a man in a lighthouse tower 30 ft. high spots a ship at sea. the angle of depression from the man to the ship is 10°. how far is the ship from the base of the lighthouse?
The man in a lighthouse tower 30 ft. high spots a ship at sea. The angle of depression from the man to the ship is 10°. How far is the ship from the base of the lighthouse?The problem involves an angle of depression, which is defined as the angle formed by a horizontal line and the line of sight that is directed downwards to an object.
A lighthouse tower is 30 feet tall. The line of sight from the man in the lighthouse to the ship forms an angle of depression of 10°.We can use trigonometry to solve for the distance between the lighthouse and the ship. We need to find the length of the side adjacent to the angle of depression. The distance we are looking for is the length of this adjacent side. So, we can use the tangent function to solve for the distance from the base of the lighthouse to the ship. The formula for tangent is tangent = opposite/adjacent. We know that the angle of depression is 10° and the opposite side is 30. The adjacent side is the distance we are trying to solve for.
tan θ = opposite/adjacent. tan 10° = 30/adjacent0.1763 = 30/adjacent Adjacent = 30/0.1763Adjacent = 170.23 feet.
In this problem, we are given the height of the lighthouse, the angle of depression, and we are asked to find the distance between the ship and the base of the lighthouse. The first step is to draw a diagram of the situation. We can see that the line of sight from the man in the lighthouse to the ship forms an angle of depression of 10°.We know that the height of the lighthouse is 30 feet. We want to find the length of the side adjacent to the angle of depression, which is the distance we are looking for. To solve for this, we can use the tangent function.
The formula for tangent is tangent = opposite/adjacent. tan θ = opposite/adjacent tan 10° = 30/adjacent. We can cross-multiply and simplify the equation to solve for adjacent. adjacent = 30/tan 10°We can use a calculator to evaluate the tangent of 10°.tan 10° = 0.1763adjacent = 30/0.1763Adjacent = 170.23 feet .The ship is approximately 170.23 feet from the base of the lighthouse.
Therefore, we can conclude that the ship is approximately 170.23 feet from the base of the lighthouse.
To know more about angle of depression :
brainly.com/question/11348232
#SPJ11
What is the Value of the expression below when w=9 and x=2
w-4x
Answer:
1
Step-by-step explanation:
Yolanda exercises for 360 minutes each week. How many minutes will she exercise in 5 weeks?
Answer: 1800 Minutes
Step-by-step explanation: 360 x 5 = 1800
Answer:
1800 minutes
Step-by-step explanation:
360×5=1800 minutes.
I don’t know how to give extra point because I’m new to this app but I would appreciate it if you could help
Answer:
n=-4
Step-by-step explanation:
First, subtract 3n on both sides. This results in -3=n+1. Then, subtract 1 on both sides. The answer is n=-4.
Answer:
B
Step-by-step explanation:
We have the equation:
[tex]3n-3=4n+1[/tex]
Let's solve for n. To do so, we want to isolate it.
Let's use the subtraction property of equality to subtract 3n from both sides:
[tex](3n-3)-3n=(4n+1)-3n[/tex]
The left side will cancel...
[tex]-3=(4n+1)-3n[/tex]
Subtract on the right:
[tex]-3=1n+1[/tex]
Remember that 1n is the same as just n. So:
[tex]-3=n+1[/tex]
Now, let's use the subtraction property of equality again to subtract 1 from both sides:
[tex](-3)-1=(n+1)-1[/tex]
The right side will cancel. Subtract on the left:
[tex]-4=n[/tex]
Symmetric property:
[tex]n=-4[/tex]
So, our answer is B.
And we're done!
Michelle spent $32 on hot dogs and hamburgers. Hot dogs were $5 and hamburgers $6. If she bought a total of 6 items, how many of each kind did she buy?
Michelle spent $32 on hot dogs and hamburgers. Hot dogs were $5 and hamburgers $6. [ If she bought a total of 6 items, Michelle buys 4 hot dogs and 2 hamburgers. Solution: x + y = 6; 5x + 6y = 32; 6x + 6y - (5x + 6y) = 36 - 32; x = 4, Put x= 4 in (1), we have, y = 6 - 4; y= 2. ]
Answer:
Michelle bought 2 hamburgers and 4 hot dogs
Step-by-step explanation:
As you've already implied, we will need a system of equations to find the amount of hot dogs and hamburgers Michelle bought.
First equation: We can allow x to represent the number of hot dogs and y the number of hamburgers. Since she bought 6 items altogether, our first equation is x + y = 6, since:
quantity of hot dogs + quantity of hamburgers = total amount of food
Second equation: Since she spent $32 altogether, hot dogs cost $5, and hamburgers cost $6, our second equation is 5x + 6y = 32 since:
(price of hot dogs * quantity) + (price of hamburgers* quantity) = total cost.
Method to solve the system: Substitution: Isolate x in the first equation and plug it in for x in the second equation to solve for y:
If we isolate x in the first equation, we get x = -y + 6.
Now we can plug in x = -y + 6 for x in the second equation to first solve for y, the number of hamburgers she bought:
5(-y + 6) + 6y = 32
-5y + 30 + 6y = 32
y + 30 = 32
y = 2
Plug in 2 for y in any of the two equations to solve for x:
We can now plug in 2 for y in the first equation to find x, the number of hot dogs she bought:
x + 2 = 6
x = 4
Thus, Michelle bought 2 hamburgers and 4 hot dogs.
Which is the better buy if Maya plans on buying a lot of milk?
Answer:
2 gallons
Step-by-step explanation:
Answer:
2 gallons for 5.98$
Step-by-step explanation:
for two gallons.
1/4g milk = 12.92
1/2g milk= 8.36
1g milk= 8.50
The city of Miami is tracking rainfall totals over the past month. They have been recording weekly totals for the month of September. The recorded data is: Week 1, 3.49″; Week 2, 1.73″; Week 3, 12.38″; and Week 4, 0.21″. The city wants to record the total rainfall in September to the nearest tenth of an inch. If they round each week's total to the nearest tenth before calculating September's total, what is the total estimated rainfall for the month?
Answer:
17.80"
Step-by-step explanation:
Weekly Rainfall total for September :
Week 1, 3.49″
Week 2, 1.73″
Week 3, 12.38″
Week 4, 0.21″
Rounding each week's total to the nearest tenth of an INCH before summing up:
WEEK 1 ; 3.50''
WEEK 2 ; 1.70"
WEEK 3 ; 12.40"
WEEK 4 ; 0.20"
TOTAL RAINFALL FOR SEPTEMBER :
(WEEK 1 + WEEK 2 + WEEK 3 + WEEK 4)
(3.50 + 1.70 + 12.40 + 0.20)
= 17.80"
2 (t+2)
distributive
Answer:
A: 2t+4
Step-by-step explanation:
Find all the missing angles and show your work.
Answer:
m∠1= 129
m∠2= 18
m∠3= 123
m∠4= 39
Step-by-step explanation:
Let's start off with finding the m∠2 in the triangle.
As you can see, this is a right triangles. So, the measure's of 72 and m∠2 sum up to 90 degrees. The equation would be: 72+m∠2= 90.
Step 1- Subtract 72 to both side.s
72+m∠2= 90
-72 -72
m∠2= 18
Now that we know the measure of m∠2, let's move on to m∠1.
Remember that a triangle always sums up to 180 degrees. So, the equation would be: 72+57+m∠1= 180.
Step 1- Add to simplify.
(72+57)+m∠1= 180
129+m∠1= 180
Step 2- Subtract 129 to both sides.
129+m∠1= 180
-129 -129
m∠1= 129
So, now we know the measure of m∠1. In order to find the m∠3, remember that a straight line always equals 180 degrees. So, the equation would be: 57+m∠3= 180.
Step 1- Subtract 57 to both sides.
57+m∠3= 180
-57 -57
m∠3= 123
Finally, to find the m∠4. As I mentioned earlier, a triangles sums up to 180 degrees. So, the equation would be: 123+18+m∠4= 180.
Step 1- Add to simplify.
(123+18)+m∠4= 180
141+m∠4= 180
Step 2- Subtract 141 to both sides.
141+m∠4= 180
-141 -141
m∠4= 39
Now we know all the measures of the missing angles!
Hope this helped you understand! :)
Which three measurements could be the lengths of the sides of a triangle?
A:25 feet, 30 feet, 60 feet
B:40 feet, 60 feet, 70 feet
C:40 feet, 175 feet, 220 feet
D:80 feet, 150 feet, 230 feet
Answer:
Choice B
Step-by-step explanation:
For a triangle to be true, the longest side has to be shorter than the two shorter sides combined. The only answer that fits this is choice be. 70<40+60
Solve the equation – 2 =
k + 7
[tex]-2 = k+7\\-2-7 = k\\-9 = k\\[/tex]
Whenever you move from the left to right or right to left of any linear equations, you have to switch from plus to minus or multiply to division.
Answer:
k= -9
Step-by-step explanation:
-2= k+7
-k= 7+2
-k = 9
k = -9
kirks goal was to save $300 for a trip. In the first week ,kirk saved $16 from his allowence and $54 from his job. He spent $5 for lunch one day and another $2 on the bus.The second week ,kirk saved $62 and another $41, but spent $2 for the bus and $4 for lunch.
c. If Kirk saves $150 in the third week, but spends $8, will he reach his goal of saving $300? Explain.
Answer:
Yes, he will have $309 during the third week.
Step-by-step explanation:
The first week, he saved $70, then spent $7, subtracting to make $63 left. The next week, he saved $103, then spent $6, subtracting again to leave him with $97. $70 + $97 = $167, which is the current total amount he now has so far. Finally, with $150 earned the third week, but he spends $8 and has $142 leftover, $167 + $142 = $309. Meaning he will exceed by $9 more and will have enough money.
A directed segment ST¯¯¯¯¯ is partitioned from S (−5,0) to T in a 32 ratio at point M (10, 15). What are the coordinates of point T?
Answer:
Point T = (4,9)
Step-by-step explanation:
Given:
S (−5,0)
M (10, 15)
m1:m2 = 3:2
Find:
Point T
Computation:
X = [m1x2 + m2x1] / [m1+m2]
Y = [m1y2 + m2y1] / [m1+m2]
X = [(3)(10) + (2)(-5)] / [3+2]
Y = [(3)(15) + (2)(0)] / [3+2]
X = 20 / 5 = 4
Y = 45 / 5 = 9
Point T = (4,9)
Which of the following is not an item in the income statement? SELECT ONLY ONE a. Discount allowed b. Furniture & Fixture c. Furniture & Fixture d. Discount received
The item that is not an item in the income statement is b. Furniture & Fixture as it is considered a fixed asset and is reported on the balance sheet instead.
The income statement, also known as the profit and loss statement, provides a summary of a company's revenues, expenses, gains, and losses over a specific period. It helps to assess the financial performance of a business. The income statement typically includes various items such as revenues, cost of goods sold, operating expenses, interest income or expense, and other gains or losses.
a. Discount allowed is a revenue item that represents the discounts given to customers as an incentive for early payment or other reasons. It is usually reported as a deduction from sales revenue.
c. Furniture & Fixture is not typically included in the income statement. Instead, it is considered a non-operating or non-recurring item and is generally classified as a fixed asset on the balance sheet. Fixed assets represent long-term investments made by a company for its operations.
d. Discount received is also not an item in the income statement. It represents the discounts received by a company from its suppliers for early payment or other reasons. Similar to discount allowed, it is usually reported as a deduction from the respective expense account.
In summary, b. Furniture & Fixture is the item that is not included in the income statement. It is considered a fixed asset and is reported on the balance sheet instead.
To know more about fixed assets, refer here:
https://brainly.com/question/14392032#
#SPJ11
Graph the solution of the inequality on the number line.
−2x + 5(x − 2) > 7x − 6
Group of answer choices
Number line with a open circle at -1 and shading to the left
Number line with a open circle at -1 and shading to the right
Number line with a open circle at 4 and shading to the right
Number line with a open circle at 4 and shading to the left
HELPP PLSSS
Answer:
x<-1 so open circle going to the left
Johanna is driving from Orlando, FL to Dallas, TX. The distance between Orlando and Dallas is 1,084 miles. Johanna's average rate of speed is 65 mph the function that represents
how many miles Johanna has left on her trip after t hours is f(t) = 1084 - 650.
Enter the number of miles Johanna has left on her trip after 12 hours of driving
Answer:
She still has 304 miles left after traveling for 12 hours
Step-by-step explanation:
Here, we want to calculate the number of miles Johanna has left on her trip.
The equation linking the distance , speed and time is;
F(t) = 1084 -65t
Now, for t = 12, we simply make a direct substitution;
F(12) = 1084 - 65(12)
F(12) = 1084 - 780
F(12) = 304 miles
HW Score: 86.36%, 19 of 22 Homework: HW 8 Question 21, 6.3.1 points Save Points: 0 of 1 Write x as the sum of two vectors, one in Span {u₁, U₂, U3} and one in Span {u4}. Assume that {₁,...,4} is an orthogonal basis for R4. 0 2 1 4 13 0 - 2 -9 U₁ = 4₂ = - 3 1 - 1 5 - 1 1 - 3 1 0 X = (Type an integer or simplified fraction for each matrix element.) U3 = u4= X=
To write x as the sum of two vectors, one in Span {u₁, u₂, u₃} and one in Span {u₄}, where {u₁, u₂, u₃, u₄} is an orthogonal basis for R⁴, we need to find the components of x that lie in each span.
The vector x can be expressed as a linear combination of u₁, u₂, u₃, and u₄, with the components found by projecting x onto each basis vector.
Given that {u₁, u₂, u₃, u₄} is an orthogonal basis for R⁴, we can express x as the sum of two vectors: one in Span {u₁, u₂, u₃} and one in Span {u₄}. Let's denote the components of x in each span as x₁ and x₂, respectively.
To find x₁, we project x onto the subspace spanned by {u₁, u₂, u₃}. Since {u₁, u₂, u₃} is an orthogonal basis, the projection of x onto each basis vector is given by the dot product of x with the respective basis vector divided by the norm of the basis vector squared. Therefore, we have:
x₁ = (x · u₁) / ||u₁||² + (x · u₂) / ||u₂||² + (x · u₃) / ||u₃||².
To find x₂, we project x onto the subspace spanned by {u₄}. Since u₄ is a basis vector, the projection of x onto u₄ is simply the dot product of x with u₄ divided by the norm of u₄ squared. Hence:
x₂ = (x · u₄) / ||u₄||².
Thus, the vector x can be written as the sum of the two vectors: x = x₁u₁ + x₂u₄. Substituting the given values for u₁, u₂, u₃, and u₄, and evaluating the dot products and norms, we can find the components x₁ and x₂, and express x as the desired sum.
Learn more about vectors here :
https://brainly.com/question/24256726
#SPJ11
how long (in years) will it take your money to triple at an annual percentage rate of 6% compounded annually? use logarithms to solve. round and show 2 decimal places.
It will take approximately 11.9 years to triple the amount of the initial investment at an annual percentage rate of 6% compounded annually. This is calculated using the compound interest formula.
To calculate the duration required for your money to triple at an annual percentage rate of 6% compounded annually, you can use the formula for compound interest given as;
A = P(1 + r/n)^(nt),
Where; P is the principal amount, R is the annual interest rate, N is the number of times the interest is compounded per year, T is the time in years.
For this question,P = $1 (since we don't know the amount)
R = 6% = 0.06N = 1 (since the interest is compounded annually)
We want to know the time required (T) to get triple the amount of the initial amount.
This means that;
A = 3P
Therefore,
3P = P(1 + r/n)^(nt)
Dividing both sides of the equation by P,
3 = (1 + r/n)^(nt)
Since we want to calculate for time (T), we can use logarithms to solve.
Therefore, taking the natural logarithm of both sides of the equation,
ln(3) = ln(1 + r/n)^(nt)
Applying logarithmic laws,
ln(3) = nt ln(1 + r/n)
Solving for time (T),
T = ln(3)/(n ln(1 + r/n))
Substituting the values we have, we get;
T = ln(3)/(1 ln(1 + 0.06/1)) = ln(3)/ln(1.06) ≈ 11.9 years
It will take approximately 11.9 years to triple the amount of the initial investment at an annual percentage rate of 6% compounded annually. This is calculated using the compound interest formula.
Learn more about compound interest visit:
brainly.com/question/14295570
#SPJ11
Julio is paid 1.4 times his normal hourly rate for each hour he works over 30 hours in a week. Last week he worked 40 hours and earned $462.00. Write and solve an equation to find Julio's normal hourly rate, r. Explain how you know that your answer is reasonable . Help me
Answer:
$10.50
Step-by-step explanation:
Let his hourly rate be represented by h
From the question,
30h + 1.4 (40 - 30)h = $462.00
30h + 1.4(10)h = $462.00
30h + 14h = $462.00
44h = $462.00
h = $462.00/44
h = $10.50
Therefore, Julio's hourly rate is $10.50
What is the measure of the angle to the nearest degree? Enter the answer in the box.
degrees
Answer:
52.814 degrees
Step-by-step explanation:
we know that
we have
Convert 51'' to minutes
Convert 48.85' to degrees
Answer:
I don't know if I'm right but I looked it up and found the same picture and it said it was 120
HELP!! 10 points pleaseee!!!!!! I beg of you!!!
Answer: 2 = x (21+22x = 5+30x)
Step-by-step explanation:
Sam can do 120 jumping jacks in two minutes, how many jumping jacks can he complete in 5 mins.? (plz answer quick)
Answer:
300 jumping jacks
Step-by-step explanation:
120 ÷ 2 = 60 jumping jacks per minute
60 × 5 = 300 jumping jacks
Sam can do 300 jumping jacks in 5 minutes.
Hope that helps.
Answer:
60
Step-by-step explanation:
120 / 2 = 60 (jumping jacks per minute)
60 * 5 = 300
Best of Luck!
Fourteen subtracted from the sum of double a number and six
Algebraic expression
Answer:
Sum= addition
lets set the problem up like this
and let the first number equal A and the second number is B
This what we know:
14 = (a ) + 2(B)
A - B = 2
We need to find A and B
Step-by-step explanation:
Vladimir buys 1.20 pounds of Skittles, 312 pounds of M&Ms, and 5.2 pounds of pretzels. If the candy cost $1.20 a pound and the pretzels cost $1.10 a pound, how much did Vladimir spend?
Answer:
its A
Step-by-step explanation:
i just did this
6 times 10 to the power of negative 2 is how many times as large as 2 times 10 to the power of negative 8 plsplsls
Andrew fish tank holds 144 gallons of water. To clean the tank, he drains the water at a rate the water at a rate of 6 gallons per minute until the level is two-thirds its original level.Write and solve a 2-step equation to determine how many minutes does it take to drain the tank for cleaning.
Answer:
8 minutes
Step-by-step explanation:
Since the level of the tank needs to be at two-thirds its original level, then this means that Andrew needs to drain only one-third of the fish tank. Therefore the amount of time it would take can easily be solved with this 2-step equation...
6t = 144 * [tex]\frac{1}{3}[/tex] .... first multiply the right side of the equation
6t = 48 ... next divide both sides by 6
t = 8
Finally, we can see that it will take Andrew 8 minutes to drain the tank to two-thirds of its original level.
Sheila is riding in a multi-day bike trip. Each day she rides a different distance in a different period of time. On the first day Sheila rides 100 miles. On the first part of the first day of the trip, Sheila rode for 6 hours and covered 75 miles.
For the second part of the trip on the first day, Sheila rode for an additional 1.8 hours. Find the average speed for the second part of the trip. Use the relationship d = rt, or distance = rate · time. Round to the nearest tenth.
Answer:
13.9
Step-by-step explanation:
Someone please help with this question.
9514 1404 393
Answer:
100°
Step-by-step explanation:
Opposite angles in an inscribed quadrilateral are supplementary:
x° +80° = 180°
x° = 100° . . . . . . . subtract 80°
7. The sum of two numbers is 48. Find the numbers if the second is three more than four times the first
If the sum of two numbers is 48, we can call our numbers x and 48 - x.
Let's call our first number x and our second number 48 - x.
Now read through the rest of the problem.
The second, 48 - x, is, equals, 3 more than 4 times the first, 4x + 3.
So we have the equation 48 - x = 4x + 3.
Solving from here, we subtract 4x from both sides and we have 48 - 5x = 3.
Now subtract 48 from both sides and we have -45 = -5x.
Finally, divide both sides by -5 and remember that
a negative divided by a negative always equals a positive.
So we have 9 = x.
So our first number is x and our second is 48 - x or 48 - 9 which is 39.
If A,B and C represent three matrices of the same size and (A+B)+C=0, then which statement is true?
Answer: a11 + ( b11 + c11 ) = 0
Step-by-step explanation:
A, B, and C represent three matrices of the same size and (A + B) + C = 0.
