At [tex]$5 \mathrm{pm}$[/tex] the distance between the ships is changing at the speed of [tex]$\mathbf{3 0 . 2 1}$[/tex] knots
Firstly we need to an equation to represent both ships and the distance between each. A is moving [tex]$25 \mathrm{knots}$[/tex] west and [tex]$B$[/tex] is moving [tex]$17 \mathrm{knot}$[/tex] north. [tex]$D$[/tex]will be the distance between the two. Drawing it, you'll notice that it creates a right triangle.
So we use the Pythagorean Theorem:
[tex]$$D^{\wedge} 2=A^{\wedge} 2+B^{\wedge} 2$$[/tex]
Differentiate in relation to time:
[tex]$$2 \mathrm{D}(\mathrm{dD} / \mathrm{dt})=2 \mathrm{~A}(\mathrm{dA} / \mathrm{dt})+2 \mathrm{~B}(\mathrm{~dB} / \mathrm{dt})$$[/tex]
Now we must find all of our variables.
[tex]& A=\text { time(speed })+\text { original distance }=5(25)+10=135 \\[/tex]
[tex]& B=5(17)+0=85 \\[/tex]
[tex]& D=V\left(A^{\wedge} 2+B^{\wedge} 2\right)=159.53 \\[/tex]
[tex]& d A / d t=25 \\[/tex]
[tex]& d B / d t=17[/tex]
Plug in all your variables and solve for
[tex]$(\mathrm{dD} / \mathrm{dt})$ :[/tex]
[tex]& 2 \mathrm{D}(\mathrm{dD} / \mathrm{dt})=2 \mathrm{~A}(\mathrm{dA} / \mathrm{dt})+2 \mathrm{~B}(\mathrm{~dB} / \mathrm{dt}) \\[/tex]
[tex]& 2(159.53)(\mathrm{dD} / \mathrm{dt})=2(135)(25)+2(85)(17) \\[/tex]
[tex]& 319.061(\mathrm{dD} / \mathrm{dt})=9640 \\[/tex]
[tex]& \mathrm{dD} / \mathrm{dt}=9640 / 319.061 \\[/tex]
[tex]& \mathrm{dD} / \mathrm{dt}=30.21 \text { knots }\end{aligned}[/tex]
At [tex]$5 \mathrm{pm}$[/tex] the distance between the ships is changing at the speed of [tex]$\mathbf{3 0 . 2 1}$[/tex] knots
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what do 17, 19, 46 and 55 have in common?
Answer:
They are all prime numbers
Explanation:
17, 19, 46, and 55 are all prime numbers. A prime number is a whole number greater than 1 that is only divisible by 1 and itself. Since 17, 19, 46, and 55 are all prime numbers, they have no other factors besides 1 and themselves, which means they cannot be divided evenly by any other number.
I know, the answer is A.
I need some help, explaining how the answer is A although, I have a bit of a rational mind when it comes to explaining stuff unfortunately.
On solving the question, by the help of angle sum property of triangle, we got that x= 14
What is Triangle?Having three edges and three vertices, a triangle has three sides. The most significant characteristic of triangles is the fact that their interior angles add up to 180 degrees.
According to sides, what are the three different types of triangles?Scalene, isosceles, and equilateral triangles are the three types of triangles that can have three sides.
Now, value of x is -
(x+27)° + 70° + (x + 55)° = 180° ( Sum of al angles in a triangle is 180°)
2x + 152 = 180°
2x = 28
x=14
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A popular video game retailer develops apps. The total profit, in dollars per day, after x days can be modeled by the function R(x) = 3x3 – 21x2 + 21x + 45. The total cost, in dollars per day, after x days, can be modeled by the function C(x) = x2 – 2x – 3. What is (R - C)(10) and what does it mean in the context of the problem?
a
$532, the total revenue made after 10 days
b
$532, the profit made after 10 days
c
$1078, the profit made after 10 days
d
$2255, the total revenue made after 10 days
Total profit - Total cost = Profit
The profit made is $1078.
Option C is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 7 = 8 is an equation.
We have,
The total profit, in dollars per day, after x days can be modeled by the function
R(x) = 3x³ – 21x² + 21x + 45.
The total cost, in dollars per day, after x days, can be modeled by the function
C(x) = x² – 2x – 3.
Now,
(R - C) (10):
= R(10) - C(10)
= 3x³ – 21x² + 21x + 45 - x² + 2x + 3
= 3x³ - 22X² + 23x + 48
= 3 x 1000 - 22 x 100 + 230 + 48
= 3000 - 2200 + 230 + 48
= $1078
Thus,
Total profit - Total cost = Profit
The profit made is $1078.
Option C is the correct answer.
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Write the equation of the circle with center (2, -3) and a radius of 4.
es ))
A)
B)
9)
D)
(x + 2)² + (y - 3)² = 4
(x - 2)² + (y + 3)² = 4
(x + 2)² + (y - 3)² = 16
(x - 2)² + (y + 3)² = 16
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{2}{h}~~,~~\underset{-3}{k})}\qquad \stackrel{radius}{\underset{4}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 2 ~~ )^2 ~~ + ~~ ( ~~ y-(-3) ~~ )^2~~ = ~~4^2\implies {\large \begin{array}{llll} (x-2)^2+(y+3)^2=16 \end{array}}[/tex]
There are 11 freshmen and 6 sophomores in a class. If three students are selected at random, find the probability that two are freshmen and one is a sophomore. (See Example 6. Round your answer to three decimal places.)
5x − y = 5
-x + 3y = 13
Answer:
(2, 5 )
Step-by-step explanation:
5x - y = 5 → (1)
- x + 3y = 13 → (2)
multiplying (1) by 3 and adding to (2) will eliminate y
15x - 3y = 15 → (3)
add (2) and (3) term by term to eliminate y
14x + 0 = 28
14x = 28 ( divide both sides by 14 )
x = 2
substitute x = 2 into either of the 2 equations and solve for y
substituting into (2)
- 2 + 3y = 13 ( add 2 to both sides )
3y = 15 ( divide both sides by 3 )
y = 5
solution is (2, 5 )
a wireless network predicts that sales will increase 110% this upcoming year. if the sales are projected to be $16000 in the future, what are they in the past?
A 1600
B 7619
C 14400
D 14545
SHOW WORK
Answer:
Step-by-step explanation:
14545
Make a basic proportion
16,000/x=110/100
Cross multiply
1,600,000=110x
Divide
x=14545
Jonathan has a points card for a movie theater. He receives 25 rewards points just for signing up. He earns 13.5 points for each visit to the movie theater. He needs at least 135 points for a free movie ticket. What is the least number of visits he needs to make in order to earn a free movie ticket?
Answer:
9
Step-by-step explanation:
You want to know the least number of visits Jonathan must make to a movie theater to have at least 135 points if he has 25 points and earns 13.5 for each visit.
PointsAfter x visits to the theater, Jonathan will have earned 13.5x points in addition to the signing bonus. His total will be ...
13.5x +25
VisitsJonathan wants that total to be at least 135:
13.5x +25 ≥ 135
13.5x ≥ 110 . . . . . . . subtract 25
x ≥ 110/13.5 ≈ 8.148
The smallest integer greater than 8.148 is 9.
Jonathan needs to make at least 9 visits to earn a free movie ticket.
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In right triangle ABC, altitude CD with length h is drawn to its
We also know AD=2 and DB=8. What is the length of
hypotenuse.
AC?
The length of the hypotenuse AC is √(h² + 4).
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
Right triangle ACD.
AC² = CD² + AD²
AC² = h² + 2²
AC² = h² + 4
AC = √(h² + 4)
Thus,
AC is √(h² + 4).
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How deep is a valley if it takes a rock 5.2 seconds to strike the bottom and it is traveling at 25 m/s?
Answer:
[tex]\huge\boxed{\sf h = 130\ m}[/tex]
Step-by-step explanation:
Given data:Time = t = 5.2 s
Velocity = v = 25 m/s
Required:Height = h = ?
Formula:h = vt
Solution:h = 25(5.2)
h = 130 m[tex]\rule[225]{225}{2}[/tex]
Answer:
The valley is 130 m deep.
Step-by-step explanation:
Formula we use,
→ Height = Time × Speed
Now the height will be,
→ Time × Speed
→ 5.2 × 25
→ 130 metres
Thus, valley is 130 m deep.
.........10 points.....
The value of angle a is 45, the value of angle b is 135, the value of angle c is 135 and d is 135.
What are lines and angles?Straight lines with little depth or width are present. You will learn about a number of lines, including transversal, intersecting, and perpendicular lines. A figure called an angle is one in which two rays originate from the same point. In this area, you might also encounter contrasting and related viewpoints.
Given that the line cutting the two parallel lines. The value of the angles will be calculated as,
Angle a will be,
a + 135 = 180
a = 180 - 135
a = 45
Angle b = 135
Angle c = 135
Angle d = 135
Therefore, the value of angle a is 45, the value of angle b is 135, the value of angle c is 135 and d is 135.
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Find h as indicated in the figure.
The indicated side of the right angle triangle is 183.
How to find the side of a right triangle?A right triangle is a triangle that has one of it's angles as 90 degrees. A right triangle sides are named according to the position of the angles.
The sides name are as follows:
opposite sideadjacent sidehypotenuse sidelet's find the value of side h using the trigonometric ratios as follows
tan ∅ = opposite / adjacent
Therefore,
tan 18.8 = h / x + 423
cross multiply
(x + 423) tan 18.8 = h
h = x tan 18.8 + 423 tan 18.8
h = 0.34042776856x + 144.000946101
tan 57.8 = h / x
cross multiply
x tan 57.8 = h
h = 1.58797305139x
Therefore,
1.58797305139x = 0.34042776856x + 144.000946101
1.58797305139x - 0.34042776856x = 144.000946101
1.24755305139x = 144.000946101
x = 144.000946101 / 1.24755305139
x = 115.426674549
Therefore,
h = 1.58797305139(115.426674549)
h = 183.294448434
h = 183
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Which statement about 199° is correct?
A. sin 199°> 0
B. tan 199° < 0
C. cos 199° < 0
The cosine of the angle 199° will be less than zero that is cos 199° < 0. Then the correct option is C.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
In the first quadrat, the angle is from 0° to 90°.In the second quadrat, the angle is from 90° to 180°.In the third quadrat, the angle is from 180° to 270°.In the fourth quadrat, the angle is from 270° to 360°.The angle of 199° lies in the third quadrant.
In the third quadrant, the sine and cosine of the angle are negative and the tangent of an angle is positive.
The cosine of the point 199° will be under zero that is cos 199° < 0. Then, at that point, the right choice is C.
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You owe $3,450.00. Which credit limit gives you an acceptable debt ratio?
O A. $4,000.00
O B. $2,000.00
O C. $7,000.00
O D. $5,500.00
Answer: C: $7,000.00
Step-by-step explanation:
The credit limit which gives an acceptable debt ratio is $7000.
What is Credit Limit?A credit limit is the most money you are permitted to spend on a credit card or line of credit by a lender. Knowing your limit, however, does not imply that going for it is a wise decision.
Given:
Owed Amount = $ 3450.0
So, Debt Ratio= (Total liabilities) ÷ (Total amount of worth possessed)
A debt ratio of approximately 0.5 is considered to be reasonable.
Money Owed by you = $ 3450.00
0.5 = 3450/credit limit
credit limit = 3450 × 10/5
credit limit = 6900
So, the Credit limit which gives Acceptable Debt of $ 3450.00 when debt ratio is approximately more or less than 0.5 is $7000.
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To celebrate Ripton's bicentennial fireworks are launched off a dam 36 ft above Lake Marley. The height of a display t seconds after it has been launched is given by h 16 64 36. After how long will the shell from the fireworks reach the water?
The shell from the fireworks will reach the water after 0.75 seconds or -0.625 seconds. Since the time cannot be negative, the shell will reach the water after 0.75 seconds.
How to find time ?To find the time it takes for the shell from the fireworks to reach the water, we need to solve the equation h = 0 for t.
The given equation for h is h = -16t^2 + 64t + 36, so we can substitute this into the equation h = 0 to get:
0 = -16t^2 + 64t + 36
To solve this equation, we can use the quadratic formula, which is:
t = (-b +/- sqrt(b^2 - 4ac)) / (2a)
In this case, a = -16, b = 64, and c = 36, so the formula becomes:
t = (-64 +/- sqrt(64^2 - 4(-16)(36))) / (-32)
Simplifying this gives us:
t = (-64 +/- sqrt(4096 - 2304)) / (-32)
which simplifies to:
t = (-64 +/- sqrt(1792)) / (-32)
Finally, simplifying gives us:
t = (-64 +/- 44) / (-32)
t = (-20 or 24) / (-32)
t = -0.625 or 0.75
Thus, the shell from the fireworks will reach the water after 0.75 seconds or -0.625 seconds. Since the time cannot be negative, the shell will reach the water after 0.75 seconds.
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Value Rent-A-Car rents a luxury car at a daily rate of $40.49 plus 5 cents per mile. A business person is allotted $120 for car rental each day. How many miles can the business person
travel on the $120?
The business person can travel miles.
(Type an integer or a decimal.)
When renting a car for $40.49 with a fixed mileage charge of $0.05, a businessperson can go 1590.2 miles.
What is expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.
Here,
The cost of car rent=$40.49
Cost for per mile=$0.05
Let him travel x miles,
40.49+0.05x=120
0.05x=120-40.49
0.05x=79.51
x=79.51/0.05
x=1590.2 miles
The business person can travel 1590.2 miles when the rent of car cost $40.49 fixed and $0.05 for every mile travelled.
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how do you solve 5/13y+25=0
Answer:
y = -100/13
Step-by-step explanation:
To solve this equation, we can first get all the terms containing the variable y on one side of the equation and all the constant terms on the other side. We can do this by subtracting 25 from both sides of the equation:
5/13y + 25 - 25 = 0 - 25
This gives us:
5/13y = -25
Next, we can divide both sides of the equation by 5/13 to get rid of the fraction:
(5/13y) / (5/13) = (-25) / (5/13)
This simplifies to:
y = -100/13
Therefore, the solution to the equation is y = -100/13.
4 + 2x + 1x - 4 = 30
How can I solve this and please explain step by step!
Answer:
x = 10
Step-by-step explanation:
To find the value of x:
1) add up like-terms
4 + 2x+1x-4=30
4 + 3x - 4 = 30
2) Add up the number on the left side
0 + 3x = 30
3x = 30
3) isolate the x
3x/3 = 30/3
x = 10
6. What is the reflection image of (5, –3) across the line y = –x? (–3, 5) (–3, –5) (3, –5) (3, 5)
Check the picture below.
What is volume of a cone that has a radius of 6cm and height of 18c
Answer:
136
Step-by-step explanation:
The formula of the volume of a cone is v=b*h.First you need to find the diameter, simple, 6*2=12, you get the 12 because the diameter is always twice as large as the radius. Next you multiply 18*12 which gives you 136!
There were 500 sweets in a box and Mrs. Miller has given out 35% as prizes. How many are left in
the box?
Answer: 325
Step-by-step explanation:
Lets rewrite this.
35% of sweets are given out of 500.
35% of 500.
35% = 0.35
0.35 x 500 = 175
This means 175 prizes were given. Now we have to subtract.
500 - 175 = 325
Use the slope formula to find the slope of the line through the points (−10,2) and (−4,−4).
The slope of the line passing through the points (10) 2, and (14), is -9/-13.
What is slope?A line's steepness and direction are measured by the line's slope.
Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all
Any two different points on a line can be used to calculate the slope of any line.
A line's slope is determine by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.
Two locations located on a straight line can be used to determine a line's slope. We can use the slope of line formula if we know the two spots' coordinates. These two points' coordinates should be-
P1 = (x1, y1) and P2 = (x2, y2)
Hence, The slope of the line passing through the points (10) 2, and (14), is -9/-13.
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a service station on the interstate changes $2.29 per gallon of
gasoline and $1.89 per quart for oil. What would be a recourable
amount to pay for 10 gallons of gasoline and 2 quarts of oil ?
A) $20
B) $23
C) $25
D) $27
Answer:
D) $27
Step-by-step explanation:
You want an estimate of a reasonable amount to pay for 10 gallons of gas at $229 per gallon, and 2 quarts of oil at $1.89 per quart.
EstimateFor estimating purposes, we like to round numbers to 1 or 2 significant figures.
The cost of 10 gallons of gas is about 10 × $2.30 = $23.
The coast of 2 quarts of oil is about 2 × $2 = $4.
So, the total cost of the gas and oil is about $23 +4 = $27.
You expect the total to be near $27.
__
Additional comment
Part of estimating is estimating the error in your estimate. Here the error is $0.01 per gallon of gas, or $0.10 for 10 gallons. The error is $0.11 per quart of oil, so $0.22 for 2 quarts. The final estimate of $27 is $0.10 +0.22 = $0.32 too high. $27 is different from the next answer choice by $2, so is still the best answer choice.
A park has two sprinklers that are used to fill a fountain. One sprinkler can fill the
fountain in 3 h, whereas the second sprinkler can fill the fountain in 6 h. How long will
it take to fill the fountain with both sprinklers operating?
It takes 2 hrs to fill the fountain with both sprinklers operating
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
A park has two sprinklers that are used to fill a fountain
One sprinkler can fill the fountain in 3 h
second sprinkler can fill the fountain in 6 h
We need to find the time required to fill the fountain by two sprinklers.
Let t = time required with both sprinklers working
t/3+t/6=1
2t+t/6=1
3t/6=1
Apply cross multiplication
3t=6
Divide both sides by 3
t=2
Hence, it takes 2 hrs to fill the fountain with both sprinklers operating
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Triangle ABC is translated 5 units to the left and 6 units down.
The result is A' B' C', as shown below.
On solving the provided question, we got the area of triangle - A = 1/2 B X H= 15 sq. units.
What is Triangle?A triangle is a shape formed when three straight lines meet. All triangles have three sides and three corners (angles). The point where two sides of a triangle meet is called a vertex. The base of a triangle can be any one of its three sides, but it is usually the bottom one. The longest side of a triangle is opposite its biggest angle, and the shortest side of a triangle is opposite its smallest angle. The three angles inside a triangle always add up to 180°.
To find the Area of triangle -
By help formula,
[tex]A = \frac{1}{2} B X H\\\\[/tex]
[tex]\\A = \frac{1}{2} (6 X 5)\\[/tex]
[tex]\\A = 15 sq.unit[/tex]
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Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The equation that is quadratic in all the equations is 6(2x+4)²=(2x+4)+2
How to Identify a quadratic equation?A quadratic equations defined as any equation that can be rearranged in standard form as ax²+bx+c=0 or -b±[tex]\frac{\sqrt{} b^{2}-4ac }{2a}[/tex]
From the list of equations the one that carries the standard form for a quadratic equation is
6(2x+4)²=(2x+4+)+2
Expand the brackets to have
6[(2x+4)(2x+4)=(2x+4)+2
6[4x²+8x+8x+16]=(2x+4)+2
Collecting like terms and opening the brackets further;
6[4x²+16x+16]=2x+4+2
=24x²+96x+96=2x+6
Collecting like terms we have
24x²+96x-2x+96-6=0
⇒24x²94x+90=0
In conclusion, the equation carries 2 as its highest power therefore, it is a quadratic equation.
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what is the slope for (1, -5) and (4, 1)?
A rectangular pool has an area of 30 sq. ft. One side is 1 more than the other side. How long are the sides?
STATISTICS - please please help ASAP!! This is for my final exam! I will give brainliest to the correct answer!
Below is a list of wait times at the Disney World ride “It’s a Small World.” You will use this data to fill in a table.
5 5 5 5 5 10 10 10 10 15
15 15 15 15 15 15 20 20 20 20
20 20 20 20 25 25 25 25 25
25 30 30 30 30 30 35 35 35 35
40 40 40 45 45 50 60 60 60 75
Fill in the Frequency table below in the Frequency column and the Relative Frequency column (in percents, example 12%, not a decimal.)
Fill in the blanks in the Frequency column and the Relative Frequency column.
(columns pictured)
Step-by-step explanation: To fill in the table, we will need to first count the number of times each wait time appears in the given data. We can then use these counts to fill in the Frequency column of the table. We will also need to calculate the relative frequency of each wait time, which is the number of times it appears in the data divided by the total number of data points. We can then use these relative frequencies to fill in the Relative Frequency column of the table, expressed as a percentage.
Here is the completed table:
Wait Time (minutes) Frequency Relative Frequency (%)
5 5 11.36
10 4 9.09
15 7 15.91
20 6 13.64
25 7 15.91
30 4 9.09
35 5 11.36
40 3 6.82
45 2 4.55
50 1 2.27
60 2 4.55
75 1 2.27
Note that the total number of data points is 44, so each relative frequency is calculated as the corresponding frequency divided by 44.
I hope this helps! Let me know if you have any other questions.
Let D be a region bounded by a simple closed path C in the xy-plane. The coordinates of the centroid x, y of D are x = 1 2A x2 dy C y = ? 1 2A y2 dx C where A is the area of D. Find the centroid of a quarter-circular region of radius a.
If D be a region bounded by a simple closed path C in the xy-plane, then the centroid of the quarter circle is (4a/3π , 4a/3π) .
In the question ,
it is given that D is the region bounded by a simple closed path C in the xy-plane .
the radius of the circle is = "a" ,
let the equation of the circle be x² + y² = a² ,
So , the area of the quarter circle is (A) = (1/4)*πa²
The coordinate of the centroid x will be :
x = [tex]\frac{1}{2A} \int\limits x^{2} dy[/tex]
x = [tex]\frac{1}{2(\frac{\pi a^{2} }{4})} \int\limits^a_0 {a^{2} -y^{2} } \, dy[/tex]
Simplifying further ,
we get ,
x = 2/πa² [{a²(a) - a³/3} - 0 ]
x = 2/πa² [a³ - a³/3 ]
x = 4a/3π
The coordinate of the centroid y will be :
y = [tex]\frac{1}{2A} \int\limits y^{2} dx[/tex]
y = [tex]\frac{1}{2(\frac{\pi a^{2} }{4})} \int\limits^a_0 {a^{2} -x^{2} } \, dx[/tex]
Simplifying further ,
we get ,
y = 2/πa² [{a²(a) - a³/3} - 0 ]
y = 2/πa² [a³ - a³/3 ]
y = 4a/3π
Therefore , the coordinates of the centroid is (4a/3π , 4a/3π) .
The given question is incomplete , the complete question is
Let D be a region bounded by a simple closed path C in the xy-plane. The coordinates of the centroid x, y of D are x = [tex]\frac{1}{2A} \int\limits x^{2} dy[/tex] , y = [tex]\frac{1}{2A} \int\limits y^{2} dx[/tex] ?
Find the centroid of a quarter-circular region of radius a.
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