical distance between the shipwreck and the boat is 89.76 feet.
To solve more questions on Heights and Distances, visit the link below -
https://brainly.com/question/14430801
#SPJ2
Related Questions
hey can someone help?
Answers
Answer:
x = 12
Step-by-step explanation:
∠4 = (8x + 4)°
∠6 = (6x + 28)°
∠4 = ∠6
(8x + 4) = (6x + 28)
-6x -6x
-----------------------
2x + 4 = 28
-4 -4
-----------------
2x = 24
÷2 ÷2
------------------
x = 12
I hope this helps!
Answer:
x = 12
Step-by-step explanation:
Angle 4 and angle 2 are congruent to each other. Angle 6 is also congruent to angle 2. If both these statements are true, angle 4 is congruent to angle 6.
This means (8x + 4) = (6x + 28)
Now, you simply solve for x:
8x + 4 = 6x + 28
- 4 - 4
8x = 6x + 24
-6x -6x
2x = 24
2x/2 = 24/2
x = 12
How long will it take to pay off a loan of $49,000 at an annual rate of 9 percent compounded monthly if you make monthly payments of $400? Use five decimal places for the monthly percentage rate in your calculations. The number of years it takes to pay off the loan is years. (Round to one decimal place.)
Answers
To pay off a loan of $49,000 at an annual interest rate of 9% compounded monthly, with monthly payments of $400, it will take approximately 12.9 years.
To determine the time it takes to pay off the loan, we can use the formula for the number of periods (n) in the compound interest formula. In this case, the loan amount is $49,000, the monthly payment is $400, and the monthly interest rate is 9% divided by 12 (0.09/12 = 0.0075). We can use the following formula:
\(n = -log(1 - (r * P) / A) / log(1 + r)\)
where r is the monthly interest rate, P is the monthly payment, and A is the loan amount.
Plugging in the values, we have:
\(n = -log(1 - (0.0075 * 49000) / 400) / log(1 + 0.0075)\)
Calculating this expression, we find that n is approximately 12.9 years. Therefore, it will take approximately 12.9 years to pay off the loan with monthly payments of $400, rounded to one decimal place.
Learn more about loan here:
https://brainly.com/question/20533349
#SPJ11
a house increases in value by 8% every year. what is the percent growth of the value of the house in ten years? what factor does the value of the house grow by every ten years?
Answers
Answer:
To calculate the percent growth of the value of the house in ten years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final value of the house
P = Initial value of the house
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
In this case, the annual interest rate is 8% or 0.08, the number of times the interest is compounded per year is 1 (since it increases annually), and the number of years is 10.
Let's assume the initial value of the house is $100,000.
P = $100,000
r = 0.08
n = 1
t = 10
A = 100000(1 + 0.08/1)^(1*10)
A = 100000(1 + 0.08)^10
A ≈ 215,892.66
The final value of the house after ten years would be approximately $215,892.66.
To calculate the percent growth of the value, we can use the formula:
Percent Growth = ((A - P) / P) * 100
Percent Growth = ((215892.66 - 100000) / 100000) * 100
Percent Growth ≈ 115.89%
Therefore, the percent growth of the value of the house in ten years is approximately 115.89%.
To find the factor by which the value of the house grows every ten years, we can divide the final value by the initial value:
Factor = A / P
Factor ≈ 215892.66 / 100000
Factor ≈ 2.1589
Therefore, the value of the house grows by a factor of approximately 2.1589 every ten years.
Perform the indicated operation and express the result as a simplified complex number. I need help with 35
Answers
Given:-
\(\frac{3+4i}{2-i}\)To find:-
The simplified form.
At first we take conjucate and multiply below and above.
The conjucate is,
\(2+i\)So now we multiply. we get,
\(\frac{3+4i}{2-i}\times\frac{2+i}{2+i}\)Now we simplify. so we get,
\(\frac{3+4i}{2-i}\times\frac{2+i}{2+i}=\frac{6+3i+8i+4(i)^2}{2^2-i^2}\)We know the value of,
\(i^2=-1\)Substituting the value -1. we get,
\(\begin{gathered} \frac{6+3i+8i+4(i)^2}{2^2-i^2}=\frac{6+3i+8i+4(-1)_{}^{}}{2^2-(-1)^{}} \\ \text{ =}\frac{6-4+11i}{2+1} \\ \text{ =}\frac{2+11i}{3} \end{gathered}\)So now we split the term to bring it into the form a+ib. so we get,
\(\frac{2+11i}{3}=\frac{2}{3}+i\frac{11}{3}\)So the required solution is,
\(\frac{2}{3}+i\frac{11}{3}\)unit 3 parallel and perpendicular lines homework 4 parallel line proofs
PLEASE HELP!!!!!!!!!!!
100 points!!!!!!!
Answers
Answer:
1) c ║ d by consecutive interior angles theorem
2) m∠3 + m∠6 = 180° by transitive property
3) ∠2 ≅ ∠5 by definition of congruency
4) t ║ v \({}\) Corresponding angle theorem
5) ∠14 and ∠11 are supplementary \({}\) Definition of supplementary angles
6) ∠8 and ∠9 are supplementary \({}\) Consecutive interior angles theorem
Step-by-step explanation:
1) Statement \({}\) Reason
m∠4 + m∠7 = 180° \({}\) Given
m∠4 ≅ m∠6 \({}\) Vertically opposite angles
m∠4 = m∠6 \({}\) Definition of congruency
m∠6 + m∠7 = 180° \({}\) Transitive property
m∠6 and m∠7 are supplementary \({}\) Definition of supplementary angles
∴ c ║ d \({}\) Consecutive interior angles theorem
2) Statement \({}\) Reason
m∠3 = m∠8 \({}\) Given
m∠8 + m∠6 = 180° \({}\) Sum of angles on a straight line
∴ m∠3 + m∠6 = 180° \({}\) Transitive property
3) Statement \({}\) Reason
p ║ q \({}\) Given
∠1 ≅ ∠5 \({}\) Given
∠1 = ∠5 \({}\) Definition of congruency
∠2 ≅ ∠1 \({}\) Alternate interior angles theorem
∠2 = ∠1 \({}\) Definition of congruency
∠2 = ∠5 \({}\) Transitive property
∠2 ≅ ∠5 \({}\) Definition of congruency.
4) Statement \({}\) Reason
∠1 ≅ ∠5 \({}\) Given
∠3 ≅ ∠4 \({}\) Given
∠1 = ∠5 \({}\) Definition of congruency
∠3 = ∠4 \({}\) Definition of congruency
∠5 ≅ ∠4 \({}\) Vertically opposite angles
∠5 = ∠4 \({}\) Definition of congruency
∠5 = ∠3 \({}\) Transitive property
∠1 = ∠3 \({}\) Transitive property
∠1 ≅ ∠3 \({}\) Definition of congruency.
t ║ v \({}\) Corresponding angle theorem
5) Statement \({}\) Reason
∠5 ≅ ∠16 \({}\) Given
∠2 ≅ ∠4 \({}\) Given
∠5 = ∠16 \({}\) Definition of congruency
∠2 = ∠4 \({}\) Definition of congruency
EF ║ GH \({}\) Corresponding angle theorem
∠14 ≅ ∠16 \({}\) Corresponding angles
∠14 = ∠16 \({}\) Definition of congruency
∠5 = ∠14 \({}\) Transitive property
∠5 + ∠11 = 180° \({}\) Sum of angles on a straight line
∠14 + ∠11 = 180° \({}\) Transitive property
∠14 and ∠11 are supplementary \({}\) Definition of supplementary angles
6) Statement \({}\) Reason
l ║ m \({}\) Given
∠4 ≅ ∠7 \({}\) Given
∠4 = ∠7 \({}\) Definition of congruency
∠2 ≅ ∠7 \({}\) Alternate angles
∠2 = ∠7 \({}\) Definition of congruency
∠2 = ∠4 \({}\) Transitive property
∠2 ≅ ∠4 \({}\) Definition of congruency
∠2 and ∠4 are corresponding angles \({}\) Definition
DA ║ EB \({}\) Corresponding angle theorem
∠8 and ∠9 are consecutive interior angles \({}\) Definition
∠8 and ∠9 are supplementary \({}\) Consecutive interior angles theorem.
At a super market a certain item has increased from 75 cents per pound to 81 cents per pound what is the percent increase in the cost of the item
Answers
Answer:
8%
Step-by-step explanation:
(81-75)/75*100=8%
what is value of 3(√3(80-x)
Answers
Answer:
= 240√3-3√3x
Step-by-step explanation:
parentheses:
=3√3 (80 – x)
Apply the distributive law:
a=3√3, b= 80, c =X
=3√3×80-3√3x
=3× 80√3 -3√3x
Multiply the numbers: 3×80 = 240
= 240√3-3√3x
a sample of employees of a large pharmaceutical company has been obtained. the length of time (in months) they have worked for the company was recorded for each employee. a stemplot of these data is shown below. in the stemplot 6|2 represents 62 months. what would be a better way to represent this data set?
Answers
A histogram would be a better way to represent this data set, as it provides a clear visual representation of the frequency of different values.
A better way to represent the data set would be to use a histogram. A histogram is a graphical representation of a data set that is used to show how frequently certain values occur in the data set. A histogram can be created by first grouping the data into equal intervals, or bins, and then plotting the frequency of each bin on the y-axis of the graph. This allows for easy comparison of the frequency of different values. For example, in the case of the pharmaceutical company’s employee data, one could create a histogram with 5 bins that represent 6-10 months, 11-15 months, 16-20 months, 21-25 months, and 26-30 months. Then, one can plot the number of employees in each bin on the y-axis of the graph. This would provide a clear visual representation of the data set and make it easier to identify any patterns or trends in the data.
A histogram would be a better way to represent this data set, as it provides a clear visual representation of the frequency of different values.
Learn more about histogram here:
https://brainly.com/question/14421716
#SPJ4
A gardener is planting two types of trees: Type A is 10 feet tall and grows at a rate of 7 inches per year. Type B is 3 feet tall and grows at a rate of 19 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.
Answers
Answer:
7 years
Step-by-step explanation:
First, create expressions to represent the problem:
\(a(x) = 10(12) + 7x \\ b(x) = 3(12) + 19x\)
Simplify:
\(a(x) = 120 + 7x \\ b(x) = 36 + 19x\)
Now make the expressions equal to each other and solve:
\(120 + 7x = 36 + 19x \\ 84 = 12x \\ x = 7\)
The answer is 7 years
define a positive integer n to be a factorial tail if there is some positive integer m such that the decimal representation of m! ends with exactly n zeroes. how many positive integers less than 1992 are not factorial tails?
Answers
On solving the provided question, we can say that there are 7975/5 - 1595 distinct positive number f(m) less than 1992, 1991-1595 = 396 positive integer.
What is integer?Zero, a positive integer, or a negative integer denoted by a minus sign are all examples of integers. A negative number is the additive reciprocal of a positive number that it corresponds to. A bold Z or a bold "mathbb Z" is frequently used in mathematical notation to denote a group of integers. A positive, negative, or zero integer—not a fraction—is referred to as an integer (pronounced IN-tuh-jer). The numbers -5, 1, 5, 8, 97, and 3,043 are examples of integers. 1.43, 1 3/4, 3.14, and other numbers are non-integer examples. Integers are a collection of integers and their antipodes. Decimals and fractions are not part of the set of integers.
suppose number of zeroes m! be f(m)
f(m) = m/5 + m/25 + m/125 + m/625 + ...
f(m) = f(m+1) = f(m+2) = f(m+3) = f(m+4)
since, f(m)< m/5 + m/25 + m/125 + m/625 + ... = m/4
f(7975) = 1991
there are 7975/5 - 1595 distinct positive number f(m) less than 1992, 1991-1595 = 396 positive integer
To know more about integer visit:
https://brainly.com/question/15276410
#SPJ4
Which story problem could be solved using the given equation? 14×35=m
Answers
Answer:
the answer is 390
Step-by-step explanation:
you see M means = when youre talking about money you put a M so the question is 14x35=390 hope it HELPS!!!!!!!!!
Theoretical Probability is?
Answers
Answer:
Theoretical probability is a probability that is expected, for example when I flip a coin 100 times I expect tails to come up 50 times and heads to come up 50 times. The theoretical probability is 0.5 for a head.
Step-by-step explanation:
Brian leaves la at 8. 00am to drive to san francisco 400km away he travels at a steady 50 mph who gets to san drancisco first
Answers
Based on the provided information of speed, A) Beth gets to San Francisco first. B) The first to arrive has to wait for 20 minutes for the second to arrive.
A) To find out who gets to San Francisco first, we need to calculate the time it takes for each of them to travel the distance of 400 miles.
For Brian, we use the formula time = distance / speed:
time = 400 miles / 50 mph = 8 hours
So Brian will arrive in San Francisco at 4:00 p.m. (8:00 a.m. + 8 hours).
For Beth, we use the same formula:
time = 400 miles / 60 mph = 6.67 hours
So Beth will arrive in San Francisco at 3:40 p.m. (9:00 a.m. + 6.67 hours).
Therefore, Beth gets to San Francisco first.
B) To find out how long the first to arrive has to wait for the second, we subtract the arrival time of the first from the arrival time of the second:
wait time = 4:00 p.m. - 3:40 p.m. = 0.33 hours = 20 minutes
So the first to arrive has to wait for 20 minutes for the second to arrive.
Note: The question is incomplete. The complete question probably is: Brian leaves Los Angeles at 8:00 a.m. to drive to San Francisco, 400 miles away. He travels at a steady speed of 50 mph. Beth leaves Los Angeles at 9:00 a.m. and drives at a steady speed of 60 mph. A) Who gets to San Francisco first? B) How long does the first to arrive have to wait for the second?
Learn more about Speed:
https://brainly.com/question/4931057
#SPJ11
hey can someone tell me why 132 is wrong? and help me with the right answer pls
Answers
Answer:
∠CBA = 132
Step-by-step explanation:
Bisectors split up an angle into two identical angles
Thus, 7x - 11 = 2x + 44
This is the equation we will use to solve for x
7x - 11 = 2x + 44
step 1 add 44 to each side
44 + 11 = 55
-11 + 11 cancels out
we now have 7x = 2x + 55
step 2 subtract 2x from each side
7x - 2x = 5x
2x - 2x cancels out
we now have 5x = 55
step 3 divide each side by 5
5x / 5 = x
55 / 5 = 11
we're left with x = 11
The question is asking for the measure of ∠CBA
To find the measure of ∠CBA we plug in 11 for x in one of the given expressions and multiply that by 2 ( this is because the two angles are identical so there is no need to find the measures of both because ∠CBD≅∠ABD )
7(11) - 11
7 * 11 = 77
77 - 11 = 66
66 * 2 = 132
please help me!!!
Round each number 1 significant figure : 17.94 ÷ 3.15
Ans:
Answers
determine whether the series converges or diverges. [infinity] n2 − 6n n3 3n 1 n = 1
Answers
If we determine if the series ∑(n=1 to ∞) n^2 - 6n / (n^3 + 3n + 1) converges or diverges, further analysis or tests, such as the comparison test or the ratio test, may be necessary.
To determine if the series ∑(n=1 to infinity) (n^2 - 6n)/(n^3 + 3n + 1) converges or diverges, we can use the limit comparison test.
First, we choose a series b_n that we know converges and has positive terms. Let's choose the series b_n = 1/n. Since b_n > 0 for all n, we can use it for the limit comparison test.
Next, we need to calculate the limit of the ratio of the two series as n approaches infinity: lim (n → ∞) [(n^2 - 6n)/(n^3 + 3n + 1)] / (1/n)
We can simplify this expression by dividing both the numerator and denominator by n^3: lim (n → ∞) [(1 - 6/n^2)/(1/n^2 + 3/n^3 + 1/n^3)]As n approaches infinity, all the terms with 1/n or higher powers of 1/n approach zero, so we can simplify further:lim (n → ∞) [1/(1/n^2)]
= lim (n → ∞) n^2
= ∞
Since this limit is finite and positive, the series ∑(n=1 to infinity) (n^2 - 6n)/(n^3 + 3n + 1) and the series ∑(n=1 to infinity) 1/n have the same convergence behavior.Since the harmonic series ∑(n=1 to infinity) 1/n diverges, we can conclude that the original series ∑(n=1 to infinity) (n^2 - 6n)/(n^3 + 3n + 1) also diverges by the limit comparison test.
To learn more about “series” refer to the https://brainly.com/question/24643676
#SPJ11
7) Given:
Name the part of the circle that segment CD represents.
Answers
How many ink cartridges can you buy with 105 dollars if one cartridge costs 15 dollars ?
Answers
Answer:
7
Step-by-step explanation:
105/15=7
7 ink cartridges you can buy with 105 dollars.
What is a linear equation in math?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.One cartridge costs = 15 dollars
No of cartridge we buy in 105 dollars = 105 /15
= 7
Therefore, 7 ink cartridges buy can with 105 dollars.
Learn more about linear equation
brainly.com/question/11897796
#SPJ4
Identify the factors of the function
y = 3x2 - 7x – 10
Answers
Answer:
(x + 1)(3x - 10)
Step-by-step explanation:
Given
3x² - 7x - 10
Consider the factors of the product of the x² term and the constant which sum to give the coefficient of the x- term.
product = 3 × - 10 = - 30 and sum = - 7
The factors are + 3 and - 10
Use these factors to split the x- term
3x² + 3x - 10x - 10 ( factor the first/second and third/fourth terms )
3x(x + 1) - 10(x + 1) ← factor out (x + 1) from each term
(x + 1)(3x - 10), thus
y = (x + 1)(3x - 10) ← in factored form
Help pls math is not my thing
Answers
Answer: 2.25 x 10^18
Step-by-step explanation:
When dividing with exponents you subtract
56-38= 18
10 cancels out
(9 x 10^18) / 4
= 2.25 x 10^18
16. Which is greater, 4^-2 or
2^-4? How do you know?
Answers
Answer: if this is a fraction 4\2 is greater
Step-by-step explanation: First you need same denominaters the lest coomon is four 2 over 4 is fine 4 over 2 two times 2 is 4 and 4 times 4 is 16 with will leave you with 16/4 or 2/4 simplfied 4/2 is greater
Answer:
The expressions are equal.
Step-by-step explanation:
Notice that \(a^{-b}=\frac{1}{a^b}\) for all (real) \(a,b\). So \(4^{-2}=\frac{1}{4^2} = \frac{1}{16}\) and \(2^{-4} = \frac{1}{2^4} = \frac{1}{16}\). Therefore, the expressions are equal.
>> Compute the requested operating costs as indicated, based on the preceding table and the following information. Use the thousands comma where applicable. Car: six-cylinder compact Years driven: first through third year Miles driven: 15,000 first year; 14,000 second year; and 13,000 third year Using method 2, the total costs for the first year, $ the second year $ dollars and cents. the third year $ and all the years $ in Unlimited Attempts Remain
Answers
Answer:
The total costs for the first year, $690 , the second year $560, the third year $442, and all the years $1692 in dollars and cents
Step-by-step explanation:
I Got it I think. I want that brainlyest?
We can calculate the operating costs for the car over the first three years using method 2. In the first year, the car was driven for 15,000 miles. From the table, we can see that the cost per mile for a six-cylinder compact car is $0.32.
To calculate the total cost for the first year, we multiply the miles driven by the cost per mile: Total cost for the first year = 15,000 miles x $0.32 per mile In the second year, the car was driven for 14,000 miles. Using the same method, we can calculate the total cost for the second year: Total cost for the second year = 14,000 miles x $0.32 per mile In the third year, the car was driven for 13,000 miles.
Again, using the same method, we can calculate the total cost for the third year: Total cost for the third year = 13,000 miles x $0.32 per mile To calculate the total cost for all three years, we sum up the costs for each individual year: Total cost for all three years = Total cost for the first year + Total cost for the second year + Total cost for the third year Make sure to substitute the values calculated for each year into this equation to find the final answer. Remember to use the thousands comma where applicable and express the answer in dollars and cents format.
To know more about cylinder here
https://brainly.com/question/23935577
#SPJ2
Solve for x
A 4
B 9
C 3
D 15
Answers
You owe $225. on your credit card. You make a $55. payment and then purchase $87 worth of clothes at Dillards. What is the integer that represents the balance owed on the credit card?
Answers
The way you would find this answer would be by subtracting $225 by $55 which would be $170 then use addition to add $87 which would end up as $257
The integer that represents the balance owed on the credit card is -257.
What is subtraction?The process of subtracting one number from another is known as subtraction.
Given that, the person owns $225 on the credit card.
The balance owed on a credit card is represented by a negative sign, therefore, the balance on the credit card is.
-255
The balance after making a $55 payment is,
-255 + 55
Now, the balance after purchasing stuff of $87 is,
-255 + 55 + 87
= -257
Hence, the integer that represents the balance owed on the credit card is -257.
To learn more about subtraction, click here:
https://brainly.com/question/2346316
#SPJ5
The figure shown is composed of a triangle within
a trapezoid. Determine the area of the
shaded region.
Answers
The area of the shaded region = area of the trapezoid - area of the = 42 - 5.25 = 36.75 m²
What is the Area of a Trapezoid?Area of ay trapezoid is determined using the formula:
Area = 1/2 × (a + b) × h, where a and b are the lengths of the bases of the trapezoid that are parallel, and h is the height or distance between the bases of the trapezoid.
What is the Area of a Triangle?
To find the area of a triangle, use:
Area = 1/2 × base × height of the triangle.
The area of the shaded region = area of the trapezoid - area of the triangle
Area of the trapezoid:
a = 5 m
b = 9 m
h = 6m
Substitute
Area of the trapezoid = 1/2 × (5 + 9) × 6
Area of the trapezoid = 1/2 × (14) × 6
Area of the trapezoid = 7 × 6
Area of the trapezoid = 42 m²
Area of the triangle:
Base = 7 m
Height = 6 - 4 1/2 = 1.5 m
Substitute
Area of triangle = 1/2 × 7 × 1.5
Area of triangle = 5.25 m².
The area of the shaded region = area of the trapezoid - area of the = 42 - 5.25 = 36.75 m²
Learn more about the area of trapezoid on:
https://brainly.com/question/1463152
#SPJ1
HELP PLEASEEEEE!!!!!!! IN NEED THE ANSWER LIKE YESTERDAY
Answers
Answer is 214
Step-by-step explanation:
because if you add them it equal that number
……………………bsjsjdjdnxnxixixmmdsijsnd dx
Answers
Please help solve this question
Answers
Answer:
1 1/6
Step-by-step explanation:
All you need to do is find common denominators and then add
What is the distance between (4, 3) and (7, 3)?
Answers
angle relationships, solve for value of x and angle measures
Answers
Answer:
if the answer is -4° then I can help u