By Pythagorean theorem and trigonometric functions, the magnitude and direction of the boat are approximately 284.403 miles and 295.043° with respect to the east.
What is the direction and magnitude of the resulting displacement with respect to the origin
In this problem we assume that the first angle is measured with respect to the east side and that the second angle is counterclockwise and measured with respect to the direction of the first vector. First, we need to determine the resulting vector by using trigonometric and vectorial formulas:
(x, y) = (240 · cos 290°, 240 · sin 290°) + (50 · cos 320°, 50 · sin 320°)
(x, y) = (120.387, - 257.666) [mi]
The magnitude is found by Pythagorean theorem:
[tex]r = \sqrt{(120.387\,mi)^{2}+(-257.666\,mi)^{2}}[/tex]
r ≈ 284.403 mi
The direction of the boat is obtained by inverse trigonometric functions:
θ = tan⁻¹ (- 257.666/120.387)
θ ≈ 295.043°
By Pythagorean theorem and trigonometric functions, the magnitude and direction of the boat are approximately 284.403 miles and 295.043° with respect to the east.
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Fully simply 15x^4y^4(−5x^3y^5)
Answer:
[tex]-75x^{7}y^{9}[/tex]
Step-by-step explanation:
PLEASE HELP
How many integers are there on the number line between $2\sqrt{10}$ and $10\sqrt{2}$?
Answer:
8
Step-by-step explanation:
To one decimal place:
[tex]2 \sqrt{10} = 6.3[/tex]
[tex]10 \sqrt{2} = 14.1[/tex]
So there are eight integers between 2√10 and 10√2: 7, 8, 9, 10, 11, 12, 13, and 14.
Can someone explain to me #2 I only need #2
Answer:
in a rectangle, opposite sides are equal in length
Step-by-step explanation:
now in this question, Pythagoras theorem is being used to find the length
we know both sides by using Pythagoras theorem find third side and get the sum to find ac+bd
Step-by-step explanation:
So it tells you that AB = 21 and AD = 28
and you to find what BD + AC is and since BD is the same length as AC
you only need to find one of them, then double it
There is a formula you use called the Pythagorean theorem
The Pythagorean theorem is A²+B²=C²
In this problem A = 21 B = 28 and C = the length of BD
so it'll look like 21²+28²=Length of BD² or BD²=21²+28² now you find BD
first do 21²+28² --> 441+784 --> 1225 Now you know that 21²+28²=1225
so BD²=1225 Then to find BD, you find √1225(square root of 1225)
Which is 35 So BD=35 and you want to know what BD+AC is
so 35+35=70
Combine the radicals 4√7 + 3√28
Answer:
10√7
Step-by-step explanation:
you can simplify the second radical and break it up into
√4 * √7 which then simplifies to 2√7 which you then multiply by 3. 4√7 + 3(2√7) which becomes 4√7 + 6√7 and then you just add the numbers Infront to get 10√7
Is 40% of 90 closer to 10 or 30?
Answer:
Closer to 30.
Step-by-step explanation:
To answer this first find 40% of 90.
90*0.4=36
0.4 is the same as 40%
Hope this helps!
If not, I am sorry.
Given that the sum to infinity of a G.P. is 10. If the first term of the series is given as 5, determine the 3rd term.
Answer:
a₃ = 1.25
Step-by-step explanation:
the sum to infinity is calculated as
S ∞ = [tex]\frac{a_{1} }{1-r}[/tex]
a₁ is the first term and r the common ratio
given a₁ = 5 and S∞ = 10 , then
10 = [tex]\frac{5}{1-r}[/tex] ( multiply both sides by (1 - r)
10(1 - r) = 5
10 - 10r = 5 ( subtract 10 from both sides )
- 10r = - 5 ( divide both sides by - 10 )
r = 0.5
then
a₂ = a₁ × r = 5 × 0.5 = 2.5
a₃ = a₂ × r = 2.5 × 0.5 = 1.25
Quayleen wants to decorate her Christmas tree. She wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as 80 cm, 40 cm and 20 cm respectively. How many square sheets of paper of side 40 cm would she require?
[tex]\bullet\:{\boxed{\tt{\red{{Given :}}}}}[/tex]
• Length of the wooden box [tex](l)[/tex] = 80cm.
• Breadth of the wooden box [tex](b)[/tex] = 40cm.
• Height of the wooden box [tex](h)[/tex] = 20cm.
• Side of the square sheet paper = 40cm.
[tex]\bullet\:{\boxed{\tt{\red{{To : Find :}}}}}[/tex]
The number of sheets required.
[tex] \bullet\:{\boxed{\tt{\red{{Formula \: \: used :}}}}}[/tex]
[tex] \star{\underline{\boxed{{\sf{{{TSA}} = \underline{\underline{{\purple\sf 2(lb+bh+hl)}}}}}}}} \star[/tex]
[tex]\star{\underline{\boxed{{\sf{{{Area \: of \: square}} = \underline{\underline{{\purple{\sf side \times side }}}}}}}}}\star[/tex]
[tex]\star{\underline{\boxed{{\sf{{{Number \: of \: sheets \: required} = {{{\purple{\sf \dfrac{TSA}{area \: of \: one \: sheet}}}}}}}}}}} \star[/tex]
[tex] \bullet\:{\boxed{\tt{\red{{Concept :}}}}}[/tex]
As Quayleen wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it. So for knowing the number of sheets required, we need two things one the TSA and Area of one sheet. Once, we will get the values we will divide them to get the answer. Let's Start !!
[tex] \bullet\:{\boxed{\tt{\red{{Solution :}}}}}[/tex]
As we know that ::
Total surface area of cuboid [tex]\large[ \sf 2(lb+bh + hl)][/tex]
Here,
✧ Length [tex](l)[/tex] = 80cm
✧ Breadth [tex](b)[/tex] = 40cm
✧ Height [tex](h)[/tex] = 20cm
Now, by putting the values we get :
[tex] \longrightarrow 2 \bigg[ (80 \times 40) + (40 \times 20) + (20 \times 80) \bigg]\sf {cm}^{2}[/tex]
[tex]\longrightarrow 2 \bigg[ (3200) + (800) + (1600) \bigg] \sf {cm}^{2} [/tex]
[tex] \longrightarrow 2 \bigg[ 5600 \bigg] \sf {cm}^{2} [/tex]
[tex] \longrightarrow 11200 \: \sf {cm}^{2}[/tex]
Hence, the total surface area of the wooden box is 11200 cm²
Now,
The area of each sheet of paper will be :
[tex] \sf \longrightarrow side \times side[/tex]
[tex]\sf \longrightarrow (40 \times 40) \: {cm}^{2} [/tex]
[tex]\longrightarrow \sf (1600) \: {cm}^{2} [/tex]
Hence, the area of each sheet of paper is 1600 cm²
Now,
For finding the number of sheets required
[tex] \longrightarrow \tt \dfrac{total \: surface \: area \: of \: box}{ area \: of \: one \: sheet} [/tex]
[tex]\longrightarrow \sf\dfrac{ \cancel{11200}_{7}}{\cancel{1600}_{1}}[/tex]
[tex] \longrightarrow \purple{ \sf 7}[/tex]
Therefore, Quayleen requires 7 sheets.
[tex]\rule{280pt}{2pt}[/tex]
Can someone pls help me with this fast thank you
Answer: Yes
Step-by-step explanation:
[tex]\frac{123}{2}=\frac{246}{4}=\frac{369}{6}=\frac{492}{8}=61.5[/tex].
Since the ratio of distance in miles and the time in hours is constant, the relationship is proportional.
I need a written answer for all three questions please.
The values of the trigonometry ratios are:
cos α = - 5/13 and cot α = 5/12cot α = -5/12 and sec α = 13/5How to solve the trigonometry ratios?1: sin α = -12/13 and tan α > 0, find cos α and cot α
Because tan α > 0, then it means that cos α and sin α are negative
So, we have:
sin²α + cos²α = 1
Substitute sin α = -12/13
(-12/13)² + cos²α = 1
This gives
cos²α = 1 - (-12/13)²
Evaluate the squares
cos²α = 1 - 144/169
Evaluate the difference
cos²α = 25/169
Take the square root of both sides
cos α = - 5/13
The cotangent ratio is represented as:
cot α = cos α/sin α
This gives
cot α = (-5/13)/(-12/13)
Evaluate
cot α = 5/12
Hence, cos α = - 5/13 and cot α = 5/12
2: tan α = -12/5 for α in quadrant IV, find sec α and cot α
Because α is in quadrant IV, then it means that sec α is positive
cot α = 1/tan α
This gives
cot α = 1/(-12/5)
Evaluate
cot α = -5/12
Also, we have:
sec²α = 1 + tan²α
Substitute tan α = -12/5
sec²α = 1 + (-12/5)²
Evaluate the squares
sec²α = 1 + 144/25
Evaluate the sum
sec²α = 169/25
Take the square root of both sides
sec α = 13/5
Hence, cot α = -5/12 and sec α = 13/5
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Angle AMO is 50 degrees. If ray MB bisects angle AMO, what would be the measure of angle AMB?
The following data shows the temperature of a city, in degrees Celsius, on consecutive days of a month:
8.5, 8.3, 8.2, 8.9, 8.4, 8.2, 8.7, 8.5, 8.3, 8.5, 8.4
Which box plot best represents the data? (1 point)
SECOND ONE
Step-by-step explanation:
Trust me
The second box plot represents the data 8.5, 8.3, 8.2, 8.9, 8.4, 8.2, 8.7, 8.5, 8.3, 8.5, 8.4 option second is correct.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
We have a box plot shown in the picture.
The data:
8.5, 8.3, 8.2, 8.9, 8.4, 8.2, 8.7, 8.5, 8.3, 8.5, 8.4
From the data given:
The minimum value = 8.2
The maximum value = 8.9
Q1 = 8.3
Q2 = 8.4
Q3 = 8.5
As we can see in the second box plot this data is represented.
Thus, the second box plot represents the data 8.5, 8.3, 8.2, 8.9, 8.4, 8.2, 8.7, 8.5, 8.3, 8.5, 8.4 option second is correct.
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what is Math?
who ever answer this question I shall mark him as brainiest.
Answer:
Maths is the subject which deals with numbers, calculations, areas, geometry etc
Various topics in maths are
trigonometry
geometry
airthmatic
etc
Look at the diagram. Which of the following is another name ∠2?
∠CDB
∠BCD
∠DCB
∠DBC
The other name for angle 2 is ∠DBC
The correct option is (D)
What is Angle?A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
We know that while naming the angle we have to consider the point where the angle is made should be at center.
Hence, the angle 2 can also be written as ∠DCB.
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Linear equations in two variables
Graph y = -4 then explain why it is not a function, can somone ELI5
Answer:
y=-4 is a function
Step-by-step explanation:
It passes the vertical line test, and each x has only one y, so it is a function.
x = -4 is NOT a function because one x has multiple y values. It does not pass the vertical line test.
A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 2 of the recall, the manufacturer fixed 192 cars. In week 4, manufacturer fixed 184 cars. Assume that the reduction in the number of cars each week is linear. Write an equation in function form to show the number of cars seen each week at the mechanic.
f(x) = 4x + 200
f(x) = 2x + 192
f(x) = −4x + 200
f(x) = −2x + 192
Answer:
the answer is f(x)=2x+192
Answer:
The answer is F(x)=2x+192
Two rigid transformations are used to map TriangleJKL to TriangleMNQ. The first is a translation of vertex L to vertex Q. What is the second transformation?
a reflection across the line containing LK
a reflection across the line containing JK
a rotation about point L
a rotation about point K
Triangle JKL is mapped to Triangle MNQ by two rigid transformations. Vertex L to vertex Q translation is the first. a rotation about point L is the second transformation. Option A is correct.
What is the triangle?A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.
Two rigid transformations are used to map Triangle JKL to Triangle MNQ. The first is a translation of vertex L to vertex Q.
The second transformation is a rotation about point L.
Hence option A is correct.
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Answer: Option 3 or C. a rotation about point L
Step-by-step explanation:
I took the quiz and got 100% correct on Edge 2022. Trust me if you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful. Good luck everyone! :)
The square below represents one whole.
Express the shaded area as a fraction, a
decimal, and a percent of the whole.
Fraction:
Decimal:
Percent:
%
Answer:
fraction:4/10 or 2/5
decimal: 0.4
percent: 40%
Step-by-step explanation:
The rectangle is divided into 10 parts, this is a total number that goes on the bottom of a fraction. 4 parts are shaded, that number goes on the top of the fraction.
4/10 is shown in the image. But 4/10 can be reduced. You should always simplify a fraction when it is possible.
4/10 = 2/5
As for the decimal, 4/10 spoken, "four tenths" tells you the decimal 0.4 (we all say "point four", but this is properly called "four-tenths" also) You can divide, because a fraction bar is a division symbol:
4÷10 OR 2÷5 and you will get the decimal 0.4
To change the decimal to a percent, multiply by 100.
0.4 × 100 is 40
0.4 is 40%
fraction:: 4/10 or 2/5 (simplified)
decimal: 0.04
percentage: 4%
Calculate the a) total tax rate, and b) sales tax.
The total tax rate and the sales tax will be given below.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Total selling price (TSP), State tax rate (STR), City tax rate (CTR), Total tax rate (TTR) and Sales tax (ST).
The table complete table is given below.
Item TSP STR CTR TTR ST
Clothing $81.39 3% 0% 3% $2.44
Cell phone $159.95 5% 0% 5% $7.99
MP3 player $195.55 4% 2% 6% $11.73
Computer $1599.75 4.88% 1.50% 6.38% $102.06
Take-out $49.85 8.13% 2.50% 10.63% $5.29
Pickup truck $38,526.42 6.50% 1.25% 7.75% $2985.79
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Find the value of x. Then find the measure of each labeled angle.
Answer:
x = 70 and the labeled angles are 110 and 70
Step-by-step explanation:
This is a trapezoid, the bases are parallel.
Since the bases are parallel, given two angles are supplementary and their sum is equal to 180:
x + 40 + x = 180 add like terms
2x + 40 = 180 subtract 40 from both sides
2x = 140 divide both sides by 2
x = 70 and the labeled angles are 110 and 70
Which of the following represents the synthetic division form of the long division problem below? (2x ^ 3 - 6x ^ 2 + 4x + 7)/(x + 3)
How do I solve this?
Answer:
x = 4
Step-by-step explanation:
The figure in the picture is a parallelogram. In parallelograms diagonals bisect each other. That means that they divide each other in half. That means that 6x + 1 is the same as 4x + 9.
6x + 1 = 4x + 9
2x + 1 = 9
2x = 8
x = 4
a motorcyclist riding North along a straight road at 50 km per hour observes that the wind appeared to have a velocity of 50 km per hour from the direction North 60 degrees West what is the velocity of the wind.
The velocity of the wind will be 50 km per hour.
What is a vector?The quantity which has magnitude, direction and follows the law of vector addition is called a vector.
A motorcyclist riding North along a straight road at 50 km per hour observes that the wind appeared to have a velocity of 50 km per hour from the direction North 60 degrees West.
Then the velocity of the wind will be
Let x be the speed of the wind. Then we have
x² = 50² + 50² - 2 x 50 x 50 x cos 60°
x² = 2500 + 2500 - 2500
x² = 2500
x = 50 km per hour
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HELP
Can someone help me with number 26 plss
Answer:
(-2,-9)
(-1,8)
(0,-5)
(1,0)
(2,7)
Step-by-step explanation:
The lines shown below are perpendicular. If the green line has a slope of
1/7 what is the slope of the red line?
A.7
B.1/7
C.-7
D. -1/7
Answer:
c: -7
Step-by-step explanation:
the slope of a perpendicular line is the negative reciprocal of the original line
a way to find this is to flip the numerator and the denominator of a slope and make it negative
1/7 --> 7 --> -7
that would be your slope
Which is a nonlinear relationship
Answer:
D. 4
Explanation:
Linear relationship refers to relationships which give straight lines when graphed. All the segments, except segment 4, show straight-line, linear relationships.
As section 4 is curved, it show nonlinear relationship.
Tariq also designs hot tubs. The diameter of the hot tub is 3 meters. What is the area of the deck that surrounds the hot tub? If necessary, round to the nearest tenth.
The area of the deck that surrounds the hot tub is 17.93 m²
What is Area?
The area is the amount of space within the perimeter of a 2D shape.
radius = 3/2 = 1.5 m
Area of deck,
=Area of square - area of circle
= side side- πr²
=5*5 - 3.14* 1.5*1.5
= 25- 7.065
= 17.93 m²
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Find x, y, and z. Help me please :)
Answer:
x = 58°
z = 60°
y = 29( 58°)
Step-by-step explanation:
The arrows on the lines are trying to tell you that these lines are parallel to each other, whenever you see parallel lines think of *FUN* method
2y = 58° (alternate angles)
y = 29
x = 58° (alternate angles)
62° + 58° + z = 180° (sum of angles on a triangle)
120° + z = 180°
z = 60°
Mike wants to make meatloaf. His recipe
uses a total of 7 pounds of meat. If he uses a 3 to one ratio of beef to pork,how Mach pork will he use?
Answer:
Mark will use 1.25 pounds of pork.
Step-by-step explanation:
Let b represent the number of pounds of pork and p represent the number of pounds of beef. Since the ratio of beef to pork is 3 to 1, we have b/p = 3/1, which then becomes b = 3p. From this:
[tex]3p + p = 7[/tex]
[tex]4p = 7[/tex]
[tex]p = 1.75[/tex]
[tex]b = 3 \times 1.75 = 5.25[/tex]
The number of boys who signed up to play winter basketball is 175 percent of what it was last year. if 320 boys played winter basketball last year, how many signed up to play this year?
The number of boys signed up to play basketball this year is 560.
Given that, the number of boys who played basketball last year = 320.
We need to find the number of boys signed up to play basketball this year.
What is a percentage?In mathematics, a percentage is a number or ratio expressed as a fraction of 100.
Now, the number of boys signed up to play basketball this year = 175 per cent of what it was last year.
So, the number of boys signed up to play basketball this year = 175% of 320
[tex]=\frac{175}{10} \times 320=1.75 \times 320=560[/tex]
Therefore, the number of boys signed up to play basketball this year is 560.
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When the greatest common divisor and least common multiple of two integers are multiplied, the product is 180. How many different values could be the greatest common divisor of the two integers
The different values that could be be the greatest common divisor of the two integers are; 1, 2, 3, 4, 6
How to find the greatest common divisor?
Let the numbers be a, b. Thus, the product of the GCD(a, b) and the LCM(a, b) will be ab.
Now, for us to get something to be a factor of the GCD we need to make it be a factor of both a, b. Thus, its' square must be a factor of 180.
Therefore, the only numbers whose square is a factor of 1800 are 1, 2, 3, 4, 6 and as such they are the only GCDs possible.
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