An observer in a lighthouse 350 ft above sea level observes two ships directly offshore. The angles of depression to the shops are 4 degree and 6.5 degree. How far apart are the ships?
Answers
The two ships are 1933.32 ft apart
Explanation:Given:
The height of the lighthouse = 350 ft
The angles of depression to the ships are 4 degree and 6.5 degree
To find:
the distance between the two ships
To determine the distance, we will use an illustration of the situation
First we will find the value of y as we need to know this value to get x
To get y, we will apply tan ratio (TOA)
[tex]\begin{gathered} tan\text{ 6.5\degree = }\frac{opposite}{adjacent} \\ opp\text{ = 350 ft} \\ adj\text{ = y} \\ tan\text{ 6.5\degree = }\frac{350}{y} \\ y(tan\text{ 6.5\degree\rparen= 350} \\ y\text{ = }\frac{350}{tan\text{ 6.5}} \\ y\text{ = 3071.9106 ft} \end{gathered}[/tex]Next is to find x using tan ratio (TOA):
[tex]\begin{gathered} angle\text{ = 4\degree} \\ tan\text{ 4\degree= }\frac{opposite}{adjacent} \\ \\ opposite\text{ = 350 ft} \\ adjacent\text{ = y + x} \\ tan\text{ 4\degree= }\frac{350}{y\text{ + x}} \end{gathered}[/tex][tex]\begin{gathered} tan\text{ 4 = }\frac{350}{3071.9106+x} \\ \frac{350}{tan\text{ 4}}\text{ = 3071.9106 + x} \\ 5005.2332\text{ = 3071.9106 + x} \\ x\text{ = 1933.3226} \\ \\ The\text{ ships are 1933.32 ft apart \lparen nearest hundredth\rparen} \end{gathered}[/tex]
Related Questions
6. Refer to the graph in question 5A) graph -f(x)B) graph f(x) -2
Answers
Given the graph of f(x):
Where the points A, B, and C have the coordinates:
[tex]\begin{gathered} A=(0,-2) \\ B=(3,2) \\ C=(5,2) \end{gathered}[/tex]Now, the transformation -f(x) is just a reflection about the x-axis. This is equivalent to a change of sign on the y-coordinate. The new points A', B', and C' are:
[tex]\begin{gathered} A^{\prime}=(0,2) \\ B^{\prime}=(3,-2) \\ C^{\prime}=(5,-2) \end{gathered}[/tex]And the graph looks like this:
Now, for the f(x) - 2 transformation, we see that this is just a shift of 2 units down. Then:
Where:
[tex]\begin{gathered} A^{\prime}^{\prime}=(0,-4) \\ B^{\prime}^{\prime}=(3,0) \\ C^{\prime}^{\prime}=(5,0) \end{gathered}[/tex]A square pyramid has a volume of 108 cubic feet and a height of 4 feet.What is the length of each side of the base of the pyramid?A 4 ftOLOB. 9 ftC. 18 ftD. 27 ftO E. 81 ftHelp please very hard
Answers
okay so the answer is 9ft so option B
now we can take a look at how we arrived to that answer
do you know the formula for the volume?
Find the measure of x.26x = [?Round to the nearest hundredth.X78°
Answers
To answer this question we will use the trigonometric function cosine.
Recall that in a right triangle:
[tex]\cos\theta=\frac{AdjacentLeg}{Hypotenuse}.[/tex]Using the given diagram we get that:
[tex]\cos78^{\circ}=\frac{x}{26}.[/tex]Multiplying the above result by 26 we get:
[tex]\begin{gathered} 26\times\cos78^{\circ}=26\times\frac{x}{26}, \\ 26\cos78^{\circ}=x. \end{gathered}[/tex]Therefore:
[tex]x\approx5.41.[/tex]Answer:
[tex]x=5.41.[/tex]
2)Find the missing coordinate (5, 7) and (8,y); m= 4/3
Answers
Answer:
y = 11
Step-by-step explanation:
Hello!
We can utilize the slope formula to create the equation for y:
[tex]\frac{y - 7}{8 - 5} = \frac{4}{3}[/tex]Solve for y[tex]\frac{y - 7}{8 - 5} = \frac{4}{3}[/tex][tex]\frac{y - 7}{3} = \frac{4}{3}[/tex] => Simplifyy - 7 = 4 => Multiply both sides by 3y = 11 => Add 7 to both sidesThe value of y is 11.
Write the nth rule for the following geometric sequence. Then find the fifth term. (you are given the first term and the common ratio)1-
Answers
The formula for determining the nth term of a geometric sequence is expressed as
Tn = ar^(n - 1)
Where
a represents the first term
r represents the common ratio.
n represents the number of terms
From the information given,
a = 2, r = 3
Thus, the rule for the nth term of the geometric sequence is
Tn = 2 x 3^(n - 1)
To determine the fifth term, we would substitute n = 5 into the equation. It becomes
T5 = 2 x 3^(5 - 1)
T5 = 2 x 3^4
T5 = 162
The fifth term is 162
write an expression such that if you apply the distributive property to your expression it would give the same result presented. 8x + 12
Answers
Solution:
Let's find a expression such that if you apply the distributive property to your expression it would give the same result presented:
• 8x + 12 = 2 (4x + 6)
,• 8x + 12 = 4 (2x + 3)
,• 8x + 12 = 8 (x + 1.5)
Any of these expressions could be the solution to the question.
Find the mean for this set of data. Write your answer as a decimal roundedto the nearest TENTH.32, 23, 34, 29, 15, 17, 23
Answers
Given:
The set of data is given as
[tex]32,23,34,29,15,17,23[/tex]Required:
To find the mean.
Formula:
[tex]\text{Mean(}\bar{\text{X}})=\frac{\Sigma x}{n}[/tex]Explanation:
Mean is the ratio of the sum of the values and the number of values.
No of values in the given data is 7.
[tex]n=7[/tex][tex]\begin{gathered} \text{Mean}=\frac{32+23+34+29+15+17+23}{7} \\ =\frac{173}{7} \\ =24.7 \end{gathered}[/tex]Final Answer:
[tex]\text{Mean}=24.7[/tex]
7(x+2)=
4(x+4)=
9(x+6)=
Answers
Answer:
Step-by-step explanation:
7(x+2) = 7x+14
7(x+2)=7x+7 times 2
4(x+4)= 4x+16
4 times x = 4x
4 times 4 = 16
= 4x+16
9(x+6) = 9x+54
9 times x = 9x
9 times 6 = 54
= 9x+54
Question 5 of 10 Solve the proportion below. 23 A 6 B. 8 C. 9 D.
Answers
solve for x
[tex]\begin{gathered} 12.6\times\frac{x}{12.6}=\frac{5}{7}\times12.6 \\ x=\frac{63}{7}=9 \end{gathered}[/tex]answer: C. 9
Suppose that the future price p(t) of a certain item is given by the following exponential function. In this function, p(t) is measured in dollars and t is the number of years from today. p(t) = 3000 * (1.019) ^ t
Answers
The growth or decay of an original quantity C that increases or decreases in a p% per year after t years is given by the following equation:
[tex]p(t)=C\cdot(1\pm\frac{p}{100})^t[/tex]If the quantity increases (i.e. it growths) we use the + symbol inside the parenthesis. If the quantity decreases we use the - symbol. This implies that for a growth the term that is raised to t is greater than 1 and for a decay that term is smaller than 1.
Now let's compare that generic equation with the function given by the question:
[tex]3000\cdot(1.019)^t=C\cdot(1\pm\frac{p}{100})^t[/tex]One of the first things you can notice is that C=3000 which means that the initial price was $3000. Just to be sure that this is correct we can evaluate p(t) at t=0:
[tex]p(0)=3000\cdot(1.019)^0=3000[/tex]So the initial price was $3000.
Now let's compare the terms inside parenthesis that are raised to t:
[tex]1.019=1\pm\frac{p}{100}[/tex]As I stated before, if the term raised to t is greater than 1 then we are talking about a growth. 1.019 is greater than 1 so this function represents a growth. What's more, in the right side of the equation we must use the + symbol. This way we have an equation for the yearly percentage of change of the price:
[tex]1.019=1+\frac{p}{100}[/tex]We can substract 1 from both sides of this equation:
[tex]\begin{gathered} 1.019-1=1+\frac{p}{100}-1 \\ 0.019=\frac{p}{100} \end{gathered}[/tex]And we multiply both sides by 100:
[tex]\begin{gathered} 100\cdot0.019=\frac{p}{100}\cdot100 \\ 1.9=p \end{gathered}[/tex]So each year the price increases in a 1.9%.
AnswerThen the answers in order are:
$3000
growth
1.9%
√121 = ?
i need help
Answers
Answer:
11 and -11. Usually you only want the positive form
Step-by-step explanation:
[tex]\sqrt{121}[/tex] is asking what number times itself is 121? 11
11 x 11 = 121
-11 x -11 = 121
Kathryn needs to include a scale drawing of a race car on her science science fair project. Her actual race car is 180 inches long and 72 inches tall. if she uses a scale factor of 1 inch= 8 inches, what will the dimensions of her scale drawing?
Answers
To find the scaled measures of the race car, you have to divide the original measures by the scale. This is:
[tex]\text{length}=\frac{182in}{8}=22.75in[/tex][tex]\text{height}=\frac{72in}{8}=9in[/tex]So the scaled measures of the race car are: length=22.75in and height=9in
14#An ecologist randomly samples 12 plants of a specific species and measures their heights. He finds that this sample has a mean of 14 cm and a standard deviation of 4 cm. If we assume that the height measurements are normally distributed, find a 95% confidence interval for the mean height of all plants of this species. Give the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)Lower limit:Upper limit:
Answers
Answer:
Lower limit: 11.7 cm
Upper limit: 16.263
Explanation:
The formula to find the lower and upper limits of the confidence interval (given the data is normally distributed) is :
[tex]CI=\mu\pm Z^*\frac{\sigma}{\sqrt{n}}[/tex]Where:
• μ = sample mean
,• σ = sample standard deviation
,• Z* = critical value of the z-distribution
,• n = is the sample size
In this case:
• μ = 14cm
• σ = 4cm
,• n = 12
The critical value of the z-distribution for a confidence interval of 95% is Z* = 1.96
Now, we can use the formula above to find the upper and lower limit:
[tex]CI=14\pm1.96\cdot\frac{4}{\sqrt{12}}=14\pm\frac{98\sqrt{3}}{75}=\frac{1050\pm98\sqrt{3}}{75}[/tex]Thus:
[tex]Lower\text{ }limit=\frac{1050-98\sqrt{3}}{75}\approx11.736cm[/tex][tex]Upper\text{ }limit=\frac{1050-98\sqrt{3}}{75}\approx16.263cm[/tex]Rounded to one decimal:
Lower limit: 11.7cm
Upper limit: 16.3cm
Add.
47+13
Enter your answer as a fraction in simplest form by filling in the boxes.
Answers
Answer: 47+13 =60
60 as a fraction should be 3/5 in simplest form.
Step-by-step explanation:
True or False? Every rectangle is a parallelogram. Every rhombus is a parallelogram. Every quadrilateral is a square. Every rectangle with four congruent sides is a square. X S True O False True O False O True False O True O False ?
Answers
Given: Different statement relating different quadrilateral
To Determine: If true or false statement
Solution
The image below summarizes the properties of a quadrilateral
From the above, we can conclude that
Vincent turned his head 30° to the side. Which of the following shows the angle that he turned his head?
Answers
Given data:
Vincent turned his head 30° to the side.
The figure in the option b is the angle that he turned his head.
Translate into a number sentence7. Four less than seven is greater than zero
Answers
In order to translate the words into a number sentence, first let's translate each word or expression separately:
Four less than seven: "7 - 4"
Is greater than: ">"
Zero: "0"
Therefore the number sentence will be:
[tex]7-4>0[/tex]Write an equation of the line with the given slope and y-intercept.
Slope
1
6
, y−intercept (0, −2)
Answers
The equation of line is [tex]6y=6x$-$12[/tex].
The given slope is [tex]\frac{1}{6}[/tex].
The [tex]y $-$[/tex]intercept is [tex](0, $-$2)[/tex].
We have to write the equation of line using the given slope and [tex]y $-$[/tex]intercept.
The equation of line with the slope m and [tex]y $-$[/tex]intercept of [tex](0,a)[/tex] is [tex]y=mx+a[/tex].
From the question,
The value of [tex]m=\frac{1}{6}[/tex]
The value of [tex]a= $-$2[/tex]
Now putting the value of [tex]m[/tex] and [tex]a[/tex] in the equation of line.
[tex]y=\frac{1}{6}x+( $-$2)\\y=\frac{1}{6}x$-$2[/tex]
Multiply by [tex]6[/tex] on both side
[tex]y\times6=6\times(\frac{1}{6}x$-$2)\\6y=6\times\frac{1}{6}x$-$6\times2\\6y=6x$-$12[/tex]
The equation of line is [tex]6y=6x$-$12[/tex].
To learn more about slope and [tex]y-[/tex]intercept form here link
https://brainly.com/question/12952118
#SPJ1
what is the equation
Answers
In the graph you can see that the line passes through 2 points (-4,0) and (0,2). With them you can obtain the equation of the line. First you find the slope of the line with the following equation
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{Where} \\ m\colon\text{ Slope of the line} \\ (x_1,y_1)\colon\text{ Coordinates of first point }on\text{ the line} \\ (x_2,y_2)\colon\text{ Coordinates of second point }on\text{ the line} \end{gathered}[/tex]So you have,
[tex]\begin{gathered} (x_1,y_1)=(-4,0) \\ (x_2,y_2)=(0,2) \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{2-0}{0-(-4)} \\ m=\frac{2}{4}=\frac{1}{2} \end{gathered}[/tex]Now, with the point slope equation you can obtain the equation of the line
[tex]\begin{gathered} y-y_1=m(x_{}-x_1) \\ y-0=\frac{1}{2}(x-(-4)) \\ y=\frac{1}{2}(x+4) \\ y=\frac{1}{2}x+\frac{1}{2}\cdot4 \\ y=\frac{1}{2}x+\frac{4}{2} \\ y=\frac{1}{2}x+2 \end{gathered}[/tex]Therefore, the equation of the line is
[tex]y=\frac{1}{2}x+2[/tex]Solve the inequality -30 10-40x and write the solution using:
Inequality Notation:
Answers
Answer:
Step-by-step explanation:
what is the nessecary information you need to know about a cube?
Answers
Answer: the width, length and height
Step-by-step explanation: multiply the width length and height of a cube and you get the area
Fifth grade > Y.5 Compare and convert Which is more, 1/2 of a pound or 6 ounces? of a pound 2. 6 ounces neither; they are equal Submit
Answers
We should know that :
1 pound = 16 ounces
The question is :
Which is more, 1/2 of a pound or 6 ounces?
so,
1/2 of a pound = 1/2 x 16 = 8 ounces
So,
8 ounces > 6 ounces
so, the answer is option 1
The more is 1/2 of a pound
A major record label has seen its annual profit decrease in recent years. In 2011, the label's profit was $128 million. By 2015, the label's profit had decreased by 30%.What was the record label company's profit in 2015? million dollars Suppose the record label wants to increase its profit to $128 million by 2017. By what percent must the label's profit increase from its 2015 value to reach $128 million within the next two years? %
Answers
the company's profit in 2015 was $89,600,000 (89.6 million dollars)
43%
Explanation:
Profit in 2011 = $128 million
Profit in 2015 decreased by 30%
% decrease = (old price - new price)/old price
old price = Profit in 2011 , new price = Profit in 2015
30% = (128,000,000 - new price)/128000000
[tex]\begin{gathered} 30percent=\text{ }\frac{128,000,000 -newprice}{128000000} \\ 0.30\text{ = }\frac{128,000,000-newprice}{128000000} \\ \text{cross multiply:} \\ 0.3(128,000,000)\text{ = }128,000,000-newprice \end{gathered}[/tex][tex]\begin{gathered} 38400000\text{ = }128,000,000-newprice \\ \text{subtract }38400000\text{ from both sides:} \\ 38400000-\text{ }38400000\text{ = }128,000,000-38400000-newprice \\ \text{0 = 89600000 }-newprice \\ newprice\text{ = 89600000 } \end{gathered}[/tex]Hence, the company's profit in 2015 was $89,600,000 (89.6 million dollars)
Percentage increase = (new price - old price)/old price
new price = 128million dollars , old price = 89.6 million dollars
% increase = [(128 - 89.6)in millions/(89.6) in millions] × 100
% increase = 38.4/89.6 × 100
% increase = 0.43 × 100
% increase = 43%
Hence, the label's profit must increase by 43% from its 2015 value to reach $128 million within the next two years
Find the interest earned on a $50,000 deposited for six years at 1 1/8 % interest, compounded continuously
Answers
To calculate the interest earned, we can use the following equation:
[tex]I=P((1+i)^n-1)[/tex]Where P is the value of the deposit, i is the interest rate and n is the number of periods of time.
First, we need to calculate the equivalent value of 1 1/8 % as:
[tex]1\frac{1}{8}\text{ \% = }\frac{1\cdot8+1}{8}\text{ \% = }\frac{9}{8}\text{ \% = 1.125\% = 0.01125}[/tex]So, replacing P by $50,000, i by 0.01125, and n by 6, we get:
[tex]\begin{gathered} I=50,000((1+0.01125)^6-1) \\ I=50,000(0.694) \\ I=3,471.3577 \end{gathered}[/tex]Answer: $ 3,471.3577
DATE IN OUT IN OUT HOURS TEMPORARY EMPLOYEE TIME CARD NAME: Eugene Mueller 8/8 7:00 4:10 8/9 6:50 11:00 DEPT Sales 8/10 8/11 12:00 4:35 Note: No overtime rate. 10:55 3:25 EMPLOYEE SIGNATURE RATE per hour: $8.50 TOTAL HOURS:
Answers
0 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 10401234 5 6 7 8 9 10OB.C.OD. +Reset Selection
Answers
Okay, here we have this:
Considering the provided inequation, we are going to identify how can be represented on a number line, so we obtain the following:
So the first thing we will do is factor to find the solution intervals, we have:
[tex]\begin{gathered} 3x^2-27x\leq0 \\ x(x-9)\leq0 \\ 0\leq x\leq9 \end{gathered}[/tex]According to this, we finally obtain that the solution interval is option D, because it satisfies the found interval and its endpoints are closed.
In Abc,AB=5 feet and BC=3 feet.Which inequality represents all possible values for the length of AC,in feet?
Answers
The smallest value of length AC would be 5 ft - 3 ft = 2 ft while the largest length would be 5 ft + 3 ft = 8ft. The answer will be
2 < Ac < 8
Recipe A calls for 2 cups of sugar and makes 48 cookles. Recipe B calls for 3 cups of sugar and makes 54 of the same sized cookies. Determine which recipe contains more sugar in each cookle. Use complete sentences to explain your reasoning.
Answers
we are given two recipes for cookies and we are asked which of the two contains more sugar. To do that we need to find the amount of sugar per cookie for each recipe.
For recipe A we have:
[tex]2cups\rightarrow48cookies[/tex]This means:
[tex]\frac{2cups}{48cookies}=\frac{1}{24}\frac{cups}{cookies}[/tex]For recipe B we have:
[tex]3cups\rightarrow54\text{cookies}[/tex]This means:
[tex]\frac{3\text{cups}}{54\text{cookies}}=\frac{1}{18}(\frac{cups}{cookies})[/tex]Since 1/18 is greater than 1/24, this means that there is more sugar per cookie in recipe B than in recipe A.
What is the distance between (-5, 5) and (1, -2)
Answers
Answer:
[tex]\displaystyle d=\sqrt{85}\text{, or about 9.22 units}[/tex]
Step-by-step explanation:
We will use the distance formula to solve.
[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]
[tex]\displaystyle d=\sqrt{(1--5)^2 +(-2-5)^2}[/tex]
[tex]\displaystyle d=\sqrt{(6)^2 +(-7)^2}[/tex]
[tex]\displaystyle d=\sqrt{36+49}[/tex]
[tex]\displaystyle d=\sqrt{85}\text{, or about 9.22 units}[/tex]
Read more about using the distance formula here: https://brainly.com/question/15691280
A whole pizza is cut into twelfths. If Dexter eats 1/2 of the pizza and Landry eats 1/3 of the pizza, then 3 what fraction of the pizza remains?
Answers
Explanation
Step 1
Let
A whole pizza = 1 pizza
Dexter eats 1/2
Landry eats 1/3
x= fraction of the pizza remains
Step 2
the r