From the top of a cliff 90 m high, the angle of depression of a boat on the sea is 26.2°. Calculate how far the boat is
a from the foot of the cliff,
b from the top of the cliff.

Answers

Answer 1

Answer:

a) 182.90 m

b) 203.85 m

Step-by-step explanation:

The relations between trig functions and measures in a right triangle are summarized in the mnemonic SOH CAH TOA. Here, we are given an angle and the side opposite, and we are asked to find the adjacent side and the hypotenuse.

The foot of the cliff to the boat is the adjacent side of the angle in our model. So, we can use the relation ...

Tan = Opposite/Adjacent

Solving for the adjacent side, we have ...

BF = (90 m)/tan(26.2°) ≈ 182.90 m

The boat is about 182.90 meters from the foot of the cliff.

The top of the cliff to the boat is the hypotenuse of the triangle we're using to model the situation. This means the applicable relation is ...

Sin = Opposite/Hypotenuse

BC = (90 m)/sin(26.2°) ≈ 203.85 m

The boat is about 203.85 meters from the top of the cliff.

From The Top Of A Cliff 90 M High, The Angle Of Depression Of A Boat On The Sea Is 26.2. Calculate How

Related Questions

1. Identify your variables using let statements.

2. Determine the equations for the linear system.

3. Determine the solution to the linear system (point of intersection)

4. Explain the meaning of the solution using a therefore statement.

Chris is mixing 2 different types of fruit juice together for a summer drink. The two types of juices he is using is one that is 30% strawberry concentrate and the other is 55% lemon concentrate. If he wants 2 L that is 40% concentrate of the fruit juices, how much of each should be used to create the drink?

Answers

The meaning of the solution is; Therefore, 1.2 liters of the strawberry concentrate and 0.8 liters of the lemon concentrate.

What is the solution to the system of equations?

It follows from the task content that the variables are;

let x be the amount of 30% strawberry concentrate.

let y be the amount of 55% lemon concentrate.

The equations of the linear system according to the task content are as follows;

x + y = 20.30x + 0.55y = (2 ×0.4)

From the first equation; x = 2-y;

Hence, upon substitution; we have;

0.30(2-y) + 0.55y = 0.8

0.25y = 0.2.

y = 0.2/0.25 = 0.8L.

Hence, x = 2- 0.8 = 1.2L.

Answers

Given expression

[tex]\\ \rm\Rrightarrow T(t)=29-5cos\left(\cfrac{2\pi (t-12)}{365}\right)[/tex]

Now

We know according to property of cosine function

It has range of [-1,1] for all intervals .

This property is enough for our calculations

Let's check

As t represents no of days hence it can't be negative

t must be a whole number set member

for positive interval

We shall use the cosine interval [0,π]

We know that

cosπ is -1cos0=1

Hence it's enough for our range [-1,1]

Now

In the expression

29 is the vertical shift

Let

[tex]\sf cos\left(\cfrac{2\pi(t-12)}{365}\right)=n[/tex]

Substitute n for lowest and highest value of range

When n=-1

[tex]\\ \rm\Rrightarrow T(\pi)=29-5(-1)=29+5=34°C[/tex]

When n=1

[tex]\\ \rm\Rrightarrow T(0)=29-5(1)=29-5=24°C[/tex]

Highest average daily high=34°Clowest average daily high=24°C

Answer:

Highest temperature: 34°C

Lowest temperature: 24°C

Explanation:

In a Normal Trigonometry Function: y = A + B sin(x) or y = A + B cos(x)

Maximum value: A + |B|

Minimum value: A - |B|

In this trigonometric function, A = 29, B = -5

Hence find minimum/maximum:

Maximum value: A + |B| = 29 + |-5| = 34

Minimum value: A - |B| = 29 - |-5| = 24

Hence, the maximum/highest temperature is 34°C and minimum/lowest temperature is 24°C in Karachi, Pakistan.

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answer...............

Answers

In the given graph point B is a relative maximum with the coordinates (0, 2).

The given function is [tex]y=x^{4}-2x^{2} +1[/tex].

In the given graph, we need to find which point is a relative maximum.

What are relative maxima?

The function's graph makes it simple to spot relative maxima. It is the pivotal point in the function's graph. Relative maxima are locations where the function's graph shifts from increasing to decreasing. A point called Relative Maximum is higher than the points to its left and to its right.

In the graph, the maximum point is (0, 2).

Therefore, in the given graph point B is a relative maximum with the coordinates (0, 2).

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question 10 please
need help

Answers

Answer:

Denes Dynamos =

2012 attendance = 34500

2013 attendance = 30705

change = 30705 - 34500= -3795

change percentage = -3795 * 100 / 34500 = -11%

Edgefield Eagles =

2012 = 24100

2013 = 21208

change = -2892

change Percentage = -2892 * 100 / 24100 = -12%

Which of the following graphs represents the solution set
x>5?

Answers

Answer:

Graph A is correct.

Step-by-step explanation:

Graph A is the graph with the open circle and the arrow pointing to the right.

53 points!!! find x. do not round your answer. 5cm 6cm 12cm x

Answers

Answer:

16.6

Step-by-step explanation:

By the property of intersecting secants.

5(5+x) = 6(6+12)

-> 25 + 5x = 6*18

-> 5x = 108 - 25

-> 5x = 83

-> x = 83/5

-> x = 16.6

Lyanna opens a bank account with a deposit of $200. She earns 3%
interest per year. How much money will Lyanna have in her account after
the first year?

Answers

Answer:

$206

Step-by-step explanation:

Lyanna will earn 3% on her capital within 1 year.
In total, she will have 103%.
$200 x 103% = $206

An adult male cheetah runs at a speed of 26 mph. That is 30% faster than his average last month. How fast did the male cheetah run last month?
Sadie makes 1.5 liters of iced tea. She pours of a liter into a pitcher to take to her neighbor. Her sister drinks of the remaining iced tea. How much tea does Sadie’s sister drink?

Answers

An expression is defined as a set of numbers, variables, and mathematical operations. The male cheetah's average speed for the last month is 20 mph.

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

A.) Let the male cheetah's average speed for the last month be represented by x.

Given the male cheetah runs at a speed of 26 mph, that is 30% faster than his average last month.

x + 30% of x = 26 mph

1.30x = 26

x = 20 mph

Hence, the male cheetah's average speed for the last month is 20 mph.

B.) Sadie makes 1.5 liters of iced tea. She pours a liter into a pitcher to take to her neighbor. Her sister drinks the remaining iced tea. Therefore,

Iced tea Sadie's sister drink = 1.56 liters - 1 liter = 0.56 liter

Hence, the amount of tea Sadie’s sister drinks is 0.56 liters.

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which equation matches this graph?

Answers

The first function represents the graph of a function provided in the picture option first is correct.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a graph of a function shown in the picture.

[tex]\rm f\left(x\right)\ =\ -\sqrt{\left(x-3\right)}\ +\ 2[/tex]

x - 3 ≥ 0

x ≥ 3

Plug x = 3

f(x) = 2

Thus, the first function represents the graph of a function provided in the picture option first is correct.

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In a stadium, 1,000 tickets were sold. Children’s tickets cost $2.50 each and adults’ tickets cost $5.00 each. The revenue collected for the game was $4,000. How many children’s tickets were sold? How many adults’ tickets were sold?

Answers

Answer:

400 children tickets and 600 adult tickets.

Step-by-step explanation:

children tickets in total cost=400x2.50

=1000

adult tickets in total cost=600x5.00

=3000

total cost is 4000

A container is an open cylinder whose height and radius are of equal length. The total surface area of the container is 300 cm³. Find the radius of the container.

Answers

Answer:

The radius of the container is approximately 4.89 cm

Step-by-step explanation:

Given

A container with:

r = hS = 300 cm²

To find

The radius of the container

Solution

Use the equation for total surface area of cylinder:

S = 2πr² + 2πrh or S = 2πr(r + h)

Since we have r = h and the value of S is known, let's solve this equation:

2πr(r + h) = 3002πr(r + r) = 3002πr(2r) = 3004πr² = 300πr² = 753.14r² = 75r² = 75/3.14r² = 23.89 (rounded)r = √23.89r = 4.89 cm (rounded)

there were 3 parts to Ritas race she ran the first part which was 4/9 of the total distance, in 20 minutes she ran the second part which was 2/5 of the remaining distance, in 12 minutes. She finally ran the third part in 15 minutes at the speed of 300 meters per minute.
How long was the first part of the race? What was Ritas speed in that section of the race?

Answers

Answer:

3/5 .................................. 6/9

Step-by-s4tep explanation:

Answer:

300 meters per minute

Step-by-step explanation:

Step 1

Determine the fraction of the total distance for each part of the race.

Given:

1st part of race = 4/9 of total distance2nd part of race = 2/5 of remaining distance

[tex]\begin{aligned} \implies \sf 2nd\:part & = \sf \dfrac{2}{5}\:of\:remaining\:distance\\ & = \sf \dfrac{2}{5} \times\left(1-\dfrac{4}{9}\right)\\& = \sf \dfrac{2}{9}\:of\:total\:distance\end{aligned}[/tex]

[tex]\begin{aligned}\implies \sf 3rd\:part & = \sf 1-1st\:part-2nd\:part\\& = \sf 1-\dfrac{4}{9}-\dfrac{2}{9}\\& = \sf \dfrac{1}{3}\:of\:total\:distance\end{aligned}[/tex]

Step 2

Determine the distance of the third part of the race.

Given:

time = 15 minutesspeed = 300 meters per minute

[tex]\begin{aligned}\sf Distance & = \sf speed \times time\\& = \sf 300 \times 15\\& = \sf 4500 \:\:meters\end{aligned}[/tex]

Step 3

If the third part of the race (which is 1/3 of the total distance) is 4500m, then the distance of the whole race is:

[tex]\begin{aligned} \sf Total\:distance & = \sf 4500 \times 3\\& = \sf 13500\:meters \end{aligned}[/tex]

Step 4

Determine the distance of the 1st part of the race:

[tex]\begin{aligned}\sf Distance\:of\:1st\:part\:of\:race & = \sf \dfrac{4}{9} \:of\:total\:distance\\& = \sf \dfrac{4}{9} \times 13500\\& = \sf 6000\:meters \end{aligned}[/tex]

Step 5

Determine the speed of the 1st part of the race:

Given:

time = 20 minutesdistance = 6000 m

[tex]\begin{aligned}\sf Speed\:of\:1st\:part\:of\:race & = \sf \dfrac{distance}{time}\\& = \sf \dfrac{6000}{20}\\ & = \sf 300\:meters\:per\:minute\end{aligned}[/tex]

The marketing manager of a cell-phone company wants to determine which cell phone model most of her customers prefer. She separates a list of her customers into three age groups and then randomly selects a sample from each group proportional to the number of customers in each group.
What sampling method did she use?

A. Simple random sampling
B. Stratified random sampling
C. Systematic random sampling
D. Non-random sampling

Answers

Answer:

Step-by-step explanation:

I guess it is the answer because the manager separates the customers into 3 ange groups and randomly selects a sample from each group

Answer:

B. Stratified random sampling

Step-by-step explanation:

Convert 203 yards into meters.

Hint: 1 yard=0.91 meters
203 yards=[blank]−−−−−− meters

Enter your answer as a number that correctly fills in the blank.

Round the answer to two decimal places, like this: 45.53

Answers

Answer:

184.73

Step-by-step explanation:

1 yard = 0.91m

203 yard=?

(203x0.91)/1=184.73.

+1(415) 450-6164

In your research study measuring the relationship between time spent playing video games and course grades, you find that grades increase at about the same rate as time spent playing video games decreases. What do you conclude

Answers

Research study measuring relationship suggests that video games may have a detrimental effect on an individual's grades.

This study analyzes the correlation between video game usage and academic performance. Scholastic Aptitude Test (SAT) and grade-point average (GPA) scores were used to gauge academic performance. The amount of time a student spends playing video games has a negative correlation with students' GPA and SAT scores. As video game usage increases, GPA and SAT scores decrease.

A chi-squared analysis found a p value for video game usage and GPA was greater than a 95% confidence level (0.005 < p < 0.01). This finding suggests that dependence exists. SAT score and video game usage also returned a p value that was significant (0.01 < p < 0.05). Chi-squared results were not significant when comparing time spent studying and an individual's SAT score. This research suggests that video games may have a detrimental effect on an individual's GPA and possibly on SAT scores. Although these results show statistical dependence, proving cause and effect remains difficult, since SAT scores represent a single test on a given day. The effects of video games maybe be cumulative; however, drawing a conclusion is difficult because SAT scores represent a measure of general knowledge. GPA versus video games is more reliable because both involve a continuous measurement of engaged activity and performance. The connection remains difficult because of the complex nature of student life and academic performance. Also, video game usage may simply be a function of specific personality types and characteristics.

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A car manufacturer has parked some new cars in 2 car parks.In the first car park there are 60 cars in the ratio 1 red car for every 2 blue cars and 3 silver cars.In the second car park there are 80 cars in the ratio 2 blue cars for every 3 red cars and 5 silver cars.

11. How many red cars are there altogether?
12.How many blue cars are there altogether?
13.How many silver cars are there together?

Answers

The total number of red cars is 34, the total number of blue cars is 36, and the total number of silver cars is 70.

How do we solve ratio problems?

The ratio problems can be solved as follows:

11. The total number of red cars can be calculated as follows:

Number of red car in the first car park = (1 / (1 + 2 + 3)) * 60 = 10

Number of red car in the second car park = (3 / (2 + 3 + 5)) * 80 = 24

Total number of red cars = 10 + 24 = 34

12. The total number of blue cars can be calculated as follows:

Number of blue car in the first car park = (2 / (1 + 2 + 3)) * 60 = 20

Number of blue car in the second car park = (2 / (2 + 3 + 5)) * 80 = 16

Total number of blue cars = 20 + 16 = 36

13. The total number of silver cars can be calculated as follows:

Number of silver car in the first car park = (3 / (1 + 2 + 3)) * 60 = 30

Number of silver car in the second car park = (5 / (2 + 3 + 5)) * 80 = 40

Total number of silver cars = 30 + 40 = 70

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If f(x)=2x² +5√(x-2), complete the following statement:

The domain for f(x) is all real numbers ____ than or equal to 2.

Free Response:

Answers

By functional analysis we have the following conclusion about the function given: The domain for f(x) is all real numbers greater than or equal to 2.

How to determine the domain of a function with radical components

Domain is the set of x-values such that the value of the function exists. By algebra we know that the domain of polynomials is the set of all real numbers, whereas the domain of radical functions is the set of x-values such that y ≥ 0. If we know that f(x) = 2 · x² + 5 · √(x - 2), then the domain is restricted by the radical component and defined by x ≥ 2.

By functional analysis we have the following conclusion about the function given: The domain for f(x) is all real numbers greater than or equal to 2.

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Work out the size of angle x.

Answers

Answer:

according to my calculation it is 13

Step-by-step explanation:

hope I helped

It’s is 13
The person who answered is correct

WILL MARK BRAINLIEST!!! According to the synthetic division below, which of the following statements are true? Check all that apply.

Answers

According to the given synthetic division, the statements that are true are; Options A, C and E

How to carry out Synthetic Division?

In the synthetic calculation we use the coefficient of the dividend

with the factors of the function.

Therefore;

3 , -13 , 4 are the coefficient of the dividend 3x² - 13x + 4

Therefore, the divisor is 4 and as such x = 4 is a root of f(x) = 3x² - 13x + 4

Also, it means that (x - 4) is a factor of the dividend F(x) = 2x² - 2x - 12

- The quotient is the last line of the synthetic division. Thus, the coefficients of quotient are 3, -1.

- The quotient is 1 degree less than the dividend and so the degree of the dividend is 2.

- The degree of the quotient is 1 and so the he quotient is 3x - 1.

Thus, options A, C and E are correct

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help its timed 12 pts

Answers

Answer:

Step-by-step explanation:

I think your right!

Answer:

Step-by-step explanation:

I think it means the roots, at which the line crosses the x-axis, in which case, the answer is B, 0 and 1.4

What are the solution(s) to the quadratic equation 9x² = 4?
0 x =
and x =
0 x =
I
69
4
and x = -
2
0 x = ² and x = -²
2
Ono real solution

Answers

Answer:

x= 2/3, -2/3

Step-by-step explanation:

9x² = 4

To solve this quadratic, divide each side by 9

x^2 = 4/9

Take the square root of each side

sqrt(x^2) = sqrt(4/9)

x = ±2/3

Answer:

x = ± [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

9x² = 4 ( divide both sides by 9 )

x² = [tex]\frac{4}{9}[/tex] ( take square root of both sides )

x = ± [tex]\sqrt{\frac{4}{9} }[/tex] = ± [tex]\frac{\sqrt{4} }{\sqrt{9} }[/tex] = ± [tex]\frac{2}{3}[/tex]

x = - [tex]\frac{2}{3}[/tex] , x = [tex]\frac{2}{3}[/tex]

can someone please help mee and graph it for me pleasee(20 points and i will give brainliest!!!)

Answers

Answer:

vertex: (3,1)

y-intercept = (0,-8)

x-intercept- Smaller=2 Larger=4

Domain= all real numbers, identity, infinite

Range= 1 is greater than or equal to y

axis of symmetry=3

Step-by-step explanation:

What is the domain of f(x) = 5x – 7?

{x | x > –7}
{x | x < –7}
{x | x > 0}
{x | x is a real number}

Answers

Answer: Choice D) x is a real number

Reason:

We can replace x with any number we want without any restriction. There's no issues dealing with division by zero errors for instance, and we also don't have negatives under square roots to worry about. The domain of any linear function is always "the set of all real numbers".

Extra info: The domain in interval notation is [tex](-\infty, \infty)[/tex] which could be thought of as [tex]-\infty < x < \infty[/tex], i.e. x is between negative infinity and positive infinity.

Answer:

Step-by-step explanation:

What are the features of the quadratic function f(x)=(x-3)(x+7)?

Answers

Answer:

It's vertex (-2,-25)x-intercept x₁=-7,x₂=3y-intercept f(0)=-21domain,xER or x is an element of real numberit's neither even nor odd function

Which are correct representations of the inequality 6x ≥ 3 + 4(2x – 1)? Select three options.

1 ≥ 2x
6x ≥ 3 + 8x – 4
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at negative 0.5 and a bold line starts at negative 0.5 and is pointing to the right.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the right.

Answers

1≥2x and 6x≥3+8x-4 are correct representations of the inequality 6x ≥ 3 + 4(2x – 1).Option A,B and C are correct.

What is the definition of inequality?

Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.

The solution to the given inequality is;

6x≥3+4(2x-1)

6x≥3+8x-4

2x≤1

x≤(1/2)

The correct options are;

A)1 ≥ 2x

B)6x ≥ 3 + 8x – 4

C)A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.

1≥2x and 6x≥3+8x-4 are correct representations of the inequality 6x ≥ 3 + 4(2x – 1).

Hence, options A, B, and C are correct.

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Answer:

A, B, C

Step-by-step explanation:

Need help please. Math and I'll give 30 points. Please and thank you. :D

And have a great day! :)

Answers

Answer:

h = 17.5 m

Step-by-step explanation:

We have 2 similar right triangles as models of the situation

one has legs with George's height and shadow

the other is the height h of the tree and length of it's shadow

the corresponding sides of the 2 triangles are in proportion, that is

[tex]\frac{6.25}{h}[/tex] = [tex]\frac{10}{28}[/tex] ( cross- multiply )

10h = 175 ( divide both sides by 10 )

h = 17.5 m

3 connecting lines are shown. Line D F is horizontal. Line D E is about half the length of line D F. Line F E is about one-third of the length of line D F.

Which inequality explains why these three segments cannot be used to construct a triangle?
EF + FD > DE
ED + EF < DF
ED + EF > DF
EF + FD < DE

Answers

Answer:

ED + EF < DF

Step-by-step explanation:

shorter side lengths added together > larger side length

however, smaller side lengths are < larger

So ED + ED < DF means that this cannot be a triangle

Answer:

ED + EF < DF

(second option listed)

Step-by-step explanation:

for a triangle, the sum of the two shorter side lengths must be greater than the larger side length

so we know that the two smaller lengths (DE and FE) would have to add up to be greater than the larger side length (DF)

because this is not the case, we know that we cannot construct a triangle

[to construct a triangle:]

smaller + smaller > bigger

DE + FE > DF; which is false/not the case

so because DE + FE < DF, we cannot form a triangle

so, ED + EF < DF explains why these three segments cannot construct a triangle

a cylinder has a height of 6 meters and a diameter that is 6 times the measure of the height. using 3.14 or pi which of the following can be used to calculate the volume of the cylinder

Answers

The volume of the cylinder with height 6 meters and the radius 18 meters is [tex]6,104.16 m^{3}[/tex].

What is a volume of a cylinder?

The volume of a cylinder is the capacity of the cylinder which calculates the amount of material quantity it can hold.

Given that, the height of a cylinder=6 meters and the diameter of a cylinder=6×6=36 meters (A diameter that is 6 times the measure of the height)

Now, radius [tex](r)=\frac{d}{2} =18 meters[/tex]

[tex]\pi =3.14[/tex]

We know that, the volume of the cylinder[tex]=\pi r^{2} h[/tex]

[tex]=3.14\times 18^{2} \times 6 m^{3}[/tex]

[tex]=6,104.16 m^{3}[/tex]

Hence, the volume of the cylinder with height 6 meters and the radius 18 meters is [tex]6,104.16 m^{3}[/tex].

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Find the surface area for the rectangular prism below.

Please answer with steps! :)

Answers

Surface Area= 62 units, just take all the squares/rectangles and find the area of the 6 of them and add them together (area= base x height)

find the value of x

Answers

Answer:

1 = 120

2 = 120

Step-by-step explanation:

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From the top of a cliff 90 m high, the angle of depression of a boat on the sea is 26.2°. Calculate how far the boat isa from the foot of the cliff, b from the top of the cliff.​

Answers

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From the top of a cliff 90 m high, the angle of depression of a boat on the sea is 26.2°. Calculate how far the boat is
a from the foot of the cliff,
b from the top of the cliff.