Anne is 3m away from Ishan at a bearing of 100°. Katniss is 7m away from Anne at a bearing of 260°. By plotting the postitions Anne and Katniss ( using a scale of 1cm : 1m), estimate the distance of Katniss from Ishan.
Answers
Answer:
The distance of Katniss from Ishan is approximately 4.305 meters
Step-by-step explanation:
The distance between Anne and Ishan = 3 m
The bearing of Ann from Ishan = 100°
The distance between Anne and Katniss = 7 m
The bearing of Ann from Katniss = 260°
From the diagram of the bearing created with MS Word, let 'a' represent the distance between Ishan and Katniss, let 'b' represent the distance between Ishan and Anne and let 'c' represent the distance between Katniss and Anne, by cosine rule, we have;
b = 3 m
c = 7 m
∠A = 20°
a² = b² + c² - 2·b·c·cos(A)
a² = 3² + 7² - 2 × 3 × 7 × cos(20)
a = √(3² + 7² - 2 × 3 × 7 × cos(20)) ≈ 4.305
By calculation, the distance from Ishan to Katniss, a ≈ 4.305 m
By measurement on MS Word, the distance from Ishan to Katniss, a = √(1.783² + 3.976²) ≈ 4.357.
Related Questions
please help me i am doing over due work and i want to finish and listen to cuco and rest
Answers
Question 14
3+6x3(1+2x)3(2x+1)You can check using the distributive and commutative properties that all of these are equivalent to 6x+3.
Question 15
(7+5)p - p = 12p - p = 11p
Question 16
7 + 5(p-p) = 7 + 5(0) = 7
Question 17
No parentheses are needed.
We had a surprise party for Grandmama she was very surprised. Find the error in the sentence
Answers
Answer:
There needs to be a (.) or an (;)
Step-by-step explanation:
Angles A and B are complementary. What is mB if mA = 15°? A. 75° B. 90° C. 105° D. 165°
Answers
Answer:
90
Step-by-step explanation:
Answer:
its 75 or A.
Step-by-step explanation:
Use the greatest common factor and the distributive property to write an equivalent expression in factored form for the following expression: 4d +12e. Do not use spaces.
Answers
Answer:
4
Step-by-step explanation:
The greatest common factor of [tex]4d+12e[/tex] is [tex]4[/tex].
[tex]4(d+3e)[/tex]
The ratio of two sums of money is 5:7 if the smaller amount is $250, what is the largest amount?
Answers
Answer:
$350
Step-by-step explanation:
[tex]\frac{250}{y} :\frac{5}{7}[/tex]
y · 5 = 250 · 7
5y = 1750
5y ÷ 5 = 1750 ÷ 5
y = 350
Answer:
$350
Step-by-step explanation:
5 is to 250 as 7 is to 'x'
5/250 = 7/x
cross-multiply:
5x = 1750
x = 350
A pyramid has a square base with sides. The height of the pyramid is that of its side. What is the expression for the volume of the pyramid?
Answers
Answer:
Step-by-step explanation:
volume = length x width x height
————————————-
3
What are the zeros of the quadratic function f(x) = 2x2 + 16x – 9?
O x=-4-
를
and x = -4+
7
2
를
O x=-4-
25
2
and x = -4+
25
V2
21
O x=-4-
LU
and x = -4 +
21
V2
끌
41
O x=-4-
41
and x = -4 +
V 2
Answers
Answer:
[tex]\mathrm{X\:Intercepts}:\:\left(\frac{-8+\sqrt{82}}{2},\:0\right),\:\left(-\frac{8+\sqrt{82}}{2},\:0\right)[/tex]
Step-by-step explanation:
[tex]f\left(x\right)\:=\:2x^2\:+\:16x\:-\:9[/tex]
- Given
[tex]\mathrm{X\:Intercepts}:\:\left(\frac{-8+\sqrt{82}}{2},\:0\right),\:\left(-\frac{8+\sqrt{82}}{2},\:0\right)[/tex]
By definition of zeros of a function, the zeros of the quadratic function f(x) = 2x² + 16x – 9 are [tex]x1=-4+\frac{\sqrt{82}}{2}[/tex] and [tex]x2=-4-\frac{\sqrt{82}}{2}[/tex] .
What is zeros of a functionThe points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.
That is, the zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.
Graphically, the roots correspond to the abscissa of the points where the parabola intersects the x-axis.
In a quadratic function that has the form:
f(x)= ax² + bx + c
the zeros or roots are calculated by:
[tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4ab } }{2a}[/tex]
This caseThe quadratic function is f(x) = 2x² + 16x – 9
Being:
a= 2b=16c=-9the zeros or roots are calculated as:
[tex]x1=\frac{-16+\sqrt{16^{2}-4x2x(-9) } }{2x2}[/tex]
[tex]x1=\frac{-16+\sqrt{256 +72 } }{4}[/tex]
[tex]x1=\frac{-16+\sqrt{328} }{4}[/tex]
[tex]x1=\frac{-16+\sqrt{4x82} }{4}[/tex]
[tex]x1=\frac{-16+2\sqrt{82} }{4}[/tex]
[tex]x1=\frac{-16}{4}+\frac{2\sqrt{82}}{4}[/tex]
[tex]x1=-4+\frac{\sqrt{82}}{2}[/tex]
and
[tex]x2=\frac{-16-\sqrt{16^{2}-4x2x(-9) } }{2x2}[/tex]
[tex]x2=\frac{-16-\sqrt{256 +72 } }{4}[/tex]
[tex]x2=\frac{-16-\sqrt{328} }{4}[/tex]
[tex]x2=\frac{-16-\sqrt{4x82} }{4}[/tex]
[tex]x2=\frac{-16-2\sqrt{82} }{4}[/tex]
[tex]x2=\frac{-16}{4}-\frac{2\sqrt{82}}{4}[/tex]
[tex]x2=-4-\frac{\sqrt{82}}{2}[/tex]
Finally, the zeros of the quadratic function f(x) = 2x² + 16x – 9 are [tex]x1=-4+\frac{\sqrt{82}}{2}[/tex] and [tex]x2=-4-\frac{\sqrt{82}}{2}[/tex] .
Learn more about the zeros of a quadratic function:
brainly.com/question/842305
What is the length of AB?
Answers
Answer:
10
I took the quiz ;)
Answer:
10
Step-by-step explanation:
First we need to find A and B
A(-7;-6)
B(1;0)
What is the slope of the line that passes through the points (-2, 3) and (-14, -5) ? ( Write your answer in the simplest form.
Answers
Answer:
⅔
Step-by-step explanation:
slope = (-5-3)/(-14+2) = -8/-12= ⅔
Please say whether they are equivalent or not
Answers
Answer:
Nothing is here. You may need to reupload question.
Above are two different models of the same rectangle. If the length of the model on the top is 6 cm, what is the length of the model on
the bottom?
A. 15 cm
В. 12cm
C. 21cm
D.36cm
Answers
Answer:
D.36cm
Step-by-step explanation:
If the top rectangle have 6 cm, it means 6×16=108 ft
If the two rectangles are the same, it means that the bottom rectangle have also 108 ft, so:
108÷3= 36 cm
David wanted to go on an amusement park ride. A sign posted at the entrance read “You must be greater than 42 inches tall and no more than 57 inches tall for this ride.” Which inequality would model the height, x, required for this amusement park ride?
Answers
Answer:
42 < x less than or equal to 57
Step-by-step explanation:
The inequality that would model the height, x, required for this amusement park ride is 57 > h > 42.
What is inequality?A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations
Now it is given that,
Lower limit of height must be greater than 42 inches
Upper limit of height must be less than 57 inches
If h is the height used for model.
Thus, h < 57 inches
and, h > 42 inches
Therefore the inequality model will be,
57 > h > 42
Thus, the inequality that would model the height, x, required for this amusement park ride is 57 > h > 42.
To learn more about inequality :
brainly.com/question/26644213
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1.) Determine the type of solutions for the function (Picture 1)
2.) Determine the type of solutions for the function (Picture 2)
3.) Use the formula b2−4ac to determine the value of the discriminant of the function f(x)=2x2+8x+6
Use Desmos Scientific (Picture 3)
4.) Describe the transformations of the function
g(x)=−25(x−4)2+6 from the transformation of the parent function
Use phrases such as: the graph is reflected or not reflected/ the graph gets wider or narrower/ the graph slides left or right _________ units and slides up or down _________ (Picture 4)
Answers
Answer:
1) 2 nonreal complex roots
2) 1 Real Solution
3) 16
4) Reflected, narrower by a factor of 2/5, slides right 4 units and slides up 6 (units)
Step-by-step explanation:
1) The graph does not intercept the x-axis, therefore, there are no real solutions at the point y = 0
We get;
y = a·x² + b·x + c
At y = 6, x = -2
Therefore;
6 = a·(-2)² - 2·b + c = 4·a - 2·b + c
6 = 4·a - 2·b + c...(1)
At y = 8, x = 0
8 = a·(0)² + b·0 + c
∴ c = 8...(2)
Similarly, we have;
At y = 8, x = -4
8 = a·(-4)² - 4·b + c = 16·a - 4·b + 8
16·a - 4·b = 0
∴ b = 16·a/4 = 4·a
b = 4·a...(3)
From equation (1), (2) and (3), we have;
6 = 4·a - 2·b + c
∴ 6 = b - 2·b + 8 = -b + 8
6 - 8 = -b
∴ -b = -2
b = 2
b = 4·a
∴ a = b/4 = 2/4 = 1/2
The equation is therefor;
y = (1/2)·x² + 2·x + 8
Solving we get;
x = (-2 ± √(2² - 4 × (1/2) × 8))/(2 × (1/2))
x =( -2 ± √(-12))/1 = -2 ± √(-12)
Therefore, we have;
2 nonreal complex roots
2) Give that the graph of the function touches the x-axis once, we have;
1 Real Solution
3) The given function is f(x) = 2·x² + 8·x + 6
The general form of the quadratic function is f(x) = a·x² + b·x + c
Comparing, we have;
a = 2, b = 8, c = 6
The discriminant of the function, D = b² - 4·a·c, therefore, for the function, we have;
D = 8² - 4 × 2 × 6 = 16
The discriminant of the function, D = 16
4.) The given function is g(x) = (-2/5)·(x - 4)² + 6
The parent function of a quadratic equation is y = x²
A vertical translation is given by the following equation;
y = f(x) + b
A horizontal to the right by 'a' translation is given by an equation of the form; y = f(x - a)
A vertical reflection is given by an equation of the form; y = -f(x) = -x²
A narrowing is given by an equation of the form; y = b·f(x), where b < 1
Therefore, the transformations of g(x) from the parent function are;
g(x) is a reflection of the parent function, with the graph of g(x) being narrower by 2/5 than the graph of the parent function. The graph of g(x) is shifted right by 4 units and is then slides up by 6 units.
EASY question: Show steps for brainliest <3
Tai sailed east from the marina for 48 miles and
then sailed south for 14 miles, as shown in the
diagram.
What is the shortest distance Tai can sail to return
to the marina?
A 62 mi
B 82 mi
C 50 mi
D 34 mi
Answers
Answer:
C 50 mi
Step-by-step explanation:
You have to use the Pythagorean theorem:
14²+48²
196 + 2304
2500
Now you make the square root of 2500 and found the result: 50 mi
ILL GIVE YOU BRAINLIEST!! 33 POINTS!!!
(ONLY IF YOU GET IT CORRECT)
Answers
Answer:
80 ft
Step-by-step explanation:
the length of an arc is equal to the degree the arc makes
Answer:
A. 28π/9 ftStep-by-step explanation:
Arc length is:
2πr*80°/360° ft = 4π*7/9 ft =28π/9 ftCorrect choice is A
If we remove all of the jacks, queens and kings from a 52-card deck, how many unique three card hand combinations can we create?
59,280
44,200
132,600
19,760
Answers
The no. of unique card combinations we can create is 59280
What is permutation and combination?
By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented.
There are 52 cards in a deck in which, there are 12 face cards and 40 numbered cards.
So, by using fundamental principle of counting=40x39x38 =59280
Therefore, the no. of unique card combinations we can create is 59280
Learn more about Permutation and combination,
https://brainly.com/question/1216161
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can i get help please
Answers
Answer:
B. 1,130.4 cm³
Step-by-step explanation:
The formula for volume of a cylinder: πr²h (π x radius x radius x height).
(3.14 is the substitute for pi).
According to the word problem, the radius is 6.
And the height is how high a shape is; the height is 10.
Now we have our whole equation.
πr²h (π x radius x radius x height)
π · 6²· 10 (3.14 · 6 · 6 · 10)
π · 6²· 10 (3.14 · 6 · 6 · 10) = 1,130.4
Therefore, 1,130.4 cm³ is the volume of this cylinder.
The Kitchen committee purchased 76 boxes of cookies for Vacation Bible School,
Monday, 14 2/3 boxes were used; Tuesday 15 boxes; and Wednesday 13 3/4 boxes.
How many boxes were used during the three days?
(Write the operation and the answer)
Answers
10. Find the outlier of the set of data: 30, 54, 47, 45, 42, 50, 54, 49 (1 point)
A 47
O 30
049
O 54
Answers
Answer:It would be 30!
Step-by-step explanation:
You need to line them all up in order and then see the one that sticks out from all of the others. All the other numbers are in the 40s and 50s and this one is 30.
Plz helppp me it’s so hard
Answers
Answer:
Hello! Your answer would be, D)
Step-by-step explanation:
Hope I helped! Ask me anything if you have questions! Brainiest plz. Hope You make a 100%! Have a nice day! -Amelia♥
Select two ratios that are equivalent to 27: 9.
Choose 2 answers:
А
3:1
B
9:3
С
6:3
9:6
E
12 : 3
Answers
Answer:
A
B
Step-by-step explanation:
Answer:
A and B are the two ratios equivalent to 27:9. All you have to do is divide 27 by 3 and 9 by 3 also and you will get 3:1. Just remember your multiplication tables, you'll find the answer easily.
Hope this helps! :)
Based upon risk, which of the following answers ranks from high to low?
Collectables
Bonds
Stocks
Mutual Funds
Answers
Answer:
stocks, bonds, mutual funds, and collectables
Step-by-step explanation:
can someone please help me with this retake question?? i don't know what i did wrong and i really need help
x = ___ units
Answers
x = 24
Step-by-step explanation:
First, find the length RT. Note that we can use the definition of sine 60:
sin 60° = (12√3)/RT
Solving for RT,
RT = (12√3)/sin60° , sin 60 = (√3)/2
= 24
Since ∆QRT is a 45°-90°-45° triangle, that means that
x = RT = 24
How do you find the unknown length for a special right angel
Answers
Answer: Pythagorean theroem
Step-by-step explanation:
The easiest method to use in terms of a missing side as long as you know at least two other variables whether its another side or angle
3/4 x 2/5 x 4/3 please helpppppppppppppppppppp
Answers
Answer:
24/60 or 0.4
Step-by-step explanation:
3/4×2/5=6/20
4/3×6/20=24/60
24/60
Which equation has two real solutions?
Answers
FAST PLEASE❗️❗️❗️❗️‼️
Answers
Which is greater 6 cups or 4 quarts
Answers
Answer:
not sure but 4 quarts i think
Answer:
4 quarts is greater because it is equal to 16 cups
If the gradient of the tangent to
[tex]y = \sqrt{x} [/tex]
is
[tex] \frac{1}{6} [/tex]
at point A, find the coordinates of A.
Answers
Answer:
Point A(9, 3)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Coordinates (x, y) Functions Function Notation Terms/Coefficients Anything to the 0th power is 1Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex] Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \sqrt{x}[/tex]
[tex]\displaystyle y' = \frac{1}{6}[/tex]
Step 2: Differentiate
[Function] Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y = x^{\frac{1}{2}}[/tex]Basic Power Rule: [tex]\displaystyle y' = \frac{1}{2}x^{\frac{1}{2} - 1}[/tex]Simplify: [tex]\displaystyle y' = \frac{1}{2}x^{-\frac{1}{2}}[/tex][Derivative] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle y' = \frac{1}{2x^{\frac{1}{2}}}[/tex][Derivative] Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{1}{2\sqrt{x}}[/tex]Step 3: Solve
Find coordinates of A.
x-coordinate
Substitute in y' [Derivative]: [tex]\displaystyle \frac{1}{6} = \frac{1}{2\sqrt{x}}[/tex][Multiplication Property of Equality] Multiply 2 on both sides: [tex]\displaystyle \frac{1}{3} = \frac{1}{\sqrt{x}}[/tex][Multiplication Property of Equality] Cross-multiply: [tex]\displaystyle \sqrt{x} = 3[/tex][Equality Property] Square both sides: [tex]\displaystyle x = 9[/tex]y-coordinate
Substitute in x [Function]: [tex]\displaystyle y = \sqrt{9}[/tex][√Radical] Evaluate: [tex]\displaystyle y = 3[/tex]∴ Coordinates of A is (9, 3).
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Can someone plz help me with this one problem plz I’m trying to get to a 70
Answers
Answer:
10 2/4
Step-by-step explanation:
Answer:
look at the picture i sent