Using vectors, and the relation between velocity and position, it is found that:
a) The speed is given by: v(t) = 2i - 5j.
b) The position vector p at time t hours is: p(t) = (2t + 8)i + (-5t + 3)j.
c) The ship is due north of the lighthouse at a time of 6 seconds.
d) The ship is 23 miles from the lighthouse at this point.
What is the relation between velocity and position?The position function is the integral of the velocity function.
As stated in the problem, the velocity is constant, hence:
The speed is given by: v(t) = 2i - 5j.
The position is the integral of the velocity, hence, integrating each component.
[tex]p(t) = \int v(t) dt[/tex]
[tex]p(t) = \int (2i - 5j) dt[/tex]
p(t) = (2t + k1)i + (-5t + k2)j.
Considering the initial position, we have that:
k1 = 8, k2 = 3.
Hence:
The position vector p at time t hours is: p(t) = (2t + 8)i + (-5t + 3)j.
The ship is due north of the lighthouse(20i - 50j) when it has the same x-coordinate, hence:
2t + 8 = 20
2t = 12
t = 6.
Hence:
The ship is due north of the lighthouse at a time of 6 seconds.
The position of the ship at t = 6 seconds is:
(2(6) + 8)i + (-5(6) + 3)j = 20i -27j.
The distance is given by:
|-50 - (-27)| = |-23| = 23.
The ship is 23 miles from the lighthouse at this point.
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Identify the segment bisector of JK
The length of JM is
If the cost, C(x), for manufacturing x units of a certain product is given by
C(x) = x² - 19x+60
find the number of units manufactured at a cost of $8900.
The number of units manufactured at a cost of $8900 will be 104 units.
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
If the cost, C(x), for manufacturing x units of a certain product is given by
C(x) = x² - 19x + 60
The number of units manufactured at a cost of $8900 will be given by factorization.
x² - 19x + 60 = 8900
x² - 19x - 8840 = 0
x² - 104x + 85x - 8840 = 0
x(x - 104) + 85(x - 104) = 0
(x - 104)(x + 85) = 0
x = 104, -85
The number of units manufactured at a cost of $8900 will be 104 units.
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Pls pls pls pls pls pls pls pls
the correct statement is the first one.
The inverse of 6^2 is 6^(1/2), then 6^(1/2) is the square root of 6.
Which statement explains why 6^(1/2) is equal to √6?Well, this is just a notation thing.
We know the following property for exponents:
(a^n)^m = a^(n*m)
And we know that the square rooth is the inverse of the square power (exponent equal to 2) such that:
√x^2 = 2
Then if we define the square root as an exponent, let's say that is an exponent "a" we will have:
√x = x^a
Rewritting the above relation again, we can write:
√(x^2) = (x^2)^a = x^(2*a)
And we know that it must be equal to x, so we get:
x^(2*a) = x
This means that 2*a = 1
then a = 1/2
√x = x(1/2)
Then the correct statement is the first one.
The inverse of 6^2 is 6^(1/2), then 6^(1/2) is the square root of 6.
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Your phone is losing charge at a rate of 2%every 7 minutes. You check and see that you have 44% left. Write the function of total charge left where x is in minutes. Find the y-intercept, x-intercept and slope.
The y-intercept, x-intercept and slope are 100, 350 and 2 / 7, respectively.
How to describe the linear equation describing the discharge of a phone
In accordance with the statement, the phone charge decreases linearly in time based on the following linear model:
c(x) = 100 - (Δy / Δx) · x
Where:
c(t) - Current charge of the cell phone, in percentage.Δc - Current charge change, in percentage.Δx - Time change, in minutes.x - Time, in minutes.If we know that Δy = 2, Δx = 7, then the linear equation is:
c(x) = 100 - (2 / 7) · x
Then, the y-intercept, x-intercept and slope are, respectively:
y-intercept
b = 100
x-intercept
0 = 100 - (2 / 7) · x
(2 / 7) · x = 100
2 · x = 700
x = 350
Slope
m = 2 / 7
The y-intercept, x-intercept and slope are 100, 350 and 2 / 7, respectively.
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In Exercises 1-16, solve the inequality. Graph the solution
1. 3y ≤ -9
By solving the inequality we get [tex]y\leq -3[/tex]
What is graphing the inequality?
The act of illustrating which area of the number line contains values that will "satisfy" the specified inequality is known as graphing the inequality. Take a look at the first inequality, "x > -5." The numbers that can be used to substitute x in our inequality to produce a true statement can be shown on a graph of our inequality.
[tex]3y\leq -9[/tex]
Dividing above equation by 3 we get,
[tex]\frac{3y}{3}\leq \frac{-9}{3}\\y\leq -3[/tex]
Graph of [tex]y\leq -3[/tex] is
Therefore by solving the inequality we get [tex]y\leq -3[/tex]
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Find the slope of the line passing through the
points (-3, 3) and (5, 9)
Answer: 3/4
Step-by-step explanation:
The slope of the line passing through the points (-3,3) and (5,9) is 3/4
The formula for calculating the slope of a line is expressed as:
Given the coordinate (-3,3) and (5,9), substitute the coordinates into the formula as shown below;
Hence the slope of the line passing through the points (-3,3) and (5,9) is 3/4
Y=-3x+6 and y=1/3x-8 determine if the equation are parallel, perpendicular, or neither
Answer:8
Step-by-step explanation:
1
Solve each system by substitution.
3u + 8 = 4v , 24v = 6 - 3u
By substitution, the solution of the system of equations, 3u + 8 = 4v and 24v = 6 - 3u, is (u , v) = (-2 , 1/2).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in u and v,
3u + 8 = 4v (equation 1)
24v = 6 - 3u (equation 2)
Using the first equation, find the value of one variable, lets say u, in terms of the other.
3u + 8 = 4v (equation 1)
3u = 4v - 8
u = (4v - 8)/3
Substitute the value of u to the second equation.
24v = 6 - 3u (equation 2)
24v = 6 - 3[(4v - 8)/3]
24v = 6 - (4v - 8)
24v = 6 - 4v + 8
Combining all terms containing the variable v on one side and the constants on the other side of the equality, and solve for v.
24v = 6 - 4v + 8
24v + 4v = 6 + 8
28v = 14
v = 1/2
Substitute the value of v in the equation for u and solve for u.
u = (4v - 8)/3
u = [4(1/2) - 8]/3
u = (2 - 8)/3
u = -6/3
u = -2
Hence, the solution of the given system of equations is (u , v) = (-2 , 1/2).
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A surveyor needs to find the distance from point A to point B across a canyon. She places a stake at A, and a coworker places a stake at B on the other side of the canyon. The surveyor then locates C on the same side of the canyon as A such that CA ⊥ AB. A fourth stake is placed at E, the midpoint of CA. Finally, a stake is placed at D such that CD ⊥ CA and D,E, and B are sited as lying along the same line.
b. If A C=1300 meters, D C=550 meters, and D E=851.5 meters, what is AB? Explain your reasoning.
The value of line AB is 550 meters.
What do we presume by the congruency of a triangle?Two triangles are said to be congruent if all three corresponding sides and angles are equal in size.To appear identical, these triangles can be moved, rotated, flipped, and turned.They will coincide if they are moved.Congruence exists when two triangles satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
First, we'll prove that △BEA ≅ △DEC.
∠A = ∠C = (BA and CD is ⊥ AC)AE = CE = (E is the midpoint of AC)∠AEB = ∠DEC = (Inversely opposite angles)So, △BEA ≅ △DEC is under ASA condition.
Then, DC is identical to AB.Therefore, the value of AB is 550 meters.
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PLSSS HURRY I REALLY NEED THIS
Answer: 1/10
Step-by-step explanation: -2/5+1/2=0.1
If we convert 0.1 into a fraction, it becomes 1/10.
Answer:
1/10 is the answer
Step-by-step explanation:if correct mark as BRAINLIEST
Find the sum of each series. Σ⁵ n=1 (3 n+1)
The sum of the given series is 50
The summation notation or sigma notation is used to simplify the writing of long summation into a single formula.
The given series in sum notation is:
[tex]\sum\limits^5_{n=1} {(3n+1)}[/tex]
Substitute n = 1 ...5 into the nth term formula inside the sum notation:
a(1) = 3 . (1) + 1 = 4
a(2) = 3. (2) +1 = 7
a(3) = 3. (3) +1 = 10
a(4) = 3. (4) +1 = 13
a(5) = 3. (5) +1 = 16
Hence, the series:
4 + 7 + 10 + 13 + 16
We can evaluate the sum directly by adding all the terms:
S(5) = 4 + 7 + 10 + 13 + 16 = 50
Or we can also use the sum formula of an arithmetic series:
S(n) = n/2 [a(1) + a(n)]
For n = 5
S(5) = 5/2 (4 + 16)
S(5) = 5/2 . 20 = 50
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The first two steps a student takes to solve the equation 2 (x-3) = 6x + 9 are shown. Step 1: Use the Distributive Property to distribute the 2. Step 2: Subtract 9 from both sides. What is most likely the next step they should take? Subtract 2x from both sides. Multiply both sides by 4. O O Add 2x to both sides. O Divide both sides by 4.
Answer:
x= negative goes on the out side of it 15 over 4
Find two numbers whose sum is 52 and whose product is as large as possible? [Hint: Let x and 52-x be the two positive numbers. Their product can be
described by the function f(x)=x(52-x).]?
The two numbers whose sum is 52 and the product is maximum are 26 and 26.
How to find the sum of algebraic fractions?Finding the least common multiples of the denominator expressions can help. Then using the similar method as we use in the sum of fractions would give the sum of algebraic fractions.
We need to find the two numbers whose sum is 52 and the product is maximum.
So, the multiples of 52 are
2, 26, 4, 13,
So, here we can see that the sum of 26 to itself would be equal to 52.
26 + 26 = 52
The product is also maximum compared to others.
26 x 26 = 676
Therefore, the two numbers are 26 and 26.
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x - (-3) = 8
what does x equal?
Answer:
x = 5
Step-by-step explanation:
Change "minus a negative" to "plus a positive"
x - (-3) = 8
x + 3 = 8
Next, subtract 3 from both sides.
x + 3 - 3 = 8 - 3
x = 5
Check it!
x - (-3) = 8
5 - (-3) = 8
5 + 3 = 8
8 = 8 Check!
David is going out for a pizza. The Pizza costs $10.50 plus $1.50 for each extra topping ,x. Write an equation to represent the total cost of the pizza, t.
Dependent variable:________
Independent variable:____
Equation:____ (Use your equation to determine the total cost of the pizza with 3 extra toppings).
10.50+1.50x=total cost
since they wanted 3 topings it would be x=3
10.50+(1.50*3)
simplify
10.50+4.50=15
I hope this helps
Can someone explain this to me??
Answer:
see attached
Step-by-step explanation:
You want the height drawn on each triangle corresponding to the base shown.
HeightThe height of a triangle is the perpendicular distance from the base to the opposite vertex. The point at which the height segment meets the base may or may not lie on the triangle.
The height segments for the two given triangles are shown in the attachment.
__
Additional comment
As this problem suggests, any side of a triangle may be designated the "base."
The height segment is also called an altitude. When all three altitudes are extended until they coincide, the point at which they meet is called the "orthocenter" of the triangle.
The orthocenter of an acute triangle lies inside the triangle. For a right triangle, it lies at the right-angle vertex. For an obtuse triangle, the orthocenter is outside the triangle.
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Mrs. Rushdan buys 4 bananas and 6 apples. What is the ratios for
bananas to apples?
Answer:
2;3, that is the ratio =)
Step-by-step explanation:
Answer:The answer would be 4 to 6 or 4:6
A small cylindrical can of tuna has a radius of 4 centimeters and a height of 3.8 centimeters. A larger and similar can of tuna has a radius of 5.2 centimeters.
b. What is the volume of the larger can? Round to the nearest tenth.
The volume of the larger cylindrical can of tuna with radius 5.2 centimeters is 419.6 cubic centimeters.
Solids of the same type that have proportional corresponding linear measures are similar solids. In the case of similar cylinder:
height of A / height of B = radius of A / radius of B
Using this scale, if the larger and similar can of tuna has a radius of 5.2 centimeters, and the small cylindrical can of tuna has a radius of 4 centimeters and a height of 3.8 centimeters, then:
radius of larger cylinder / radius of smaller cylinder = 5.2 cm/4cm = 13/10
height of larger cylinder / height of smaller cylinder = 13/10
height of larger cylinder = 13/10 (3.8 cm)
height of larger cylinder = 4.94 cm
Solving for the volume of the larger can using the formula for the volume of cylinder:
V = πr^2h
V = π(5.2 cm)^2(4.94 cm)
V = 419.6464068 cubic centimeters
Rounding off to the nearest tenth.
V = 419.6 cubic centimeters
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Which value of x is the solution to this equation?
5x² 30x45
=
A rectangular painting measures 13 inches by 20 inches and contains a frame of uniform width around the four edges. The perimeter of the rectangle formed by the painting and its frame is 98 inches. Determine the width of the frame.
The width of the frame is 8 inches.
We are given that:
The measures of the rectangular painting are:
Length = 13 inches
width = 20 inches
Now, the frame is of uniform with around the corner.
Let it be x inches.
So the new dimensions will be:
Length = 13 + x inches
Width = 20 + x inches.
Also, we are given that:
Perimeter = 98 inches
So, we get that:
P = 2(l + b)
Substituting the values, we get that:
98 = 2 (13 + x + 20 + x)
98 = 2( 33 + 2 x)
98 = 66 + 4 x
4 x = 98 - 66
4 x = 32
x = 32 / 4
x = 8 inches.
Therefore, the width of the frame is 8 inches.
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PLEASE HELP! NEED THIS ASAP! PLS HELP!!
Nick mowed about 3/7 of the school lawn yesterday. he mowed another 1/4 of the lawn this morning. how much is left to mow?
Answer:
9/28 of the lawn is left
Step-by-step explanation:
Make 3/7 and 1/4 have the same denominator
3/7 becomes 12/28 and 1/4 becomes 7/28
added together is 19/28
[tex]log_5 11= ?[/tex]l
Answer:
1.48
Step-by-step explanation:
Redefined the logarithm into its decimal form within the base.
Hope this helps.
um can u guys pls help
Answer:
if I can't explain in one line, then I will include the steps in the explanation.
2x - 7 2x - 7 = x + 97Step-by-step explanation(Q3):
[tex]3^2-\left(5-3\right)^3+6\\5-3=2\\3^2-2^3+6\\3^2=9\\9-2^3+6\\2^3=8\\9-8+6\\9-8=1\\1+6\\1+6=7\\=7[/tex]
Hope it helps!
Unit: NUMBER RELATIONSHIPS
and COMPUTATION
Objective: Estimate to determine the quotient of a decimal.
89.904 divided by 34??
The quotient of the decimal number 89.904 divided by 34 will be 2.65.
What is the quotient?In mathematics, the sum obtained by diluting two numbers is known as a quotient. In mathematics, the word "quotient" is widely used, and it is sometimes referred to as the integer part of a division, a fraction, or a ratio.
The decimal numeral system is widely used to express both integer and non-integer numbers.
Given numbers are 89.904 and 34. The quotient will be calculated as below:-
Quotient = 89.904 / 34
Quotient = 2.65
Therefore, the quotient of the decimal number 89.904 divided by 34 will be 2.65.
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Workoutthe size of angle x [parrallel lines in a triangle]
The size of angle is X=13
y + 98 =180(LP)
Y =180-98
Y=82
<AOB + <OAB + <OBA=180(Sum of all angles of triangles)
85 + X + 82 =180
167 + X =180
X = 180-167
X=13
In Euclidean geometry, any three points that are not collinear produce a singular triangle angle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle angle is contained in a plane, and there is only one plane that contains that triangle. All triangles angle are enclosed in a single plane if all of the geometry is the Euclidean plane, however, this is no longer true in higher-dimensional Euclidean spaces.
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Things are usually pretty uneventful during the day in the reptile building as the snakes prefer their beauty sleep, but the critters are stirring as they sense freedom. The python is the first one to leave her cage, and she begins to slowly slither towards the exit at a pace of 1 mile per hour. The anaconda decides to snooze for another 30 minutes before beginning the long trek ahead. He leaves his cage after the python has already traveled half a mile, and he slithers at a pace of 5 miles per hour. Write an equation to represent this scenario letting x represent the number of hours it would take.
The linear functions that model the positions of the Python and of the Anaconda are given as follows:
P(x) = 0.5 + x.A(x) = 5x.What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For the functions in this problem, we have that:
The initial position is the intercept.The velocity is the slope.Considering their velocities, and that when the Anaconda leaves the Python has already traveled half a mile, the functions are given as follows:
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Write an equation in slope-intercept form for the line described.
passes through (-12,3), perpendicular to y=-2/3x-11
The equation in slope-intercept form for the line that passes through (-12,3), perpendicular to y = -(2/3)x-11 is y = (3/2)x + 21.
The slope intercept form of a line is:-
y = mx + b
Where:-
m represents the slope of a line
b represents the y-intercept of a line
x and y represent the ordered pairs (x,y) throughout a line
We are given the line y = - (2/3)x-11 is perpendicular to the line whose equation we have to find.
Hence,
slope of the line*(-2/3) = -1
slope of the line, m = 3/2
Also, (-12,3) passes through the line,
Hence,
3 = (3/2)*(-12) + b
3 = -18 + b
b = 21
Hence, the equation of the line in slope intercept form is y = (3/2)x + 21.
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Find the value of A if the 4-digit number 3A5A is divisible by 15.
Answer:
let 3A5A be equal to 15
3A5A=15
A=1
Answer:
a = 5
Step-by-step explanation:
3555/15 is 237 which means it is divisible
Caroline walks 9 and 1/2 inches per second. Give the rate in miles per hour. Round to the nearest tenth.
Please help.
Suppose Emma is hosting a party and knows at least 3 are
coming. The party is capped at 12 guests. Let g(x) model
the number of tables Emma needs to set up if x guests
attend. What is the domain of the function? Use set
notation.
Guests
3-6
7 - 10
11 - 12
Tables Needed
1
2
3
Step-by-step explanation:
the first answer is -3 the second answer is -2/3 outside -1
