The angle that the vector [tex]\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}[/tex] makes with the y-axis is (B) tan⁻¹ 2/3.
What do we mean by a vector?Vector is a colloquial term in mathematics and physics that refers to some quantities that cannot be expressed by a single number (a scalar) or to elements of some vector spaces.Vectors were first used in geometry and physics (typically in mechanics) to represent quantities with both a magnitude and a direction, such as displacements, forces, and velocity. In the same way that distances, masses, and time are represented by real numbers, such quantities are represented by geometric vectors.To find the angle of the given vector:
Given: [tex]\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}[/tex]
So,
[tex]\begin{aligned}&\overrightarrow{\mathrm{A}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}} \\&\overrightarrow{\mathrm{A}} \cdot \hat{\mathrm{j}}=\sqrt{13} \cos \theta \\&3=\sqrt{13} \cos \theta \\&\theta=\cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\end{aligned}[/tex]
Using the formula [tex]\tan \left(\cos ^{-1} x\right)=\frac{\sqrt{1-x^2}}{x}[/tex], we obtain:
[tex]\begin{aligned}&\theta=\tan ^{-1} \frac{\sqrt{1-\frac{9}{13}}}{\frac{3}{\sqrt{13}}} \\&\theta=\tan ^{-1}\left(\frac{2}{3}\right)\end{aligned}[/tex]
Therefore, the angle that the vector [tex]\overrightarrow{\mathrm{A}}=22_1^{\mathrm{A}}+3 \hat{\mathrm{j}}[/tex] makes with the y-axis is (B) tan⁻¹ 2/3.
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The correct question is given below:
The angle that the vector [tex]\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}[/tex] makes with the y-axis is:
(A) tan⁻¹ 3/2
(B) tan⁻¹ 2/3
(C) sin⁻¹ 2/3
(D) cos⁻¹ 3/2
-5/9 - (-7/27)
Can someone help
Answer:
[tex]\frac{-8}{27}[/tex]
Step-by-step explanation:
[tex]\frac{-5}{9}[/tex] - [tex]\frac{-7}{27}[/tex] Subtracting a negative is the same as adding a positive. So I would change the form to addition.
[tex]\frac{-5}{9}[/tex] + [tex]\frac{7}{27}[/tex] Now to add, we need a common denominator. Let's us 27
[tex]\frac{-5}{9}[/tex] = [tex]\frac{-15}{27}[/tex] We multiple the numerator and denominator (top and bottom) by 3 to make an equivalent fraction.
[tex]\frac{-15}{27}[/tex] + [tex]\frac{7}{27}[/tex] the bottom number stays the same and we add the top numbers
-15 + 7 = -8
[tex]\frac{-8}{27}[/tex]
Answer: -8/27
Step-by-step explanation:
[tex]\displaystyle\\-\frac{5}{9} -(-\frac{7}{27} )=\\\\-\frac{5*3}{9*3} +\frac{7}{27} =\\\\\frac{-15}{27}+\frac{7}{27}=\\\\ \frac{-15+7}{27}=\\\\ \frac{-8}{27} =\\\\-\frac{8}{27}[/tex]
You are given two wind instruments of identical length. one is open at both ends, whereas the other is closed at one end. which is able to produce the lowest frequency?
The wind instrument with the closed end.
Why is it known as a node?
Node is the actual name in use. It was initially intended to be used as a web application, but the author changed the name to node after realizing it could be applied to a variety of situations.
Pipe standing wave resonances exhibit a number of intriguing characteristics. When sounding a resonance, the closed end of the pile must have a "node." An "anti-node" is required if a pipe's end is open.The lowest frequency resonance occurs in the case of a pipe that is closed at one end when there is just one node at the closed end and an anti-node at the other end. This sound has a wavelength that is four times as long as the pipe. This is referred to as a quarter-wave resonator.When a pipe is opened on both ends, the lowest frequency resonance has an anti-node at either end and a node in the center. A half-wave resonance is present here; The pipe is able to contain half of the wavelength. The frequency of this resonance will be twice that of the closed pipe if this pipe is the same length as the closed pipe.Learn more about node
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answer this question
Answer: 166
We’ll give it your best mate keep it up
The percentage of organ donors who died from drug overdoses changed by 9.34% - 1.10% =8.24% between 2000 and 2015. what is this as a percentage of donors dying from drug overdoses in 2000?
The current percentage in comparison to in the year 2000 is 88.22%.
We are given the percentage of death in the year 2000, 2015 and the difference. Now, we have to find the percentage of donors between change and the original deaths in the year 2000.
To find this, we will use the following formula -
Percentage change = Difference between the percentage change in the year 2000 to 2015 ÷ Percentage of deaths in the year 2000 ×100
Now, keep the values in formula to find the percentage change.
Percentage change = [tex]\frac{8.24}{9.34} *100[/tex]
Performing division to find the percentage change
Percentage change = 0.882*100
Further performing multiplication to get the answer in the form of percentage
Percentage change = 88.22%
Hence, the comparison of difference with the percentage of donors dying from drug overdoses in 2000 is 88.22%.
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Bruce made 6 pans of brownies. He cut each pan into 9 brownies. How many brownies did Bruce end up with?
Answer:
54
Step-by-step explanation:
9 x 6 = 54 Bruce will end up with 54 brownies if he cuts each of the 6 brownie pans of brownies into 9.
A plumber needs to install handles in 9 sinks. Each sink has a hot water handle and a cold water handle.he has 19 handles. Does he have enough handles?
The plumber has enough handles to install the entire 9 sinks
How to calculate the amount of handles needed for installation ?A plumber needs to install handles in 9 sinks
Each sink has a hot water handle and a cold water handle, that means each sink will require 2 handles. This means the multiplication of 9 and 2
= 9 × 2
= 18
The plumber has a total of 19 handles and 18 handles are required for the installation. This means that he has enough handles and he will be left with one handle.
Hence, there will be enough handles for the installation.
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Passes through (-3,2) and perpendicular to the line containing (2,3) and (1,-2)
Answer:
(1,-2)
Step-by-step explanation:
Passes through (-3,2) and perpendicular to the line containing (2,3) and
What is 4/7-(-3/8) ?
_____________________
Solution:
Exact Form:
[tex]\frac{4}{7}-(-\frac{3}{8}) = \frac{53}{56}[/tex]
______________________
(^Note^)
To subtract fractions, find the LCD (Least Common Denominator), then combine.
Hope this helps! If so, please lmk! Thanks and good luck!
Answer: 53/56
Step-by-step explanation:
sorry if im wrong but since there is 2 negative signs it is going to become positive. so..
4/7+3/8
then make the denominators the same (56)
then multiply the numerators by the number you multiplied for the denominator for the question.
answer: 32/56+21/56 = 53/56
Use the numbers 1,2,3,4,5,6 to fill in the circles to make the equations true. Use each number once.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Write a function to describe the following scenario.
A taxi driver charges a flat rate of $7.25 plus
$0.65 per mile.
y = [?] + [?]x
Answer: Taxi driver has at most $10 to spend on the cab ride, he can travel at most 12.7 miles.
Step-by-step explanation:
A Taxi driver charges a flat rate = 7.25 dollars
taxi fare for 1 mile = 0.65 dollars
Suppose we consider Total money taxi driver can spend = 10 dollars
Let taxi driver travel x miles
Total charges = flat rate charge + taxi fare for each mile(distance) travelled
Find the value y = [?] + [?]x
suppose these two question marks indicate z1,z2
replace with y=10 and z1=1.75 and z2=0.65 values
Then y = [z1] + [z2]x
10 = 1.75 + 0.65(x)
0.65(x) = 10 - 1.75
0.65(x)= 8.25
x = 8.25/0.65
x = 12.7 miles
If Taxi driver has at most $10 to spend on the cab ride, he can travel at most 12.7 miles.
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Can someone please help me? :(
What you have to do first is you have 5 owners correct? well you take anything they are sharing in the case it is delay/debt. so you divide $110 by 5 and you should get the amount $22. This means that each owner has to pay $22 to the delay.
what value of x makes the equation 2(3 - 7x) = 4 - 6x true?
Linear equations are equations that has a leading degree of 1. The value of x that makes the equation true is 1/4
Solving linear equationsLinear equation are equations that has a linear degree of 1. The standard linear equation is y = mx + b
Given the expression below
2(3 - 7x) = 4 - 6x
Expand
6 - 14x = 4 - 6x
Collect the like terms
6 - 14x = 4 - 6x
-14x + 6x = 4 -6
-8x = -2
Divide both sides by -8
-8x/-8 = -2/-8
x = 1/4
Hence the value of x that makes the equation true is 1/4
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If you have the x and y components of a vector, which trigonometry function can you use to determine its angle relative to the x-axis?.
If we have the x and y components of a vector, the trigonometry function that can be used to determine its angle relative to the x-axis is cosine function.
For given question,
Let α be an angle between vector a and vector b.
The angles between two vectors is given by,
cos(α) = [tex]\frac{\vec a . \vec b}{|\vec a | | \vec b|}[/tex]
The x component of vector is usually denoted by [tex]\vec i[/tex]
Let vector be [tex]x\vec i + y\vec j[/tex]
Let [tex]\vec a=\vec i, ~ \vec b=x\vec i + y\vec j[/tex]
[tex]\vec a . \vec b=x[/tex]
[tex]|\vec a|=1[/tex]
[tex]|\vec b|=\sqrt{x^2+y^2}[/tex]
So, the angle between the vector and x-axis is [tex]cos^{-1}(\frac{x}{\sqrt{x^2+y^2} } )[/tex]
Therefore, if we have the x and y components of a vector, the trigonometry function that can be used to determine its angle relative to the x-axis is cosine function.
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The Oompa-Loompas are 4
inches tall when they are
children. The Hyperion tree is
1,000 times greater in height.
How tall is the Hyperion tree?
Answer:
4000inches
Step-by-step explanation:
1000*4 = 4000inches
Answer: 4,000 inches
Step-by-step explanation:
this is because 4 times 1000 is 4000 so the Hyperion tree would be 4000 inches tall
What is the quotient -3 divided by 9 fractions
Answer:
well it would be [tex]-\frac{1}{3}[/tex]
Step-by-step explanation:
Simply put [tex]-\frac{3}{9}[/tex]. The top and bottom are divisible by 3 so you simplify and you end up with negative one third.
help pls! example is not needed
Answer: 401
Step-by-step explanation:
-177 + 578 = 401
Write 0.5 as a fraction. Do not try to simplify your answer.
Answer:
1/2
Step-by-step explanation:
0.5 is half of 1 so 1/2 is 0.5 as a fraction
1. √256
O 12
14.
016h
O 18
Answer:
16
Step-by-step explanation:
[tex]16^{2} =256[/tex]
Solve 7x2 - 2x = −3
Please
Answer:
I think the answer to this question is the last multiple choice answer
Step-by-step explanation:
Researchers wanted to determine if there was an association between the level of happiness of an individual and their risk of breast cancer. The researchers studied 1813 people over the course of 5 years. During this 5-year period, they interviewed the individuals and asked questions about their daily lives and the hassles they face. In addition, hypothetical scenarios were presented to determine how each individual would handle the situation. These interviews were videotaped and studied to assess the emotions of the individuals. The researchers also determined which individuals in the study experienced any type of breast cancer over the 9-year period. After their analysis, the researchers concluded that the happy individuals were less likely to experience breast cancer. (a) What type of observational study was this? Explain. (b) What is the response variable? What is the explanatory variable?
The answers to all the subparts of the question are shown below.
What is an observational study?An observational study is used in fields such as epidemiology, social sciences, psychology, and statistics to draw conclusions from a sample to a population where the independent variable is not under the researcher's control due to ethical concerns or logistical constraints. One common observational study is about the potential effect of a treatment on subjects, where the assignment of subjects to a treated versus a control group is beyond the investigator's control.(A) What type of observational study was this?
Because all information about the individuals was gathered at one point in time, this was a cross-sectional study.(B-1) What is the response variable?
Whether or not the woman has IDC breast cancer is the response variable. The qualitative response variable is used.(B-2) What is the explanatory variable?
Whether or not the woman has IDC breast cancer is the explanatory variable.Therefore, the answers to all the subparts of the question are shown.
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Approximate 5√3 to the nearest tenth.
A local hamburger shop sold a combined total of 380 hamburgers and cheeseburgers on Saturday. There were 70 fewer cheeseburgers sold than hamburgers.
How many hamburgers were sold on Saturday?
Answer:
310 hamburgers were sold on Saturday
Step-by-step explanation:
1x + 70 =380
-70 -70 Reverse
1x = 310
/1 /1 Divide
x =310
What is the value of 1/4(38-14)+3^3 divided by 9?
Answer:
9
Step-by-step explanation:
[tex]38-14\\\bold{24}\\\rightarrow 1\div \:4\cdot \:24+3^3\div \:9\\3^3\\\bold{27}\\\rightarrow 1\div \:4\cdot \:24+27\div \:9\\1\div \:4\cdot \:24\\\frac{1}{4}\cdot \:24\\\bold{6}\\\rightarrow 6+27\div \:9\\27\div \:9\\\bold{3}\\6+3\\=9[/tex]
Shantira is thinking of a number n, and she wants her sister to guess the number. her first clue is that nine less than five times her number is at least six and at most twenty-one. write a compound inequality that shows the range of numbers that shantira might be thinking of
The value of the integer number n is greater than 5 and less than 9.
Inequality is simply a type of equation that does not have an equal sign in it. Inequality is defined as a statement about the relative size as we will as is use it to compare two statements.
Simplification is to make something easier to do or understand and to make something less complicated.
Shantira is thinking of a number n.
Her first clue is that six less than six times her number is between twenty-four and forty-eight.
Let n be the integer number.
Then according to the condition,
Her first clue is that six less than six times her number is between twenty-four and forty-eight.
24 < 6n - 6 < 48
Add 6, then
30 < 6n < 54
Divide it by 6
5 < n < 9
So the value of the integer number n is greater than 5 and less than 9.
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Find the centroid of the region in the first quadrant bounded by the given curves. y = x4, x = y4
The given bounded region is the set
[tex]R = \left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^4 \le y \le x^{1/4} \right\}[/tex]
assuming the curves are [tex]y=x^4[/tex] and [tex]x=y^4\implies y=x^{1/4}[/tex] (since [tex]x>0[/tex] in the first quadrant).
The coordinates of the centroid are [tex](\bar x, \bar y)[/tex] where [tex]\bar x[/tex] and [tex]\bar y[/tex] are the average values of [tex]x[/tex] and [tex]y[/tex], respectively, over the region [tex]R[/tex]. These are given by the ratios
[tex]\bar x = \dfrac{\displaystyle \iint_R x \, dA}{\displaystyle \iint_R dA} \text{ and } \bar y = \dfrac{\displaystyle \iint_R y\,dA}{\displaystyle \iint_R dA}[/tex]
Compute the area of [tex]R[/tex].
[tex]\displaystyle \iint_R dA = \int_0^1 \int_{x^4}^{x^{1/4}} dy \, dx \\\\ ~~~~~~~~ = \int_0^1 \left(x^{1/4} - x^4\right) \, dx \\\\ ~~~~~~~~ = \frac45 - \frac15 = \frac35[/tex]
Integrate [tex]x[/tex] and [tex]y[/tex] over [tex]R[/tex].
[tex]\displaystyle \iint_R x \, dA = \int_0^1 \int_{x^4}^{x^{1/4}} x \, dy \, dx \\\\ ~~~~~~~~ = \int_0^1 x \left(x^{1/4} - x^4\right) \, dx \\\\ ~~~~~~~~ = \int_0^1 \left(x^{5/4} - x^5\right) \, dx \\\\ ~~~~~~~~ = \frac49 - \frac16 = \frac5{18}[/tex]
[tex]\displaystyle \iint_R y \, dA = \int_0^1 \int_{x^4}^{x^{1/4}} y \, dy \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 \left((x^{1/4})^2 - (x^4)^2\right) \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 \left(x^{1/2} - x^8\right) \, dx \\\\ ~~~~~~~~ = \frac12 \left(\frac23 - \frac19\right) = \frac5{18}[/tex]
Then the centroid's coordinates are
[tex]\bar x = \dfrac{\frac5{18}}{\frac35} = \boxed{\frac{25}{54}} \approx 0.463[/tex]
[tex]\bar y = \dfrac{\frac5{18}}{\frac35} = \boxed{\frac{25}{54}}[/tex]
Find the sum of 2.53 x 1019 and 3.197 x 1017. 2.56197 x 1019 3.2223 x 1019 2.56197 x 1036 3.2223 x 1036
17716.09385 is sum of multiplication .
What does multiply mean?
Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.= 2.53 x 1019 + 3.197 x 1017 + 2.56197 x 1019 + 3.2223 x 1019 + 2.56197 x 1036 + 3.2223 x 1036
= 2578.07 + 3251.349 + 2610.64743 + 3283.5237 + 2654.20092 + 3338.3028
= 17716.09385
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Answer:
180
Step-by-step explanation:
Because its true
Find the largest possible area for a rectangle with base on the x-axis and both upper vertices are on the curve y=11-x^2
The largest area of rectangle can be A= (11√11)/√2
What is area of rectangle?To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
Area = l × w. l = length. w = width.
Given:
y=11-x²
Consider,
x is the length of the base
y is the vertices on the curve (width)
As, the area of a rectangle with its base on the x-axis.
So, base =2x
Then Area of rectangle
A = 2x(11-x²)
Foe maximum area, dA/dx=0
dA/dx = 22-4x²
22-4x² =0
22=4x²
11/2 = x²
x=√(11/2)
Now, Put x=√(11/2) in area
A= 2*√(11/2) ( 11-11/2)
A= √22(11/2)
A= (11√11)/√2
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BELL RINGER # 6
If the function f is defined by f(x) = 3x + 4,
then 2 f(x) + 4 =
(A) 5x + 4
(B) 5x + 8
(C) 6x +4
(D) 6x+8
(E) 6x + 12
Answer:
(E) 6x+12
relations: A relation R is the subset of the cartesian product of X x Y, where X and Y are two non-empty elements. It is derived by stating the relationship between the first element and second element of the ordered pair of X × Y. The set of all primary elements of the ordered pairs is called a domain of R and the set of all second elements of the ordered pairs is called a range of R.
functions: A relation ‘f’ is said to be a function, if every element of a non-empty set X, has only one image or range to a non-empty set Y.
f(x) = 3x + 4
2 * f(x) + 4 = (2 × f(x)) + 4
From above equation
= (2 × (3x + 4)) + 4
= (2 × 3x) + (2 × 4) + 4
= 6x + 8 + 4
= 6x + 12
Therefore, the value of 2f(x) + 4 is ′6x + 12′.
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Travis painted for 6 2/3 hours. He received $27 an hour for his work. How much was Travis paid for doing this painting job?
Answer:
$180
Step-by-step explanation:
Well because it is $27 per hour, you can start with the whole hours:
6*27=162
then because you are working with fractions you can find what 1/3 of 27 is:
27* (1/3)=9
this tells us that one-third of an hour is worth 9 dollars but because it is 2/3 then you just add another 9. This means 2/3 of 27 is 18.
Then you just add it all up:
162+18=180
Last year, 63 new houses were built in a neighborhood. So far 6/7 of them have been sold. How many new houses have been sold this year?
Write your answer in simplest form
Answer is 54. Here is a trick for you. Write 63 as a fraction, with the denominator as 1. 63/1. Then insert the fraction you are calculating, 6/7: (6*63)/7*1. Do the multiplication, 6*63=378, 7*1=7. Then write as 378/7. What's 378/7? Your answer 54.
