Answer:
1. The distance of the ship from the base of the lighthouse is approximately 1.24 miles
2. a)The horizontal distance the plane must start descending is approximately 190.81 km
b) The angle the plane's path will make with the horizontal is approximately 18.835°
3. The depth of the submarine is approximately 107.51 m
Step-by-step explanation:
The
1. From the question, we have;
The height of the observer above the water = 80 ft.
The angle of depression of the ship from the observer, θ = 0.7°
Let the position of the observer be 'O', let the location of the ship be 'S', let the point directly above the ship at the level of the observer be 'H', we have;
[tex]tan(\theta) = \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length} = \dfrac{HS}{OH}[/tex]
[tex]The \ horizontal \ distance \ of \ the \ ship, OH = \dfrac{HS}{tan(\theta) }[/tex]
HS = The height of the observer = 80 ft.
Therefore, we get;
[tex]The \ horizontal \ distance \ of \ the \ ship, OH = \dfrac{80 \, ft.}{tan(0.7^{\circ}) } \approx 6,547.763 \ ft.[/tex]
The distance of the ship from the base of the lighthouse ≈ 6,547.763 ft. ≈ 1.24 miles
2. The elevation of the plane, h = 10 km
The angle of the planes path with the ground, θ = 3°
Similar to question (1) above, the horizontal distance the plane must start descending, d = t/(tan(θ))
∴ d = 10 km/(tan(3°)) ≈ 190.81 km
The horizontal distance the plane must start descending, d = 190.81 km
b) If the pilot start descending 300 km from the airport, the angle the plane's path will make with the horizontal, θ, will be given as follows;
From trigonometry, we have;
[tex]tan(\theta) = \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length}[/tex]
Where the opposite leg length = The elevation of the plane = 10 km
The adjacent leg length = The horizontal distance from the airport = 300 km
[tex]\therefore tan(\theta) = \dfrac{10 \, km}{300 \, km} = \dfrac{1}{3}[/tex]
[tex]\theta = arctan\left(\dfrac{1}{3} \right ) \approx 18.835^{\circ}[/tex]
The angle the plane's path will make with the horizontal, θ ≈ 18.835°
3. The angle at which the submarine makes the deep dive, θ = 21°
The distance the submarine travels along the inclined downward path, R = 300 m
By trigonometric ratios, we have;
The depth, of the submarine, 'd' is given as follows;
[tex]si(\theta)= \dfrac{Opposite \ leg \ length}{Hypotenuse \ length} = \dfrac{d}{R}[/tex]
∴ d = R × sin(θ)
d = 300 m × sin(21°) ≈ 107.51 m
The depth of the submarine ≈ 107.51 m
What is the answer??
Answer:
multiply both sides of the equation by 3
Step-by-step explanation:
When your trying to solve for a variable, do steps where you are isolating that variable.
In the equation given, to isolate b, get rid of the division first and we can do that through multiplication.
What is the value of -3 2/3 +1/3
Exact Form:
−10/3
Decimal Form:
−3.3...
Mixed Number Form:
−3 1/3
Answer:
-10/3
Step-by-step explanation:
Estimate 1.9 x 4.4
A. Between 4 and 10
B. between 12 and 20
C. between 1 and 5
D Between 1 and 12
Answer:
A
Step-by-step explanation:
it's 8.36 which is between 4 and 10
HELP ASAP!
Use the quadratic equation y = –2x^2 + 4x +5 to complete the statements.
Answer:
Step-by-step explanation:
Given quadratic equation is,
y = -2x² + 4x + 5
y = -2(x² - 2x) + 5
y = -2(x² - 2x + 1 - 1) + 5
y = -2(x² - 2x + 1) + 2 + 5
y = -2(x - 1)² + 7
This equation is in the vertex form of the quadratic equation,
y = a(x - h)² + k
where, (h, k) is the vertex of the parabola.
Therefore, vertex of the given quadratic equation is (1, 7)
The equation can be rewritten as y = -2(x - 1)² + 7.
Therefore, the vertex of the graph of the function y = -2x² + 4x + 5 in the xy-coordinate plane is located at the point (1, 7).
A group of 10 people is choose a chairperson and vice-chairperson. They put all 10 peoples names into a bar. The first name drawn becomes chair. The second name drawn becomes vice-chair. How many possible combinations of chair and Vice-chair are there ?
Answer:
90
Step-by-step explanation:
A group of 10 people is choose a chairperson and vice-chairperson. They put all 10 peoples names into a bar. The first name drawn becomes chair. The second name drawn becomes vice-chair. How many possible combinations of chair and Vice-chair are there ?
This is calculated using the Permutation formula
nPr = n!/(n - r)!
Where:
n = 10 people
r = 2 = 2 positions to be filled , Chairman and Vice chairman
Hence:
10P2 = 10!/(10 - 2)!
= 90 ways
WHAT IS THE TOTAL SURFACE AREA OF THE SQUARE PYRAMID BELOW!?!??!?!
Answer:
the answer is going to be 203 square inches
Step-by-step explanation:
7 x 11 = 77
77 x 2 = 154
7 x 7 = 49
154 + 49 = 203
NOTICE:11.5 is useless, don't get tricked.
Answer:
Solution given:
side of base[a]=7in
height[h]=11in
slant height [l]=11.5in
THE TOTAL SURFACE AREA OF THE SQUARE PYRAMID=a²+2ah=7²+2*7*11=203in²
The total surface area of square pyramid is 203in².
Given this figure on a coordinate plane, determine which of the following statements
could prove ABCD is a parallelogram.
I need help plzzz
A cylindrical container of paint with radius 6 in. is 15 in tall. If all of the surfaces except
the top are made of metal, how much metal is used to make the container? Assume the
thickness of the metal is negligible. Show your answer to the nearest square inch.
HELP ME PLZZZ ASAP!
Factor to create an equivalent expression: 36a-16 .
Answer:
4(9a - 4)
Step-by-step explanation:
Answer:
4(9a - 4)
Step-by-step explanation:
Given
36a - 16 ← factor out 4 from each term
= 4(9a - 4)
HELPPP MEEE PLEASEEE!!!!
Answer:
1) 3 , 2)Add 8 floats 3) -2 4) Remove 8 anchors.
Step-by-step explanation:
HELP!!! i need an answer quick
Answer:
14 that's the answer I think so hope its it
One kitten weighs 2 pounds, 4 ounces, and a second kitten weighs 2 pounds, 2 ounces. What is their combined weight in ounces? *
I WILL GIVE BRAINLEST BECAUSE I WANT TO BE NICE
jason goes to the sandwich shop for lunch the prices for sandwiches are listed below
peanut butter and jelly $1.75
meatball $2.50
ham and cheese $2.25
what number completes the sentence 3m = ?
15x-7y=-49 standard form to slope-intercept form
Answer:
y= \frac{15}{7}x + 7
not sure if that will work so
y = 15x/7x + 7
Step-by-step explanation:
can anyone answer this????
Answer:
4x^2[tex]\sqrt{7x^{2} }[/tex]
The distribution of the number of blocks a young child can stack before their tower falls is approximately Normally distributed with a mean of 12.7 blocks and a standard deviation of 1.4 blocks. If 6 of the child’s towers are randomly selected, what is the probability that the mean number of blocks is more than 11 blocks? 0.0015 0.1123 0.8877 0.9985
Answer:
0.9985
Step-by-step explanation:
In parallelogram ABCD, if m angle C= 110° and m angle D - 70°, what is the sum of the measures of LA and 28?
409
909
180°
360°
Answer:
180°
Step-by-step explanation:
ABCD is a parallelogram.
Measures of the opposite angles of a parallelogram are equal. Here [tex] \angle A, \:\: \angle C \: \: and\:\: \angle B, \:\: \angle D[/tex] are opposite angles.
[tex] \therefore m\angle A = m\angle C = 110\degree [/tex]
[tex] \& \:m\angle B = m\angle D = 70\degree [/tex]
[tex] m\angle A + m\angle B =110\degree + 70\degree [/tex]
[tex] m\angle A + m\angle B =180\degree [/tex]
Which of these choices show a pair of equivalent expressions? Check all that
apply.
A. 89/2 and ( 18 )
B. 121/7 and (172)
C. (2/125) and 1253/7
D. 45/2 and (1)
Step-by-step explanation:
I think it's B, if you are missing a decimal point and the second term is 17.2 and not 172. otherwise none are equivalent
Answer:
D. 45/2 and (1)
A. 89/2 and ( 18 )
Step-by-step explanation:
ap3x
6 to the 2 power −2(5+1+3)
Answer:
18
Step-by-step explanation:
What is the importance of polynomial functions and how this real life applications improve or contribute to the value of life
Answer:
What is the importance of polynomial functions?
Polynomials are an important part of the "language" of mathematics and algebra. They are used in nearly every field of mathematics to express numbers as a result of mathematical operations. Polynomials are also "building blocks" in other types of mathematical expressions, such as rational expressions.
How these real-life applications improve or contribute to the value of life?
Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example. Engineers use polynomials to graph the curves of roller coasters and bridges.
-2(x - 14) help me? I need help so I can get my grade up in algebra and pass my class so please help me?
Answer:
[tex] - 2x + 28[/tex]
Step-by-step explanation:
1) Expand by distributing terms.
[tex] - 2x - 2 \times - 14[/tex]
2) Simplify 2 × -14 to -28.
[tex] - 2x - ( - 28)[/tex]
3) Remove parentheses.
[tex] - 2x + 28[/tex]
Therefor, the answer is - 2x + 28.
4 +y = 12. Substitute 8 for x.
Answer:
where should I substitute 8 for x? if its like this 4(8)+y=12 than its y=-20
Step-by-step explanation:
i need help please asap
Answer:
4$ per minute. You make 20 dollars in 5 minutes so 20 divided by 5 is 4.
B. Noah writes the equation 3 (x+7)=57 to represent the situation. DO YOU agree with him? Explain your answer.
Answer:
Yes , i agree with Noah that the equation would be 3(x + 7) = 57
Step-by-step explanation:
P.S - The exact question is -
To find - Noah writes the equation 3 (x+7)=57 to represent the situation.
DO YOU agree with him? Explain your answer.
Proof -
Yes , i agree with Noah
Because in the figure we can see that there is x written 3 times and 7 written 3 time and whole the values is equal to 57 .
Because 57 is divided into x 7 x 7 x 7
∴ we can write it as
3 times x + 3 times 7 = 57
⇒3(x) + 3(7) = 57
⇒3(x+7) = 57
Ans Noah give the same equation 3 (x+7)=57
So, I agree with Noah.
The sum of the squares of two consecutive even integers is 1684. What are the integers?
Answer:
Step-by-step explanation:
Let the 2 consecutive integers be x and x+1.
x²+(x+1)²=1684
x²+(x+1)(x+1)=1684
x²+x²+x+x+1=1684
2x²+2x-1683=0
Using quadratic formular
Find the common difference of the arithmetic sequence
-17, -15, -13, ...
Answer:
term 1 - term 2 = sequence
so
-17-(-15) = -2
and if you minus the rest by -2 it will give you the next term
-15-(-2) = -13
-13-(-2) = -11
Answer:
2
Step-by-step explanation:
:0
Out of the 4,500 people who attend the rock concert, forty-six percent purchase a T-shirt. How many people buy T-shirts?
The number of people that bought T-shirt is 2070 people
What is percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"
To find the percentage of those that bought the T-shirt
We find 45% of 4,500
45/100 * 4500
2070
Hence, 2070 people out of the 4,500 people who attend the rock concert bought the T-shirt
Learn more about percentage at:https://brainly.com/question/24304697
#SPJ1
This is 7th grade math so pls answer asap
1: v/8=2
2:16=k/11
3:18+m=8
v/8=2
x8 x8
v=16
16=k/11
x11 x11
176=k
18+m=8
-18 -18
m=-10
---
hope it helps
Will give brainlist for correct answer.
Answer:
(-5, -1)
Step-by-step explanation:
When two lines intersect, their x and y values are equal. So,
x = 3y - 2 must equal -7 - 2y = x
x = 3y - 2 = -7 - 2y = x
Let's look at the two middle equations and solve for y.
3y - 2 = -7 - 2y
Add 2y to both sides
5y - 2 = -7
Add 2 to both sides.
5y = -5
y = -1
Now, let's find x. You can use either equation for this step.
When y = -1, then 3y - 2 =
(3)(-1) - 2 = -3 - 2 = -5
So, x = -5, and y = -1
Thus, the answer is (-5, -1)
I hope this helps! Feel free to ask any questions!
The first two steps in the derivation of the quadratic formula by completing the square are shown below.
Which answer choice shows the correct next step?
Step 1: ax^2+bx+c =0
Step 2: ax^2+bx=-c
Answer: C
Step-by-step explanation:
Answer:
c
Step-by-step explanation: