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
If 1 can of ketchup contains 13 cups, how many are there in 3.5 cans
Answer:19.5
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer: 45.5
Step 1: 13 cups x 3.5 can = 45.5 cups
Jubaraj and Kristopher need to buy new pencils for school. Their old pencils are less than 2 inches long. They found a bargain on pencils at a local store. Four pencils cost $1.00, including tax. If the boys buy 12 pencils, how much will they pay?
Answer:
3
Step-by-step explanation:
4 pencil = 1$
we need 12
So: 12÷4=3
3x1$= 3$
Help i am so confused and I need this asap!!
Answer:
25 tickets were purchased ahead of time
Explanation and Check part below
Hope this helps :)
Step-by-step explanation:
1)
25
× 11
------
275
2)
625
-275
--------
350
3)
350 ÷ 14 = 25
Check:
350 (dollars from purchased ahead of time)
+275 (dollars from purchased at the door)
--------
$ 625 (total ticket sales stated in the word problem)
ok, help me out with this one
A zebra runs 600ft per 10 seconds, how many miles per hour does it run?
Answer: 40.91 mph
Step-by-step explanation:
600 ft/10 seconds=
600*6 ft/(10*6) seconds=
3600 ft/60 seconds=
3600 ft/1 minute =
3600*60 ft/(1*60) minute=
216000 ft/60 minutes=
216000 ft/hour=
(216000/5280) miles/hour= 40.91 mph
Solve for the value of e.
see picture below!!
Answer:
11
Step-by-step explanation:
90=55+3e+2
33=3e
e=11
What is 0.29 as a fraction in simplest form ?
Answer:
Step-by-step explanation:
0.29 as a fraction is 29/100. Anytime you have a decimal, just turn it into a whole number and simplify it. However, 29/100 is already in its simplest form.
Which of the following statements about the box-and-whisker plot below is not true? 70 72 74 76 78 80 02 16 O The midrange of the data set shown is 85.5. O Both 72 and 99 are values in the set of data. The median of the data set shown is 81. 94 There are fewer data points in the lower two quartiles than in the upper two quartiles.
The false statement regarding the box-and-whisker plot is given by:
There are fewer data points in the lower two quartiles than in the upper two quartiles.
What is the missing information?The box-and-whisker plot is not given for this problem, but from it, we have that:
The minimum value is 72.Q1: 75.Median: 81.Q3: 90.Maximum: 99.What does a box-and-whisker plot shows?A box and whisker plot shows five things:
The minimum value.The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The maximum value.The false statement is:
There are fewer data points in the lower two quartiles than in the upper two quartiles.
Because 50% values are below the median and 50% are above, meaning that there is an equal number of data points in the lower two quartiles than in the upper two quartiles.
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Hi I need help solving and graphing this. Both in interval and set builder notation as well 4<2y+6<10
Answer:
Step-by-step explanation:
5 Read what Alicia says.
The angles of this pentagon are 100°, 105°, 72°, 126° and 127°.
Explain why she must be wrong.
Answer:
all the angles of the pentagon do not add up to 540
Step-by-step explanation:
total degree in a shape
180 × (n-2) where n is the number of side
a pentagon has 5 sides so
180 × (5-2)
= 540
100+105+72+126+127= 530
all the angles of the pentagon do not add up to 540
Find the mean of the integers: 11, -7, -14, 10, 5
The mean of the integers in the set of numbers is 1
How to calculate the mean ?Mean can be described as the average of a set of numbers
The integers are given as 11, -7, -14, 10 , 5
The mean can be calculated as follows
11 + (-7) + (-14) + 10 + 5/5
= 5/5
= 1
Hence the mean of the integers is 1
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How do I find the value of x that make lines u and v parallel
=======================================================
Explanation:
The square marker in the top left corner tells us we have a 90 degree angle. The 8x+10 must also be 90 degrees for lines u and v to be parallel. Refer to the alternate exterior angle theorem. Ignore the diagonal lines. Your teacher likely put them there as a distraction.
8x+10 = 90
8x = 90-10
8x = 80
x = 80/8
x = 10
Which is the graph of 5x+4y ≥ 2?
Answer:
b
Step-by-step explanation:
5x + 4y [tex]\geq[/tex] 2
4y [tex]\geq[/tex] - 5x + 2
y [tex]\geq[/tex] (-5/4)x + (1/2)
Point S is located at -10. Points T and U are each 5 units away from point S. Where are T and U located?
Triangle ABC with coordinates A (3, 4), B (7, 7), and C (8, 1) is translated 6 units left and 7 units down. What is the new coordinate for Point A'?
The new coordinate for Point A' is A' = (-3, -3)
How to determine the new coordinate for Point A'?The coordinates of the triangle are given as:
A (3, 4), B (7, 7), and C (8, 1)
The translation is given as:
6 units left and 7 units down
This can be represented as:
(x, y) = (x - 6, y - 7)
When the above translation rule is applied on vertex A, we have:
A' = (-3, -3)
Hence, the new coordinate for Point A' is A' = (-3, -3)
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Due tomorrow Help Please
how any tablespoon of kernals per cup of popcorn
Answer:
2 Tablespoons make 4 cups. Popcorn pops to 40 times its original size. One ounce. 2 Tablespoons of kernels makes about 4 cups of popcorn. Four cups of popcorn have 125 calories :))
Authors note:
I really hoped this helped! :)))
what is the slope of the line that passes through the points (-9,0) and (-17,4)? write your answer in simplest form
Answer: -1/2
Step-by-step explanation:
The stadium is to be renovated with a new seating capacity of 20790 seats.after the renovation what will be the percentage increase in the number of seats
Although part of your question is missing, you might be referring to this full question: The stadium has 15400 seats and it is to be renovated with a new seating capacity of 20790 seats. After renovation what will be the percentage increase in the number of seats?
The initial capacity of the stadium = 15400 seats
Planned new capacity = 20790 seats
Increment in the number of seats = 20790 - 15400 = 5390 seats
Percentage increase in the number of seats = (Increment in seats/Initial capacity of the stadium)*100
Therefore,
(5390/15400)*100 = 0.35*100 = 35%
So the percentage increase in the number of seats after renovation will be 35%
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Verify the identity.
secx-secxsin^2x= cos x
The identity is verified, yes. secx-secxsin^2x=cos x
What is an identity?
An identity in mathematics is an equality connecting two mathematical expressions, A and B, such that both expressions provide the same result for any value of the variables falling within a given range of validity.
An identity is an equation that, regardless of the values used, is always true. 2 x + 3 x = 5 x is an identity because, according to the preceding equation, 2 x + 3 x will always equal 1 regardless of the value;
According to given information;
secx = 1/cosx
cos²x+sin²x= 1
**sin²x = 1-cos²x
by (*) :
secx - secx sin²x=(1/cosx) -(1/cosx) sin²x
= (1/cosx) (1- sin²x)....factory :(1/cosx)
by(**)
sec x-sec x sin²x = (1/cos x)cos²x
sec x-sec x sin²x = cos x
( simplify by : cos x)
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Solve the equation t − 3 = 17 for t.
Answer:
t = 20
Step-by-step explanation:
add 3 to both sides to isolate t:
t = 17 + 3
t = 20
Answer: t= 20
Step-by-step explanation:
161=wx14
161/14
w=11.5
16. The weather report gives the temperature as 35 degrees Celsius. Fin
equivalent temperature in degrees Fahrenheit. C = (F-32) X
35° = CF-32) F-32=5 (35)
E
■7.
17. A rectangle has perimeter 182 in. and length 52 in. What is the wic
182-104-78
78/2
8. A triangle has base 7 m and area 17.5 m². What is the height?
enVisionTM Algebra 1 Teaching Resources
. A triangle has a base 7 m and area 17.5m squared. What is the height?
For which function is f(5) = 2?
Answer: f = 2/5 (0.4)
Step-by-step explanation:
1. Re-order terms so constants are on the left
f x 5 = 2 OR f(5)=2
2. Divide both sides by the same factor
f(5)=2 --> 5f/5 = 2/5
What is the solution set for the equation l3x + 2 = 5?
Answer:--------X=3/13---------
Step-by-step explanation:
31.693 rounded to the nearest tenth
Answer:
31.7
Rounded to the nearest Tenths Place.
Which of the following is the solution set of the
problem?
O (-∞, -3)
(-∞, -3]
O
[-3,00)
O (-3,00)
DONE
The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;
(-∞, -3]How can the solution set of an inequality be found?A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;
2•x + 3 ≤ -3Solving the above inequality, we have;
2•x + 3 ≤ -3
2•x ≤ -3 - 3 = -6
2•x ≤ -6
Therefore;
x ≤ -6 ÷ 2 = -3
x ≤ -3
Which gives;
-∞ < x ≤ -3-∞ < x ≤ -3 in interval notation is (-∞, -3]
The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;
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what is unit rate for graph
Step-by-step explanation:
To find the unit rate of a graph find two points. and set up this equation
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Then solve for the Unit rate which can also be referred to as slope, or change in y over x
Hope this helps!
Which ones are the correct answers
The result obtained are-
smallest value = 4.largest value = 48.median = 24first quartile {Q1} = 12third quartile {Q3} = 36What is defined as the frequency table?A frequency table is merely a "t-chart" or two-column table that illustrates the numerous possible outcomes and associated frequencies demonstrated in a sample.
Part 1: Smallest value;
As the frequency table is continuous distribution with a initial value of 4.
Thus, the smallest value of the table is 4.
Part 2: largest value;
As the frequency table is continuous distribution with a final value of 48.
Thus, the largest value of the table is 48.
Part 3: Median
The median is the number in the middle of a sorted list of numbers, and it is more descriptive of the data set than that of the average.
For even number of frequencies.
median = n/2
median = 12/2 = 6
Thus, the 6th term is the median.
median = 24.
Part 4: first quartile {Q1}
When data points are organized in increasing order, the lower quartile, or the first quartile (Q1), is indeed the value at which 25% of them are found.
Thus, Q1 = 12.
Part 3: third quartile {Q3}
When arranged in increasing order, the upper quartile, as well as third quartile (Q3), has been the value at which 75% of data points are found.
Q3 = 36.
The result for the frequency distribution is obtained.
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Help!!
Find the number of round-trip commuter rail tickets sold. (1) Thirty times as many round-trip tickets as 12-ride tickets were sold. (2) The total number of tickets sold represented 1440 rides.
Answer:
no. of round trip is 600
Step-by-step explanation:
lets be n is number of 12-ride tickets
and 30n is number of round trip
60n+12n=1440
72n=1440
n=20
30(20)=600
So,the answer of number of round trip is 600
Histograms, tables, and pie charts are examples of
A. Data organization
B. Data analysis
C. Data Gathering
D. Data Creation
Answer:
B.DATA ANALYSIS
Step-by-step explanation:
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