To find the perpendicular components of a displacement vector with a magnitude of 20 meters, use trigonometry and the Pythagorean theorem.
Explanation:The question asks for the perpendicular components of a displacement vector with a magnitude of 20 meters. Perpendicular components of a vector can be determined using trigonometry. Let's assume the vector has components Ax and Ay.
Using the Pythagorean theorem, Ax^2 + Ay^2 = 20^2. Since the components are perpendicular, we can set up a right triangle and solve for the components using the sine and cosine functions. For example, if one component is Ax = 10 meters, the other component Ay can be calculated using Ay = sqrt(20^2 - 10^2) = 10*sqrt(3) meters. Similarly, if one component is Ay = 10 meters, the other component Ax can be calculated using Ax = sqrt(20^2 - 10^2) = 10*sqrt(3) meters.
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There are 5,280 feet in 1 mile. If Riley ran 26,400 feet, how many miles did she run? [Type your answer as a number.]
Answer:
She ran 5 miles
Step-by-step explanation:
To solve this, we can easily use proportion.
The question state that there are 5,280 feet in a mile, We are ask to find the number of miles Rily run, if she ran 26,400 feet.
Using proportion;
Let x = the number of miles Rily can run
5,280 feet = 1 mile
26,400 feet = x
Cross-multiply
5280x = 26,400
To get the value of x, we will divide both-side of the equation by 5280
5280x/5280 = 26400/5280
(On the left-hand side of the equation, 5280 will cancel-out 5280 leaving us with x and on the right-hand side of the equation 26400 will divide 5280)
x = 26400 / 5280
x=5 mile
Therefore, If Rily ran 26400 feet, then she has ran 5 miles.
What is the image of (5,-1) under same translation?
The image of point (5, -1) under the same translation that maps point P to P' is (1, -8). This translation vector is obtained by subtracting the coordinates of P from P'.
To find the image of point (5, -1) under the same translation T that maps point P to P', we can calculate the vector that represents the translation from P to P' and then apply the same translation to point (5, -1).
The translation vector is given by:
Translation vector = P' - P = (-6, -4) - (-2, 3) = (-4, -7)
Now, to find the image of point (5, -1) under the same translation, we simply add this translation vector to (5, -1):
Image of (5, -1) = (5, -1) + (-4, -7) = (5 - 4, -1 - 7) = (1, -8)
So, the image of point (5, -1) under the translation T is (1, -8). Therefore, the correct answer is B. (1, -8).
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The graph of g(x) is the graph of f(x)=12x+6 compressed vertically by a factor of 13 .
Which equation describes the function g?
g(x)=12x+2
g(x)=4x+6
g(x)=4x+2
g(x)=36x+6
Find the greatest common factor of 75, 8, and 21
the temperature was -3 degrees last night. it is now -4 degrees . what was the change in the temperature
Write the parametric equations x = 4 \sin^2 \theta , \quad y = 3 \cos^2 \theta in the given cartesian form.
The Cartesian form of equation is,
3x + 4y = 12
We have to given that,
The parametric equations are,
x = 4 sin² θ
y = 3 cos² θ
Now, Change the parametric equations into cartesian form as,
x = 4 sin² θ
sin² θ = x/4 .. (i)
y = 3 cos² θ
cos² θ = y/3 (ii)
Add equation (i) and (ii),
sin² θ + cos² θ = x/4 + y/3
1 = x/4 + y/3
1 = (3x + 4y)/12
12 = 3x + 4y
3x + 4y = 12
Therefore, The Cartesian form of equation is,
3x + 4y = 12
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what is the value of the function f(x)=1/4x-3 when x=12
6
1
0
-6
What is the least common multiple of 50, 60, and 72?
The function H(t) = −16t2 + 48t + 12 shows the height H(t), in feet, of a cannon ball after t seconds. A second cannon ball moves in the air along a path represented by g(t) = 10 + 15.2t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 0 through 3 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)
Part B: Explain what the solution from Part A means in the context of the problem. (4 points)
We are given a function H(t) that represents the height of a cannon ball after t seconds as:
[tex]H(t)=-16t^2+48t+12[/tex]
and a second cannon ball is represented by the function g(t) as:
[tex]g(t)=10+15.2t[/tex]
PART A:
t 0 1 2 3
H(t) 12 44 44 12
g(t) 15.2 25.2 40.4 55.6
Hence, between t= 2 seconds and t=3 seconds the ball will meet
such that H(t)=g(t)
Since, we know that the Height H(t) decreases from 44 feet to 12 feet between t=2 to t=3 seconds.
and height g(t) increases from 40.4 feet to 55.6 feet between t=2 to t=3 seconds.
Hence, the two cannon balls will definitely meet between t=2 to t=3 seconds.
and the time at which they meet is calculated by solving:
[tex]H(t)=g(t)\\\\i.e.\\\\\\-16t^2+48t+12=10+15.2t\\\\\\i.e.\\\\\\16t^2-32.8t-2=0\\\\\\i.e.\\\\\\t=-0.059\ and\ t=2.109[/tex]
As t can't be negative.
Hence, we get:
t=2.109 seconds
PART B:
The solution from PART A means that the one of the ball first reach the highest point at 44 feet and then returns back to the initial position and hence follows a parabolic path while the second cannon ball reach a greater height with the increase in time and hence in this phenomena the two balls will definitely meet.
3469131824 what would be the next number
Assembly Line A produces 45 units in the same time that it takes Assembly Line B to produce 37 units. If Line B produces 555 units, how many units does Line A produce during the same time?
Assembly Line A will produce 24975 units during the same time that Line B produces 555 units.
Explanation:Let's assume that the time it takes for Assembly Line A to produce 45 units is equal to the time it takes for Assembly Line B to produce 37 units. This means that the time it takes for Line A to produce 1 unit is equal to the time it takes for Line B to produce 1 unit.
Now, we can set up a proportion to find how many units Line A will produce during the same time that Line B produces 555 units:
45 units / 1 unit = x units / 555 units
Cross-multiplying, we get:
45 * 555 = x units * 1
x units = 24975 units
Therefore, Line A will produce 24975 units during the same time that Line B produces 555 units.
A total of 900 tickets were sold for a game for a total of $1,150. if adult tickets sold for $2.00 and children's tickets sold for $1.00, how many of each kind of ticket were sold?
the equation 5x+4y=20 represents a linear function in two variables. Identify the slope, x-intercept and y-intercept of this linear function
Multiply 5x2(2x2 + 13x − 5). 10x4 + 65x3 − 25x2 10x2 + 65x − 25 7x2 + 18x − 10 7x4 + 18x3 − 10x2
Answer:
[tex]10x^4+65x^3-25x^2[/tex]
Step-by-step explanation:
Multiply 5x^2(2x^2 + 13x − 5)
[tex]5x^2(2x^2 + 13x - 5)[/tex]
Multiply 5x^2 inside the parenthesis
[tex]5x^2 * 2x^2 = 10x^4[/tex]
[tex]5x^2 * 13x = 65x^3[/tex]
[tex]5x^2 * (-5) = -25x^2[/tex]
Collect all the terms together
[tex]10x^4+65x^3-25x^2[/tex]
Suppose an investment of $10,000 doubles in value every 13 years. How much is the investment worth after 52 years? After 65 years?
A: $80,000; $100,000
B: $160,000; $320,000
C: $520,000; $650,000
Answer:
Step-by-step explanation:
The answer is actually B. $160,000; $320,000
The reason for this is because -
$10,000 is the constant, so let a= 10,000.
The investment doubles every 13 years, so let b=2.
Let x= the number of 13-year periods.
The value of a $10,000 investment doubling every 13 years will be $160,000 after 52 years and $320,000 after 65 years.
Explanation:To calculate the value of an investment that doubles every 13 years, you can determine the number of times the investment will double over a given period. In this case, after 52 years, the investment will have doubled 4 times (since 52 divided by 13 is 4), and after 65 years, it will have doubled 5 times (since 65 divided by 13 is 5).
The formula for the future value of an investment that doubles is: Future Value = Present Value × (2^number of doublings).
After 52 years, the investment's worth would be calculated as follows:
$10,000 × (2^4) = $10,000 × 16 = $160,000
After 65 years, the investment's worth would be:
$10,000 × (2^5) = $10,000 × 32 = $320,000
Therefore, the correct answers are $160,000 after 52 years and $320,000 after 65 years, which corresponds to choice B.
Joan has a credit card that uses the previous balance method. The opening balance of one of her 30-day billing cycles was $6390, but that was her balance for only the first 3 days of the billing cycle, because she then paid off her entire balance and didn't make any new purchases. If her credit card's APR is 17%, which of these expressions could be used to calculate the amount Joan was charged in interest for the billing cycle?
Answer:
Step-by-step explanation:
(0.17/365 x30)(6390)
The expression that represents the amount Joan was charged in interest for the billing cycle is $26.84.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To calculate the amount Joan was charged in interest for the billing cycle using the previous balance method, we need to find the average daily balance for the billing cycle, which is calculated as the sum of the daily balances divided by the number of days in the billing cycle.
The daily balance is the balance at the end of each day, and it is calculated by adding new purchases and subtracting payments and credits from the previous day's balance.
In this case,
Joan had a balance of $6390 for the first 3 days of the billing cycle, so her average daily balance for the billing cycle can be calculated as:
((3 x 6390) + (27 x 0)) / 30
= 1917
This means that her average daily balance for the billing cycle was $1917.
To calculate the amount of interest Joan was charged for the billing cycle, we can use the following expression:
Interest = Average Daily Balance x Daily Interest Rate x Number of Days in Billing Cycle
The daily interest rate is calculated as the APR divided by 365 since there are 365 days in a year. In this case, the daily interest rate is:
0.17 / 365
= 0.000465753
So, the expression that can be used to calculate the amount of interest Joan was charged for the billing cycle is:
Interest = 1917 x 0.000465753 x 30
= $26.84 (rounded to the nearest cent)
Therefore,
The expression that represents the amount Joan was charged in interest for the billing cycle is $26.84.
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The length of a rectangle is 10 m less than three times the width, and the area of the rectangle is 77 m2 . find the dimensions of the rectangle
The length and width of the rectangle are 11 m and 7 m respectively.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
Given that,
Length of the rectangle is 10 m less than three times the width,
And area of rectangle = 77 m²
Let the width of rectangle is x m,
Then length of rectangle = 3x -10 m.
The area of rectangle = 77
length × width = 77
x × (3x - 10) = 77
The value of x = 7 satisfy the equation,
Therefore, the width of rectangle is x = 7 m
And length of the rectangle is 3x - 10 = 21 - 10 = 11 m
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The sum of twice a number and four is fourteen. find the number.
2x +4 =14
2x =10
x =5
the number is 5
Yeet! I need some help! 16 points to whoever answers!
180 is 10 % more than witch number ?
The volume of a rectangular prism can be computed using the formula v = lwh. what is the length of a prism that has a volume of 1344 cubic centimeters, a width of 8 centimeters, and a height of 12 centimeters?
a. 111 cm
b. 18 cm
c. 896 cm
d. 14 cm
We are given the formula:
V = l w h
and the following values:
l = ?
V = 1344 cm^3
w = 8 cm
h = 12 cm
SO rewriting the formula in terms of l:
l = V / w h
l = 1344 cm^3 / (8 cm * 12 cm)
l = 14 cm
Answer:
d
The answer would be 14
Apply THe ORder of operations to simplify the expression
90/ [10+(3² - 4)]
most with best answer gets brainliest please help.
The simplification form of the expression 90/ [10+(3² - 4)] is 6 the answer is 6.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
As we know, the expression can be defined as the combination of constants and variables with mathematical operators.
To begin, either multiply or divide the value in parentheses (32-4), which equals 5.
Add the number in the parentheses once more: 90/[10+5 (always do the parenthesis first) [10+5]= 15.
Finally, divide 90/15 by 6, always keeping that in mind (PEMDAS)
Thus, the simplification form of the expression 90/ [10+(3² - 4)] is 6 the answer is 6.
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How to calculate standard deviation given mean and sample size?
Factor the expression 20k + 50
What happens to a line when the y-intercept is changed ?
Find the square root of the fraction 64/100
Please help with these two questions thank you.
Which is the correct simplified form of the expression x^1/2y^-1/3/x^1/4y^1/2
Answer:
(A)[tex]\frac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]
Step-by-step explanation:
The given expression is:
[tex]\frac{x^{\frac{1}{2}}y^{\frac{-1}{3}}}{x^{\frac{1}{4}}y^{\frac{1}{2}}}[/tex]
Upon solving the given expression, we get
=[tex]{x^{\frac{1}{2}-\frac{1}{4}}{\cdot}}{y^{\frac{-1}{3}-\frac{1}{2}}}[/tex] (using the property of exponents and powers that if base is same then the powers gets added.)
=[tex]x^{\frac{1}{4}}{\cdot}y^{\frac{-5}{6}}[/tex]
=[tex]\frac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]
which is the required simplified form of the given equation.
Hence, option A is correct.
Leo is going to use a random number generator 400 times. Each time he uses it, he will get a 1 , 2 , 3 , 4 , or 5.What is the best prediction for the number of times that Leo will get an odd number?
Answer:
Close to 240 times but probably not exactly 240 times
Step-by-step explanation:
How many true conditional statements may be written using the following statements?
n is a rational number.
n is an integer.
n is a whole number.
a.
2 conditional statements
c.
4 conditional statements
b.
3 conditional statements
d.
5 conditional statements