A hand glider dives at 25 mph in a direction 60° below
horizontal. What is the component form of the velocity vector?
a. (25-2, 25squareroot3/2)
b. (25/2, -25squareroot3/2)
c. (-25/2, 25squareroot3/2)
d. (-25/2, -25squareroot3/2)
Answers
Answer:
\(b.)= (\frac{25}{2} , \ -25\frac{\sqrt{3} }{2})\ mph\)
Step-by-step explanation:
Given;
velocity of the diver, v = 25 mph
direction of his dive, θ = 60°
The vertical component of the velocity is given by;
\(-V_y = vsin\theta \ \ (below \ horizontal \ is \ in \ negative\ y-direction)\\\\V_y =-(25)(sin 60)\\\\V_y =-(25)(\frac{\sqrt{3} }{2} )\)
The horizontal component of the velocity is given by;
\(V_x =vcos\theta\\\\V_x =(25)(cos 60 )\\\\V_x =(25)(\frac{1 }{2} )\\\\V_x = \frac{25}{2}\)
Therefore, the component form of the velocity vector is given by;
\((V_x, \ V_y) = (\frac{25}{2} , \ -25\frac{\sqrt{3} }{2})\ mph\)
correct option = \(b.)= (\frac{25}{2} , \ -25\frac{\sqrt{3} }{2})\ mph\)
Answer:
B: (25/2, - 25√3/2)
Step-by-step explanation:
First find the values
v = 25 mph
θ = 60°
Vertical:
\(V_{y}\) = -vsin(θ) (Negative because it is below the x axis.)
\(V_{y}\) = (-25)(sin(60))
\(V_{x}\) = (-25)(\(\frac{\sqrt{3} }{2}\))
\(V_{y}\) = \(\frac{-25\sqrt{3} }{2}\)
Horizontal:
\(V_{x}\) = vcos(θ)
\(V_{x}\) = (25)(cos(60))
\(V_{x}\) = (25)(1/2)
\(V_{x}\) = \(\frac{25}{2}\)
Putting them together we get:
(\(\frac{25}{2}\), \(\frac{-25\sqrt{3} }{2}\)) or B
Related Questions
Explain with steps please and thank you! :)
Answers
Using the information in the given diagram, the value of the missing angle is: m∠1 = 75°
How to find the missing angle?The transverse line theorem states that If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.
Now, when we draw a horizontal line parallel to lines a and b and directly cutting across the vertex of angle 1, we can see that angle 1 will be composed of two angles.
Now, for the transverse line theorem we can say that:
Angle 1 will be composed of two angles namely:
48 degrees and (180 - 153) degrees.
Thus:
m∠1 = 48° + 27°
m∠1 = 75°
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The ratio of your monthly allowance compared to your friends monthly allowance is five to three and totally you and your friend make $40 how much money do you make
Answers
A gardener is building a flower garden with a border of mulch around it. A model of the design is shown.
A large rectangle with dimensions of 10.5 feet by 16 feet. A smaller rectangle with dimensions of 5.5 feet by 8 feet inside of the larger one.
Part A: Find the area of the mulch border that surrounds the 5.5 ft by 8 ft flower garden. Show all work. (6 points)
Part B: If the mulch cost $3.64 per sq ft, how much will the mulch for this project cost? Show all work. (6 points)
Answers
The area of the mulch border around a flower garden with dimensions of 5.5 ft by 8 ft inside a 10.5 ft by 16 ft rectangle is 124 sq ft. The cost of the mulch for this project, at a rate of $3.64 per sq ft, is $451.36.
To find the area of the mulch border, we need to find the area of the large rectangle and the area of the small rectangle, and then subtract the area of the small rectangle from the area of the large rectangle. The result will be the area of the border.
Area of large rectangle = length x width = 10.5 ft x 16 ft = 168 sq ft
Area of small rectangle = length x width = 5.5 ft x 8 ft = 44 sq ft
Area of border = area of large rectangle - area of small rectangle = 168 sq ft - 44 sq ft = 124 sq ft
Therefore, the area of the mulch border that surrounds the flower garden is 124 sq ft.
If the mulch costs $3.64 per sq ft, we can multiply the area of the mulch border by the cost per sq ft to find the total cost of the mulch.
Total cost of mulch = area of border x cost per sq ft = 124 sq ft x $3.64/sq ft = $451.36
Therefore, the mulch for this project will cost $451.36.
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A lighthouse is located on a small island 5 km away from the nearest point P on a straight shoreline and its light makes six revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? (Round your answer to one decimal place.)
Answers
Answer:
The beam of light is moving along the shoreline at a velocity of approximately 196 kilometers per second.
Step-by-step explanation:
The statement is described geometrically in the image attached below by means of a right triangle. All variables are described below:
\(OP\) - Minimum distance between lighthouse and the straight shoreline, in kilometers.
\(PP'\) - Distance along the straight shoreline, in kilometers.
\(\theta\) - Angle of rotation of the lighthouse, in sexagesimal degrees.
To find the rate of change of distance along the straight shoreline (\(\frac{dPP'}{dt}\)), in kilometers per minute, we use the following trigonometric relationship:
\(PP' = OP \cdot \tan \theta\) (1)
Then, we differentiate this expression in time:
\(\frac{dPP'}{dt} = OP\cdot \dot \theta \cdot \sec^{2}\theta\) (2)
Where \(\dot \theta\) is the rate of change of the angle of rotation of the lighthouse, in radians per minute.
The angle at the given instant is calculated by (1): \(OP = 5\,km\), \(PP' = 1\,km\)
\(\theta = \tan^{-1} \left(\frac{PP'}{OP} \right)\)
\(\theta \approx 11.310^{\circ}\)
If we know that \(\dot \theta = 37.699\,\frac{rad}{min}\), \(\theta \approx 11.310^{\circ}\) and \(OP = 5\,km\), then the rate of change is:
\(\frac{dPP'}{dt} \approx 196,035\,\frac{km}{min}\)
The beam of light is moving along the shoreline at a velocity of approximately 196 kilometers per second.
Algebra transformation
f(x) =
f(x) =
f(x) =
f(x) =
Answers
Algebra transformation
for Graph1 f(x)=f(x)+4
for Graph2 f(x)=-f(x-4)
for Graph3 f(x)=f(x-7)
for Graph4 f(x)=f(x-2)-5
Define reflection of graphIn mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.
Graph1
Transform the graph by +4 units in y direction.
f(x)=f(x)+4
Graph2
Transform the graph by +4 units in x direction.
f(x)=f(x-4)
Now take the reflection of graph about x axis
f(x)=-f(x-4)
Graph3
Transform the graph by +7 units in x direction.
f(x)=f(x-7)
Graph5
Transform the graph by -5 units in y direction.
f(x)=f(x)-5
Now Transform the graph by -2 units in x direction.
f(x)=f(x-2)-5
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Triangle DEF has coordinates D (5,2), E (5,-2), and F(-4, 0). Which of thefollowing statements is true about triangle DEF?*The triangle has no lines of symmetry.Both
Answers
The answer is the last statement.
The x axis is the only axis of symmetry
girl name are April, may, June, what is the name the mother?
Answers
mary is the 4th childs nam,e
I NEED HELP ASAP PLEASE HELP!!!!!!!
Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither.
(A) 6x + 5x – 4 = 24 + 9x
(B) 25 - 3x = 15 – 3x +10
(C) 4x + 8 = 2x + 7 +x - 20
Answers
Answer:
(A) 6x+5×
or, 11x-4=24+9x
or, 11x-9x=24+4
or, 2x=28
or, x=28÷2
or, x=14
(C) 4x+8=2x+7+x-20
or, 4x-2x-x=7-20-8
or, 2x-x=-13-8
or, x=21
Step-by-step explanation:
B cannot be solved.
How much simple interest would Kaitlin earn on $300 at 6% for 3 months?
A. 27
B. 9
C. 54
D. 18
Answers
Answer:
C) $54.00
Step-by-step explanation:
300*6%*3
300*0.06*3
which is $54.
Hope this helps plz hit the crown :D
What is t in t/3 = 4/9?
Answers
Answer:
\(t = \frac{4}{3} \)
Step-by-step explanation:
1) Multiply both sides by 3.
\(t = \frac{4}{9} \times 3\)
2) Use this rule: a/b × c = ac/b.
\(t = \frac{4 \times 3}{9} \)
3) Simplify 4 × 3 to 12.
\(t = \frac{12}{9} \)
4) Simplify 12/9 to 4/3.
\(t = \frac{4}{3} \)
Therefor, the answer is, t = 4/3.
and in decimal form it would be, 1.333333.
FILL IN THE BLANK. (n) does not extend beyond the boundaries of a particular organization. group of answer choices internet extranet intranet arpanet
Answers
ARPANET does not extend beyond the boundaries of a particular organization.
ARPANET is considered the forerunner of the internet.
ARPANET stands for Advanced Research Projects Agency Network. It was established by the Department of Defense of the United States in 1969, and it used two protocols that were determinant for the invention of the Internet: the packet-switching network and the TCP/IP protocol suite. The scientist that participated in the development of the research were Paul Baran, Lawrence Robles, and Donald Davis. So ARPANET is considered the forerunner of the internet.
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Twice a number is more than the sum of that number and 14
Answers
let assume a number x
According to question Twice a number is more than the sum of that number and 14
So we can write it as:
\(2x>x+14\)Solving the above ineqaulity:
\(\begin{gathered} 2x>x+14 \\ 2x-x>x-x+14 \\ x>14 \end{gathered}\)So the number should be greater than 14.
Please help me and I'll give you Brainly star
Answers
X = 30 degrees
Explanation:
Angle BAC = 60 degrees because of equilateral triangle. Therefore angle BAD = 120 degrees because of angles on a straight line
Angle CBA = 60 degrees, therefore angle DBA = 30 degrees because line DB and BC meet at 90 degrees.
Now do 180 - (30 + 120) = 30. X = 30
5) What is the slope of the line?
50 POINTS PLS HELP ASAP AND THANK YOU
Answers
Answer:
The answer is C.
give the sum of difference 4/9+1/6
Answers
Answer:
11/18
Step-by-step explanation:
4/9 + 1/6
Get a common denominator of 18
4/9 * 2/2 = 8/18
1/6 * 3/3 = 3/18
8/18+3/18
11/18
Answer:
11/18
4/9 + 1/6
Get a common denominator of 18
4/9 * 2/2 = 8/18
1/6 * 3/3 = 3/18
8/18+3/18
11/18
ez
Step-by-step explanation:
Solve the equation below
-1/5x-18=2
Answers
-x - 18(5) = 2(5)
-x = 10 + 90
-x = 100
x = -100
1
5
−
1
8
=
2
1
5
x
−
18
=
2
51x−18=2
1
5
−
1
8
=
2
1
x
5
−
18
=
2
51x−18=2
2
Multiply by 1
1
5
−
1
8
=
2
1
x
5
−
18
=
2
51x−18=2
5
−
1
8
=
2
x
5
−
18
=
2
5x−18=2
3
Find common denominator
5
−
1
8
=
2
x
5
−
18
=
2
5x−18=2
5
+
5
(
−
1
8
)
5
=
2
x
5
+
5
(
−
18
)
5
=
2
5x+55(−18)=2
4
Combine fractions with common denominator
5
+
5
(
−
1
8
)
5
=
2
x
5
+
5
(
−
18
)
5
=
2
5x+55(−18)=2
+
5
(
−
1
8
)
5
=
2
x
+
5
(
−
18
)
5
=
2
5x+5(−18)=2
5
Multiply the numbers
+
5
(
−
1
8
)
5
=
2
x
+
5
(
−
18
)
5
=
2
5x+5(−18)=2
−
9
0
5
=
2
x
−
90
5
=
2
5x−90=2
6
Multiply all terms by the same value to eliminate fraction denominators
−
9
0
5
=
2
x
−
90
5
=
2
5x−90=2
5
⋅
−
9
0
5
=
5
⋅
2
5
⋅
x
−
90
5
=
5
⋅
2
5⋅5x−90=5⋅2
7
Cancel multiplied terms that are in the denominator
5
⋅
−
9
0
5
=
5
⋅
2
5
⋅
x
−
90
5
=
5
⋅
2
5⋅5x−90=5⋅2
−
9
0
=
5
⋅
2
x
−
90
=
5
⋅
2
x−90=5⋅2
8
Multiply the numbers
−
9
0
=
5
⋅
2
x
−
90
=
5
⋅
2
x−90=5⋅2
−
9
0
=
1
0
x
−
90
=
10
x−90=10
9
Add
9
0
90
90
to both sides of the equation
−
9
0
=
1
0
x
−
90
=
10
x−90=10
−
9
0
+
9
0
=
1
0
+
9
0
x
−
90
+
90
=
10
+
90
x−90+90=10+90
10
Simplify
Add the numbers
Add the numbers
=
1
0
0
Ana works 25 hours a week at the library. If she is paid $10 an hour, and her net salary each week is $212.50, what percent of her salary is withheld for taxes?
Answers
Approximately 17.65% of Ana's salary is withheld for taxes.
To calculate the percentage of Ana's salary that is withheld for taxes, we need to determine the amount of tax withheld and then express it as a percentage of her net salary.
Number of hours worked per week (H) = 25 hours
Hourly wage (W) = $10
Net salary (S) = $212.50
Calculate the total earnings before taxes:
Total earnings = Hours worked * Hourly wage
Total earnings = 25 hours * $10/hour
Total earnings = $250
Determine the amount of tax withheld:
Tax withheld = Total earnings - Net salary
Tax withheld = $250 - $212.50
Tax withheld = $37.50
Calculate the percentage of salary withheld for taxes:
Percentage withheld = (Tax withheld / Net salary) * 100
Percentage withheld = ($37.50 / $212.50) * 100
Percentage withheld ≈ 17.65%
Therefore, approximately 17.65% of Ana's salary is withheld for taxes.
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Inverse function for f(x)=(x-4)^3+2
Answers
Answer:
picture attached
on a certain hot summer day 629 people use the public swimming pool The daily prices are $1.25 for children and $2.50 for adults The receptionist for admission totaled $1,200 how many children and how many adults swim at the public pool that day
Answers
Let the number of children be "c" and the number of adults be "a".
There are a total of 629 adults and children.
Thus, we can write an equation:
\(c+a=629\)Price of each children admit is 1.25 and each child admit is 2.50 for a total of $1200.
Thus, we can write an equation to represent this information as:
\(1.25c+2.50a=1200\)We can solve the system of 2 equations we got and find out the values of "a" and "c".
Solving the first equation for c:
\(\begin{gathered} c+a=629 \\ c=629-a \end{gathered}\)We substitute it into second equation and figure out a:
\(\begin{gathered} 1.25c+2.50a=1200 \\ 1.25(629-a)+2.50a=1200 \\ 786.25-1.25a+2.50a=1200 \\ 1.25a=1200-768.25 \\ 1.25a=413.75 \\ a=\frac{413.75}{1.25} \\ a=331 \end{gathered}\)Now, we simply find out c:
\(\begin{gathered} c=629-a \\ c=629-331 \\ c=298 \end{gathered}\)Answer:
Children = 298Adults = 331A quadratic equation, y = ax^2 - 6x + 10, has exactly one real root. Calculate the value of a.
Answers
Answer:
a = 0.9
Step-by-step explanation:
For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.
For the given equation:
\(y = ax^2 - 6x + 10\),
• a = a
• b = -6
• c = 10.
Substituting these values into the formula for discriminant, we get:
\((-6)^2 - 4(a)(10) = 0\)
⇒ \(36 - 40a = 0\)
⇒ \(36 = 40a\)
⇒ \(a = \frac{36}{40}\)
⇒ \(a = \bf 0.9\)
Therefore the value of a is 0.9 when the given quadratic has exactly one root.
The inverse of G(X) is a function.
A. True
B. False
Answers
Answer:
true its just a filp with the y and x and resolved
Step-by-step explanation:
Find the value of the expression
b · 4.4
for b = 0.2.
Answers
Answer:
0.88
Step-by-step explanation:
0.2 * 4.4 =
0.88
Find the graphing slope through the giving points (0,1) m=4
Answers
Answer:
y=mx+b
y=4x+1
slope: 4
y-intercept: 1
Step-by-step explanation:
hopefully this helps :)
The temperature outside changed from 76°F to 41°F over a period of five days. If the temperature changed by the same amount each day, what was the daily temperature change?
A.
35°F
B.
-35°F
C.
7°F
D.
-7°F
Answers
Explanation: 76-41=35 35/5=7
Answer:
C. 7°F
Step-by-step explanation:
David says that a triangle with side measures 9 cm, 12 cm, and 17 cm is a right triangle. Susie says it is not. Who is correct? Explain
your reasoning.
12 cm
17 cm
9 cm
Answers
Susie is correct as it is not a right triangle
How to prove the nature of the triangle?According to Pythagoras theorem, In a right triangle ,the square of the hypotenuse side in a right-angled triangle equals the sum of the squares of the other two sides.Here let the hypotenuse side = 17 (longest )
Square of the hypotenuse side = 289
Squares of the other two sides = 12 * 12 = 144
=9 * 9 = 81
Sum of the squares of the other two sides = 144 + 81
= 225
So, here 225 ≠ 289
The square of the hypotenuse side of this triangle does not equal the sum of the squares of the other two sides. So this is not a right triangleThus, Susie is correct as it is not a right triangle.To learn more about Pythagoras theorem, refer:
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In circle O, secants ADB and AEC are drawn from external point A
such that points D, B, E, and C are on circle O. If AD = 8, AE = 6,
and EC is 12 more than BD, the length of BD is
(1) 6
(2) 22
(3) 36
(4) 48
Answers
The length of BD is 22.
In the given scenario, let's consider the following information.
AD = 8
AE = 6
EC is 12 more than BD.
To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.
From the given information, we know that AD = 8 and AE = 6.
Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.
First, let's find the intercepted arc corresponding to AD:
Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16
Similarly, we can find the intercepted arc corresponding to AE:
Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12
Now, we know that EC is 12 more than BD.
Let's assume the length of BD as x.
BD + 12 = EC
Now, let's consider the intercepted arcs theorem:
Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C
16 - 12 = Angle B - Angle C
4 = Angle B - Angle C.
Since Angle B and Angle C are vertical angles, they are congruent:
Angle B = Angle C.
Therefore, we can say:
4 = Angle B - Angle B
4 = 0
However, we have reached an inconsistency here.
The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.
As a result, we cannot determine the length of BD based on the given information.
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How many 7-digit numbers are there such that the digits 1, 2, and 3 each appear at least once?
Answers
Using the principle of inclusion-exclusion, we can see that the total number of numbers with the given restrictions is:
586,071
How many 7-digit numbers are there such that the digits 1, 2, and 3 each appear at least once?o find the number of 7-digit numbers where the digits 1, 2, and 3 each appear at least once, we can use the principle of inclusion-exclusion.
Step 1: Find the total number of 7-digit numbers without any restrictions.
Since each digit can be chosen independently from 0 to 9 (excluding leading zeros), there are 9 options for the first digit (1-9) and 10 options for each subsequent digit (0-9). Therefore, the total number of 7-digit numbers without any restrictions is 9 * 10⁶.
Step 2: Subtract the number of 7-digit numbers that do not contain 1, 2, or 3.
The number of 7-digit numbers that do not contain 1, 2, or 3 is equal to the total number of 7-digit numbers with digits from 0 to 9 (excluding 1, 2, and 3). So for each digit position, there are 7 options (0, 4, 5, 6, 7, 8, 9). Thus, the total number of 7-digit numbers without 1, 2, or 3 is 7⁷.
Step 3: Add back the number of 7-digit numbers that do not contain two of the digits 1, 2, or 3.
The number of 7-digit numbers that do not contain two of the digits 1, 2, or 3 is equal to the total number of 7-digit numbers with digits from 0 to 9 (excluding two of 1, 2, and 3). For each digit position, there are 6 options (0, 4, 5, 6, 7, 8, 9). Thus, the total number of 7-digit numbers without two of 1, 2, or 3 is 6⁷.
Step 4: Subtract the number of 7-digit numbers that do not contain all three digits 1, 2, and 3.
The number of 7-digit numbers that do not contain all three digits 1, 2, and 3 is equal to the total number of 7-digit numbers with digits from 0 to 9 (excluding all three of 1, 2, and 3). For each digit position, there are 4 options (0, 4, 5, 6, 7, 8, 9). Thus, the total number of 7-digit numbers without all three of 1, 2, and 3 is 4⁷.
Now we can apply the principle of inclusion-exclusion to find the desired count:
Total number of 7-digit numbers = 9 * 10⁶ - 7⁷ + 6⁷ - 4⁷
Calculating this expression, we find:
Total number of 7-digit numbers = 586,071
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O GRAPHS AND FUNCTIONSGraphing the inverse of a function given its graph
Answers
EXPLANATION :
To graph the inverse of a function :
1. List all the points on the graph.
(-3, 4), (0, 6), and (8, 7)
2. Reverse x and y coordinates :
(-3, 4) will be (4, -3)
(0, 6) will be (6, 0)
and
(8, 7) will be (7, 8)
3. Graph the new points and draw the lines.
I need the answer to number 1
Answers
What is the probability that the highest level of education of an adult is a high school diploma, given that they have completed at least one of the education levels shown?
A. 0.04
B. 0.16
C. 0.47
D. 0.84
Answers
Answer:
Probability = 0.04 (Approx)
Step-by-step explanation:
Given:
High school diploma = 0.03
Total holder = 0.03+0.44+0.26+0.11 = 0.84
Find:
Probability
Computation:
Probability = 0.03 / 0.84
Probability = 0.0357
Probability = 0.04 (Approx)