The given vector can be expressed as B = B (cos θ x ^ + sin θ y ^)
The strength of the field and its angle with respect to a particular coordinate axis must be known in order to express the magnetic field B using unit vectors. Trigonometry can be applied after this information is known.
Let's utilize trigonometry if the angle we have is with respect to the x-positive axis's side.
cos θ = Bₓ / B
sin θ = B / B
Bx = By cos θ
B_{y} = B sin θ
so the resulting vector is
B = Bₓ i ^ + B_{y} j ^
unit vectors
x ^ = i ^
y ^ = j ^
B = B (cos θ x ^ + sin θ y ^)
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rewrite: [tex]15\frac{1}{6}[/tex] as a decimal. Round to the nearest thousandths.
Answer:
[tex]15 \frac{1}{6}=15.167\:\:\sf(nearest\:thousandth)[/tex]
Step-by-step explanation:
[tex]15 \frac{1}{6}=15+\dfrac{1}{6}[/tex]
Convert ¹/₆ into a decimal by using long division:
[tex]\large \begin{array}{r}0.1\:6\:6\phantom{..}\\6{\overline{\smash{\big)}\,1. 0 \:0\: 0\: \phantom{.}}}\\{-~\phantom{(}\underline{0.6\:0\phantom{-)}}\\0.4\:0\:\:\phantom{))}\\-~\phantom{()}\underline{0.3\:6\:\:\phantom{))}}\\0.0\:4\:0\:\:\phantom{}\\-~\phantom{()}\underline{0.0\:3\:6\:\:\phantom{}}\\0.0\:0\:4\:\:\phantom{}\\\end{array}[/tex]
Therefore, ¹/₆ = 0.166666.....
[tex]\begin{aligned}\implies 15 \frac{1}{6} & =15+\dfrac{1}{6}\\\\& = 15 + 0.166666...\\\\& = 15.166666...\\\\& = 15.167\:\:\sf(nearest\:thousandth)\end{aligned}[/tex]
Find the quotient: (-y5 - 9y) = y
The quotient of the equation (-y5 - 9y) = y
= 0What is Quotient?The term "quotient" is used frequently in mathematics, and it may also refer to a fraction or a ratio as well as the integer portion of a division (in the case of Euclidean division)[2] (in the case of proper division). In the Euclidean division sense, and in the proper division sense, the quotient is "6 with a remainder of 2" when 20 (the dividend) is divided by 3 (the divisor). A quotient in the second meaning is only the proportion of a dividend to its divisor.
According to the given value,
-y*5-9y=y
Mutiply
-5y-9y=y
Combine like terms
-14y=y
Rearrange the terms
-14y -y= O
Combine the terms
-15y =O
divide on both sides
y=o
Hence , the Quotient is 0.
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The quantity z varies directly with y and inversely with x When y = 12 and x = -12, z = -6. What is the value of k, the constant of variation?
Write your answer in the form A or A/B, where A and B are constants or variable expressions.
Answer:
Z = ky/x where y=12, x=-12 and z=-6
-6= k(12)/-12
-k = - 6
K = 6
4x-2y=6 for y in terms of x
Determine f –1(x) if f of x is equal to the quantity x plus 2 end quantity over the quantity x minus 3 end quantity where x ≠ 3.
f inverse of x is equal to the quantity x minus 3 end quantity over the quantity x plus 2 end quantity
b
f inverse of x is equal to the quantity x minus 2 end quantity over the quantity x plus 3 end quantity
c
f inverse of x is equal to the quantity x minus 1 end quantity over the quantity 3 times x plus 2 end quantity
d
f inverse of x is equal to the quantity 3 times x plus 2 end quantity over the quantity x minus 1 end quantity
The inverse function of f(x) = (x + 2)/(x - 3) is given as follows:
[tex]f^{-1}(x) = \frac{3x + 2}{x - 1}[/tex]
How to obtain the inverse function?The function in this problem is defined as follows:
f(x) = (x + 2)/(x - 3).
Using the notation y = f(x), it is given as follows:
y = (x + 2)/(x - 3).
To obtain the inverse, the first step is exchanging the variables x and y, as follows:
x = (y + 2)/(y - 3).
Now the variable y must be isolated to obtain the inverse function, as follows:
xy - 3x = y + 2
xy - y = 3x + 2
y(x - 1) = 3x + 2
y = (3x + 2)/(x - 1).
Hence the inverse function is given by:
[tex]f^{-1}(x) = \frac{3x + 2}{x - 1}[/tex]
Meaning that the fourth option is correct.
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max observes the zoo and the library from a helicopter flying at a height of 300 times square root of 3 feet above the ground, as shown below
The distance between the zoo and library is 600 feet, as seen with the help of concept of applications of trigonometry.
What is the concept of applications of trigonometry?To roof a home, to make the roof slant (in the case of single-family bungalows), to determine the height of the roof in buildings, etc., utilize trigonometry. The navy and aviation industries use it. It's applied to cartography (creation of maps). Trigonometry is also used in satellite navigation systems.Given: height of helicopter = 300√3 feet from the ground.
To find: Distance between zoo and library.
Finding:
(Refer to the image attached.)
Let the distance from the plane to the zoo and library be d1 and d2 respectively.
Then, with the help of concepts of applications of trigonometry,
For the zoo:[tex]tan(60) = \frac{300\sqrt{3}}{d1}[/tex]
=> [tex]\sqrt{3}=\frac{300\sqrt{3}}{d1}[/tex]
=> d1 = 300 feet
For the library:[tex]tan(30) = \frac{300\sqrt{3}}{d2}[/tex]
=> [tex]\frac{1}{\sqrt{3}}=\frac{300\sqrt{3}}{d2}[/tex]
=> d2 = 300 (3) = 900 feet
The distance between zoo and library = d2 - d1 = 900 - 300 = 600 feet.
Hence, the distance between the zoo and library is 600 feet, as seen with the help of concept of applications of trigonometry.
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does someone mind helping me with this? Thank you!
find the vertex and write the quadratic function in vertex form (which our openstax textbook also calls the standard form).
The vertex is (3,16) and the quadratic equation in vertex form is [tex]f(x)=(x-3)^{2}+16\\[/tex].
What is quadratic equation?Any equation in algebra that can be put into standard form is called a quadratic equation (from the Latin quadratus, which means "square").
As well as being referred to as the roots or zeros of the expression on the left-hand side of the equation, the values of x that satisfy it are known as solutions of the equation. There are only two possible answers to a quadratic equation. A double root is said to exist if there is only one solution. In the case where all of the coefficients are real values, there are either two real solutions, one real double root, two complex solutions that are complex conjugates of one another, or all three of the aforementioned options. If complex roots are taken into account, then a quadratic equation will always have two roots, with a double root counting as one. An equivalent equation can be created from a quadratic equation.
Calculations:
[tex]f(x)=x^{2} -6x+25\\ = x^{2} -2.x.3+(3^{2} )-(3^{2} )+25\\=(x-3)^{2} -9+25\\=(x-3)^{2}+16\\[/tex]
Comparing this from the vertex, y=[tex]a[/tex][tex](h-x)^{2} +k\\[/tex]
h=3 and k=16
Hence, vertex is (3,16).
[tex]f(x)=(x-3)^{2}+16\\[/tex]
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Evaluate j(k+2), when j=5 and k=3.
Answer:
25
Step-by-step explanation:
j(k + 2)
5(3 + 2)
5(5)
25
Find the value of x?
Step-by-step explanation:
so, we have a kite here.
a kite is a quadrilateral, that is totally symmetric along one of its diagonals.
the sum of all internal angles of a quadrilateral is always 360°.
remember, the sum of all angles around one point on one side of a line is always 180°.
a full circle airways represents 360°.
the inner angle at 140° is
180 - 140 = 40°
the inner angle at 250° is
360 - 250 = 110°
the inner angles at x and its opposing corner are equal (due to the symmetry) and are in sum with the other 2 inner angles 360°.
so, we have for the inner angles
360 = 110 + 40 + 2×xinner
210 = 2×xinner
the inner angle of x = 105°.
x (the outer angle of the inner angle of x) is
x = 360 - 105 = 255°
Find each angle measure in the figure.
A triangle with angles labeled 4 y degrees, 20 degrees, and left-parenthesis y minus 10 right-parenthesis degrees.
The angle measures are $20\degree$,
°, and
\left(y-10\right)
°.
Question 2
Use the equation to justify your answer.
$20+\left(y-10\right)+4y=$
$y=$
Based on the triangle sum theorem:
20° + (y - 10)° + 4y° = 180
y = 34
What is the Triangle Sum Theorem?The triangle sum theorem states that if we add up all the three interior angles in a triangle, the sum we would get would be equal to 180 degrees.
Given the following are interior angles of a triangle:
4y°(y - 10)°20°Based on the triangle sum theorem, we have the following equation:
20° + (y - 10)° + 4y° = 180
Solve for y
20 + y - 10 + 4y = 180
10 + 5y = 180
5y = 180 - 10
5y = 170
5y/5 = 170/5
y = 34
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Reply and I’ll do your work for you for a week
Answer:
Graph the solution to this inequality on the number line.
0.3(x − 4) > -0.3
Step-by-step explanation:
what is 34-/5=
please help me with this question and i don't know the answer to this
Answer:
34-5=29
Step-by-step explanation:
Answer:
29
Step-by-step explanation:
hope it helps and have a nice day! :)
5 1/2 + 3 4/5 + 1 1/4 =
Answer:
[tex]10\frac{11}{20}[/tex]
Step-by-step explanation:
[tex]5\frac{1}{2} + 3\frac{4}{5} + 1\frac{1}{4}[/tex]
1.Find the LCM(Least Common Multiple).
That would be 20.
2.Multiply so all denominators are equal.
[tex]5\frac{10}{20} + 3\frac{16}{20} + 1\frac{5}{20}[/tex]
3. Add
[tex]9\frac{31}{20}[/tex]
4. Simplify
[tex]10\frac{11}{20}[/tex]
Sally can plant 14 plants in 2 hours. How many plants can Sally plant in 6 hours?
Answer:
42 plants
might be easier to find how many plants are planted in 1 hour then multiply that by 6. In this case, 7 plants will be planted within an hour. So, multiply 7 x 6 to get 42.
Please help will mark brainliest
Answer:135
Step-by-step explanation:6075/45=135 hope this helps
Answer:
135
Step-by-step explanation:
Let x be the number of sessions.
Create an equation.
45x=6075
Divide 45 from both sides.
x=135
135 practice sessions.
Hope this helps! :)
Use a decimal number to fill in the blank. a 16 input mux has _____ select lines.
Use a decimal number to fill in the blank. a 16 input mux has 4 select lines.
What is a decimal number?
A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities. For instance, there is one complete pizza and a half of another pizza in the photograph.How do you write decimal numbers?
To write a decimal in word form, follow these steps:
Write the whole number part.Write "and" for the decimal point.Write the decimal part the same way you would write a whole number.Write the. place value. of the last digit.Learn more about decimal numbers
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The length of the enclosure for the pancake tortoise must be greater than the height. The volume of the enclosure is expressed in terms of the width, w.
w^3+6w^2-40w
Factor the expression, then match the factors to the dimensions they represent.
The factors of the expression w³ + 6w² - 40w = 0 is (w - 4) and (w + 10)
(w - 4) will be the height
(w + 10) will be the length
Given,
The length of the enclosure for the pancake tortoise will be greater than the height, that is: l > h
The volume of enclosure = w³ + 6w² - 40w
Where w is the width.
Now, factorize the expression:
w³ + 6w² - 40w = 0
10 - 4 = 6
10 × (-4) = -40
Therefore, the factors of the expression w³ + 6w² - 40w = 0 is (w - 4) and (w + 10)
Here, we know that length is greater than height.
So, (w - 4) will be the height and (w + 10) will be the length.
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-3(-3v+4w-5) without parentheses
Answer:
Step-by-step explanation:
56/89
giving branliestb: The depth of a local river averages 20 ft, which is represented as |−20|. In January, it measured 6 ft deep, or |−6|, and in July, it was 22 ft, or |−22|. What is the difference between depths in January and July?
2 feet
28 feet
14 feet
16 feet
The difference between depths in January and July is equal to: D. 16 feet.
What is an absolute value function?An absolute value function can be defined as a type of function that consist of an algebraic expression, which placed within absolute value symbols
How to determine the difference between depths?In order to determine the difference between depths, we would calculate the magnitude of the depth for each of the month.
For January, we have:
January depth = 20 - 6
January depth = 14 feet.
For July, we have:
July depth = 20 - 22
July depth = -2 feet.
Now, we can calculate the difference between depths in January and July:
Difference = 14 - (-2)
Difference = 14 + 2
Difference = 16 feet.
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Communicate and Justify:
Tau says that the
sum of -1 3/4 and 2 1/2 is the same as the difference
between 2 1/2 and 1 3/4. Is Tau correct? Explain why
or why not.
Tau is correct, the sum between -(1 ³/₄) and (2 ¹/₂) is equal to the difference between (2 ¹/₂) and (1 ³/₄)
Is Tau correct?
Remember that the sum between a number A and a negative number -B is written as:
A + (-B)
And that is equal to the difference between A and B.
A - B
In this case, Tau says that the sum between:
-(1 ³/₄) and (2 ¹/₂)
Is written as:
(2 ¹/₂) + (-(1 ³/₄) )
(2 ¹/₂) - (1 ³/₄)
And, using the above property, we conclude that this is equal to the difference between (2 ¹/₂) and (1 ³/₄)
So Tau is correct.
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solve the equation show your solution x plus 12 equals 7
Answer:
-5+12=7
Step-by-step explanation:
7-12=-5
Answer:
-5
Step-by-step explanation:
x + 12 = 7
x + 12 - 12 = 7 - 12
x = -5
simplify 9 +(-2)^3
A. 3
B. 1
C.17
Answer:
B
Step-by-step explanation:
9+(−2)^3
=9+ −8
=1
Answer:
b is your answer
Solve for x.
Your answer must be simplified.
X/3>-33
The simplified equation of the X/3 ≥-33 is will be X ≥ -99.
Define Equation simplification:Solving a math problem is another way of saying simplifying an expression. When you simplify an expression, you are attempting to write it in the most straightforward manner feasible. Finally, no more adding, subtracting, multiplying, or dividing should be required.
What is meant by simplification?To make anything simpler or simpler to reduce it to the fundamentals. to reduce in scope or complexity: to streamline management procedures.
Solving:Given = X/3>-33
This can be written as:
X/3 ≥-33
X ≥ -33 * 3
X ≥ -99
The simplified equation of the X/3 ≥-33 is will be X ≥ -99.
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charlotte denning earns both $13/hour and $26 for every sale she completes. during the most recent week, she worked 47 hours and made a total of 71 sales.
The problem solving plan identifies the tester w as "what do you need to do to solve the problem"? Which of the following answer choices are included in the problem solving plan for the letter W?
Check to discover if an issue even exists before attempting to address it. not just to you, but also to those it will effect. You may create the criteria to compare and evaluate the potential remedies by developing an understanding of what makes this a problem in the first place.
What is evaluation of Problem solving?Before programming starts, evaluation enables us to think through a problem's solution, ensure that it satisfies the original design requirements, yields the right answer, and is appropriate for the task at hand.
Three methods can be used to evaluate your problem-solving skills: asking for examples of times you've previously solved an issue; posing you with potential scenarios and asking you to reply; and observing how you use your problem-solving abilities in various exams and activities.
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I need some help with this
The properties used, in order, are:
Distributive.Addition or subtraction property of equality.Addition or subtraction property of equality.multiplicationn or division property of equality.What is used in each step of the demonstration?We start by writing the linear equation:
3*(x + 2) = 4x + 1
The first step is using the distributive property to distribute the left product.
3x + 6 = 4x + 1
Then we use the addition property of equality to subtract 4x in both sides, we will get:
-x + 6 = 1
And we use it again to subtract 6 in both sides:
-x = 1 - 6 = -5
Finally, we multiply both sides by -1 (multiplication property of the equality)
x = 5
That is the solution of the linear equation.
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HELP 50 PTS AND BRAINLY!!!
Answer:
7x
Step-by-step explanation:
The bowling alley charges $8 per person for a bowling party, and they accept parties of 8 to 40
people. Write the equation that best fits the situation. Write the reasonable Domain and Range for the
situation.
The reasonable Domain and Range for the situation.
The Domain of this situation is y ≥ 64 and the Range is 8≤ x ≤40Given that
The bowling alley charges $8 per person for a bowling party.they accept parties of 8 to 40 peoples.To find
he reasonable Domain and Range for the situation.So, according to the question
We have,
The bowling alley charges per person = $8.They just accept parties of 8 to 40 peoples.So, we can say that
Total charges = 8 (total number of peoples in a party)
Let's assume
Total charges = y , and
Total number of peoples in a party = x
Then, we get a equation of this problem,
y = 8x ------------(1)
So, the domain of this equation will be greater then and equal to 64. and range will be greater then and equal to 8 and less then and equal to 40.
Answer:
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what is the total area under the normal curve? a. it depends on the mean b. 0.5 c. 1 d. it depends on the standard deviation
The total area under the normal curve is 1.
Why is there a standard deviation?
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.The more the data is distributed, the greater will be the standard deviation of that data. The standard deviation is used in finance by business owners to understand risk management and make better business decisions. It helps in calculating the margins of error that occur in the survey reports.the total area under the normal curve is 1.
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