To express the vector v = (-7,8) in the form (|v|cosθ, |v|sinθ), you first correctly found the magnitude |v| using the Pythagorean theorem. Then, to find the angle θ, use the arctangent function applied to the y/x components of your vector. Ensure the angle is in the correct quadrant by modifying it if necessary.
Explanation:To find the magnitude of the vector v = (-7,8), you've correctly done the Pythagorean theorem and found sqrt(113), which is the absolute value of your vector, written as |v|. Now, to express the vector in the form (|v|cosθ, |v|sinθ), we need to find the angle θ. This is found using the arctangent function (also known as the inverse tangent or atan). θ = atan(y/x), where x and y are the x and y components of your vector respectively. Be careful with the sign as atan can only return values from -π/2 to π/2.
In your case θ = atan(8/-7), but since this gives a negative answer and the vector is in the second quadrant where angles are positive, you should add π to your result to get the correct angle. Then you can substitute |v| and θ into the expressions for the x and y components.
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Photography World has a portrait special. A three-pose portrait package has a sitting fee of $35, and a six-pose package has a sitting fee of $60. On a Saturday, $690 was collected in sitting fees. Which equation can be used to represent x, the number of three-pose portrait packages and y, the number of six-pose portrait packages?
The equation that can be used to represent the number of three-pose and six-pose portrait packages is: 35x + 60y = 690
What are word problems?Word problems in mathematics are methods and approaches applied in solving real-life scenarios. Data can be modeled from the certain information given.
From the parameters given, Let us assume that:
x represents a three-pose portrait package that has a sitting fee of $35y represents a six-pose package that has a sitting fee of $60Now, on Saturday a total amount of 690 was collected. This data can be modeled as:
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Whats the unit rate of $3.60
Listed below are four different cases in which a comparison of means was conducted. match the case to the appropriate set of equations needed to compare the means.
The cases can be categorized by comparing the means as follows: 'B. Two proportions' apply to situations like income bracket and voter likelihood comparison, 'C. Matched pairs, dependent groups' apply to dependent groups like a math test given to third graders, 'D. exclusive groups' represent separate unaffected and experimental groups, and 'A. Two independent means, normal distribution' refers to situations where two separate groups are compared.
Explanation:From the details given, we can classify the cases by comparing the means as follows:
B. Two proportions: This would apply to the question of politicians comparing the proportion of individuals from different income brackets who might vote for them. It implies two independent groups and hence a comparison of two population proportions. C. Matched pairs, dependent groups: This could describe a scenario like a math exam given to the third-grade children attending ABC school. Two random samples of scores were taken. This represents a dependent groups design in which two means are compared, for instance before and after a treatment. D. exclusive groups: These likely represent two independent means involving separate unaffected (control) groups and experimental groups. An example of this is studies that compare various diet and exercise programs. A. Two independent means, normal distribution: This refers to a situation where two separate groups are compared, such as studies involving independent samples where the sample values selected from one population are not related in any way to the sample values selected from the other population. Learn more about Comparison of Means here:
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Solve the equation.
-3(y - 5) = 24
y = ______?
The value of Equation is y = -3.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have Equation,
-3(y-5) = 24
Now, solving for y
Divide both side by (-3) we get
-3(y-5) / (-30= 24/ (-3)
y-5 = -8
Add 5 to both side
y- 5 +5 = -8 + 5
y = -3
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six people share 3/5 pound of peanuts equally. What fraction of a pound of peanuts does each person recieve?
Convert 95 pints to gallons. Round to one decimal point. Please show your work
What is five times two
convert 0.045 to a fraction
Find 3/7⋅9/10 . Write your answer as a fraction in simplest form.
The value of the multiplication of the fractions will be equal to 27 / 70.
What is multiplication?Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the fractions are 3/7 and 9/10. The multiplication of the number will be calculated as,
M = 3 / 7 x 9 / 10
M = 27 / 70
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28 is 32% of what number?
divide:
28 / 0.32 = 87.5
Yolanda's club has 50 members. It's rules require that 60% of them must be present for any vote. At least how many members must be present to vote?
Given quadrilateral XYWZ determine whether WX and YZ are parallel, perpendicular, or niether. W(0,-3), X(-1,5), Y(2,5), Z(-1,2)
Question 26(multiple choice worth 1 points) (02.02) simplify . −4 4
Twice the sum of a number and 3 is the same as 5 subtracted from the number. find the number.
Twice the sum of a number and 3 is the same as 5 subtracted from the number. Then the number will be -11.
Sum refers to the addition of terms, while subtraction means removal.
Let the number be x
Following the given information:
sum of a number and 3 = x+3
Expression 1
Twice the sum of a number and 3 =2(x+3)
Expression 2
5 subtracted from the number=x-5
On equating both the expressions as follows:
2(x+3)=x-5
Solving the equation to get the value of x:
2x+6=x-5
2x-x=-5-6
x=-11
Thus, the number is -11.
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5/8 divided by 5 3/4
Which equation correctly applies the distributive property?
A. 2.4⋅(−3.4)⋅(−1.25)=−3.4⋅2.4⋅(−1.25)
B. −3⋅(6.48)=(−3⋅6)+(−3⋅0.4)+(−3⋅0.08)
C. −2.5⋅(4⋅3.67)=(−2.5⋅4)⋅3.67
D. (42⋅3.5)+(42⋅1.3)+(42⋅5.2)=42+(3.5+1.3+5.2)
Answer:
B
Step-by-step explanation:
In isosceles ∆ABC the segment BD (with D ∈ AC ) is the median to the base AC . Find BD, if the perimeter of ∆ABC is 50m, and the perimeter of ∆ABD is 40m.
The length of the height triangle ABC is BD i.e., [tex]15\;units[/tex].
According to the question, In isosceles [tex]∆ABC[/tex] the segment BD is the median to the base AC . Also, the perimeter of ∆ABC is 50m, and the perimeter of the triangle [tex]ABD[/tex] is 40m.
Let the length of the equal sides of the isosceles triangle be [tex]x \;meters[/tex] and the length of the base of the isosceles triangle is [tex]2y\;meters[/tex].
[tex]Perimeter_{ABC}=x+x+2y\\2x+2y=50\\x+y=25\\x=25-y----(i)[/tex]
Also,
[tex]Perimeter_{ABD}=x+y+BD\\x+y+\sqrt{x^2-y^2}=40\\x+y+\sqrt{(25-y)^2-y^2}=40\\25+\sqrt{625-50y}=40\\\sqrt{625-50y}=15\\625-50y=225\\y=8\;units[/tex]
So,
[tex]x=25-8\\x=17\;units[/tex]
Now,
[tex]BD=40-x-y\\BD=40-17-8\\BD=15\;units[/tex]
Hence, the length of the height triangle ABC is BD i.e., [tex]15\;units[/tex].
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Dakota runs a half-marathon every 6 weeks, and Madison runs a half-marathon every 15 weeks. If they start now, in how many weeks will they again be running a half marathon at the same time?
Answer:
30 weeks
Step-by-step explanation:
Given : Dakota runs a half-marathon every 6 weeks,
Madison runs a half-marathon every 15 weeks
To Find : . If they start now, in how many weeks will they again be running a half marathon at the same time?
Solution :
Since Dakota runs a half-marathon every 6 weeks, Madison runs a half-marathon every 15 weeks
So, to calculate If they start now, in how many weeks will they again be running a half marathon at the same time
We will take the LCM (lowest common factor) of 6 and 15
3 | 6,15
2 | 2,5
5 | 1,5
| 1,1
LCM = 3*2*5 =30
The LCM of 6 and 15 is 30
So, If they start now, in 30 weeks they will again be running a half marathon at the same time
A vector a has a magnitude of 60m and directed as shown. find the x and y components of this vector
Final answer:
To find the x and y components of a vector, use the cosine and sine functions, respectively, with the given angle. For a vector of 60m at 38°, the components are approximately 47.28m (x) and 36.96m (y).
Explanation:
To find the x and y components of a vector given its magnitude and a direction, you can use trigonometric functions. Assuming the vector Δr is the one you're referring to, with a magnitude of 60m and an angle of 38° (from the x-axis, presumed direction), you can apply the cosine function for the x-component and the sine function for the y-component of the vector.
For the x-component: x = magnitude × cos(angle) = 60m × cos(38°) = 60m × 0.788 = 47.28m
For the y-component: y = magnitude × sin(angle) = 60m × sin(38°) = 60m × 0.616 = 36.96m
Therefore, the x and y components of the vector are approximately 47.28m and 36.96m, respectively.
ax+3x=bx+5 what is the answer for x
Suppose that in a particular sample, the mean is 70.07 and the standard deviation is 10.27. what is the z score that corresponds to a raw score of 80?
The librarian, Ms. Barrett, wants to buy new books for the school library. She posts a sign in the library to raise money, and 75 students donate $0.50 each for the book drive. If she splits the money donated evenly between two genres (fiction and non-fiction), how much money does she have to spend on each genre? A) $18.75 B) $187.50 C) $28.50 D) $37.50
Answer:
A
Step-by-step explanation:
if x -6 is one factor of x^2 - 10x +24, which is the other factor?
write an expression that represents the product the of q and 5 divided by 2
There are 691 students at Palmer Elementary School and 1,293 students at Palmer Middle School. About how many students are there in all at both school?
There are 1,984 students in total at Palmer Elementary School and Palmer Middle School combined, showing an example of increasing school enrollments. This is calculated by simply adding the number of students from both schools.
Explanation:Calculating the Total Number of Students
To find out how many students are in all at both Palmer Elementary School and Palmer Middle School, we add the number of students at each school together. Palmer Elementary School has 691 students, and Palmer Middle School has 1,293 students.
To determine the total, we perform the following addition:
691 (Palmer Elementary School students)+ 1,293 (Palmer Middle School students)= 1,984 students in totalTherefore, there are approximately 1,984 students in total at both schools combined. This calculation helps us understand the scale of student populations within a small section of the education system, reflecting broader national trends where school enrollments are increasing.
Using mental math, the approximate tip to leave for a bill of $81.79, if you tip 15% would be _____..
4 1/2 + 8 3/4
A. 12 2/3
B. 12 1/3
C. 13 1/4
D. 13 2/3
4 1/2 + 8 3/4
4+8 = 12
1/2 + 3/4 = 2/4 + 3/4 = 5/4 = 1 1/4
12 + 1 1/4 = 13 1/4
Answer is C
The point (2, -3) lies in quadrant I II III IV
Write a number sentence to show the distributive property. 7x6=
Answer:
According to the distributive property of multiplication,
a . (b + c ) = (a . b) + (a . c)
Given: 7 × 6
which can be rewritten as: a) 7 . (4 + 2), b) 7 . (3 + 3), c) 7 . (1 + 5)
Rewriting the given expression using the distributive property of multiplication:
a) 7 . (4 + 2) = (7 . 4) + (7 . 2)
7 . (6) = 28 + 14
42 = 42
b) 7 . (3 + 3) = (7 . 3) + (7 . 3)
7 . (6) = 21 + 21
42 = 42
c) 7 . (1 + 5) = (7 . 1) + (7 . 5)
7 . (6) = 7 + 35
42 = 42
As the left hand side is equal to the right hand side in each case, therefore, it proves the distributive property.
Find the critical numbers of the function. (Enter your answers as a comma-separated list.)
f(θ) = 8sec θ + 4tan θ, 0 < θ < 2π
The critical numbers of the function f(θ) = 8sec(θ) + 4tan(θ) are where the derivative is undefined, specifically at θ = π/2 and θ = 3π/2.
Explanation:To find the critical numbers of the function f(θ) = 8sec(θ) + 4tan(θ), we need to take its derivative and set it equal to zero or find where the derivative does not exist. First, we compute the derivative of the function. Recall that the derivative of sec(θ) is sec(θ)tan(θ) and the derivative of tan(θ) is sec2(θ).
Thus, the derivative f'(θ) is 8sec(θ)tan(θ) + 4sec2(θ). We look for where this derivative is undefined or equal to zero. The derivative is undefined when sec(θ) is undefined, which occurs at θ = π/2 and θ = 3π/2. To find where the derivative is zero, we can factor out 4sec(θ):
4sec(θ)(2tan(θ) + sec(θ)) = 0
The second factor will never be zero because sec(θ) and tan(θ) will not be zero for the same θ in the interval given. Therefore, the critical numbers are where the derivative is undefined, which is θ = π/2 and θ = 3π/2.
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