find the angle between the vectors. (first find an exact expression and then approximate to the nearest degree.) a = i 2j − 2k, b = 4i − 3k
Answers
The angle between the vectors a and b is approximately 48 degrees.
To find the angle between two vectors a and b, we can use the formula:
cos θ = (a · b) / (|a| |b|)
where a · b is the dot product of a and b, and |a| and |b| are the magnitudes of a and b, respectively.
First, let's find the dot product of a and b:
a · b = (i)(4) + (2j)(0) + (-2k)(-3) = 4 + 6 = 10
Next, let's find the magnitudes of a and b:
|a| = √(1^2 + 2^2 + (-2)^2) = √9 = 3
|b| = √(4^2 + 0^2 + (-3)^2) = √25 = 5
Substituting these values into the formula for cos θ, we get:
cos θ = 10 / (3 * 5) = 2/3
To find the angle θ, we can take the inverse cosine (cos^-1) of 2/3:
θ = cos^-1(2/3) = 48.19 degrees
Therefore, the angle between the vectors a and b is approximately 48 degrees.
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Related Questions
Multiple choice. Answer
Answers
The function g(x) = (x - 5)² has a translation of 5 units to the right.
What are some rules for the transformation of functions?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over x-axis, (-x, y).
-f(x) = Reflection over y-axis, (x, -y).
The parent function is a quadratic f(x) = x².
Now, The transformed function g(x) = (x - 5)² is a horizontal transformation of 5 units to the right.
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which angles form a linear pair giving brainliest and points
Answers
Angles 6 and 8 are adjacent, they are Linear pair οf angles.
What is Linear pair?Linear pair οf angles are fοrmed when twο lines intersect each οther at a single pοint. The angles are said tο be linear if they are adjacent tο each οther after the intersectiοn οf the twο lines. The sum οf angles οf a linear pair is always equal tο 180°. Such angles are alsο knοwn as supplementary angles.
Angles 1 and 4 are not adjacent, they are vertically opposite.
Angles 5 and 8 are not adjacent, they are vertically opposite.
Angles 6 and 8 are adjacent, they are Linear pair οf angles
Angles 1 and 5 are corresponding exterior angle, so the are not linear pair.
Thus, Angles 6 and 8 are adjacent, they are Linear pair οf angles
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Brian has $100 in his pocket. As he is walking home 1/4th of the money falls out of his wallet. Of the remaining money, he uses $15 to buy girl scout cookies. Lastly, of the remaining money he loses 1/3rd. How much money does he have left by the time he makes it home?
Answers
Answer:
$40
Step-by-step explanation:
Brian starts at $100, then loses 1/4th of the money,
100/4 = 25,
then you subtract 25 from 100, which gives you 75
With the remaining $75, he spends $15 on girl scout cookies,
75 - 15 = 60
He then has $60 remaining, but while walking home, loses 1/3 of the total amount.
60/3 = 20,
you then subtract 20 from 60, which gives you 40
Therefore, $40 is what is remaining.
What is the formula for SSS triangle?
Answers
A type of triangle congruence rule called Side-Side-Side (SSS) asserts that two triangles are congruent if their three sides are equal to their respective three sides of another triangle.
What is a triangle?
A triangle is a closed shape with three vertices, three sides, and three angles. △PQR is used to denote a triangle with the vertices P, Q, and R. Sandwiches and signboards in the shape of triangles are two of the triangles that are most frequently seen.
SSS congruence postulate:
A type of triangle congruence rule called Side-Side-Side (SSS) asserts that two triangles are congruent if their three sides are equal to their respective three sides of another triangle. When the dimensions of the matching sides and angles of two or more triangles match, the triangles are said to be congruent.
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Lincoln makes beaded necklaces. Each necklace has three sections. The first section is made
3
1
from-inch beads, the second section is made from-Inch beads, and the third section is
2
made from -inch beads. Each section has the same number of beads, b.
Which expressions represent the length
of one of Lincoln's necklaces?
Choose ALL that apply.
1
MIN
+
What is the length of a necklace that has
10 of each type of bead?
II
inches
OOO
7
4
8
5
6
2
04
X+
+
Answers
Answer: 110 inches.
Step-by-step explanation: The length of a necklace that has 10 of each type of bead can be represented by the expression:
1310 + 2110 + 3210 = 30+20+60 = 110 inches
So the correct answer is 110 inches.
Answer:
The answer is 15.
Explanation:
Got it right on i-Ready!
Find angle X.
I am not sure if it should add up to 360 degrees or 180 degrees
Answers
Answer:
195
Step-by-step explanation:
Since this figure is a quadrilateral you would be subtracting the inner angles from 360
360-87-40-38=195
For which type of triangle are the incenter, circumeter, centroid, and orthocenter always inside the triangle?
A) right
B) acute
C) obtuse
D) isosceles
Answers
If the incenter, circumcenter, centroid, and orthocenter are always inside the triangle, the correct answer is an acute triangle (option B).
In an acute triangle, all three angles are less than 90 degrees. The incenter, which is the center of the inscribed circle, lies inside the triangle. The circumcenter, which is the center of the circumscribed circle, also lies inside the triangle.
The centroid, which is the point of intersection of the medians, is located inside the triangle as well. Finally, the orthocenter, which is the point of intersection of the altitudes, is inside the triangle in an acute triangle.
In contrast, a right triangle has one angle measuring 90 degrees, an obtuse triangle has one angle greater than 90 degrees, and an isosceles triangle has two equal side lengths. These types of triangles may have some of the points (incenter, circumcenter, centroid, orthocenter) located outside the triangle.
Therefore, the correct answer is option B, acute triangle.
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Enter an algebraic expression to model the given context. Give your answer in the simplest form.The principal amount P originally deposited in a bank account plus 0.6% interest The algebraic expression is _____+______= ______
Answers
Given:
Principal amount = P (o
Interest = 0.6% = 0.006 (divide by 100 since it's in percentage)
The algebraic expression is:
P + 0.006P = 1.006P
ANSWER:
P + 0.006P = 1.006P
In circle Q with the measure of arc ⌢=118∘PR⌢ =118 ∘ , find m∠PQRm∠PQ
Answers
Explanation
We are given the measure of arc PR = 118°.
We are required to find m∠PQR.
We know that an arc measure is an angle the arc makes at the center of a circle. Therefore, we have:
\(\begin{gathered} obtuse\text{ }m\angle PQR=118\degree \\ obtuse\text{ }m\angle PQR+reflex\text{ }m\angle PQR=360\degree\text{ }\lbrace angles\text{ }at\text{ }a\text{ }point\rbrace \\ reflex\text{ }m\angle PQR=360\degree-obtuse\text{ }m\angle PQR \\ reflex\text{ }m\angle PQR=360\degree-118\degree \\ reflex\text{ }m\angle PQR=242\degree \end{gathered}\)Hence, the answer is:
\(\begin{gathered} obtuse\text{ }m\angle PQR=118\degree \\ reflex\text{ }m\angle PQR=242\degree \end{gathered}\)But since Q is the measure of the angle, then the final answer is 118°.
suppose taht the weight of ore in a randomly selected car is 70.7 tons. would thta fake make you suspect that the loading mechanism is overfilling the cars?
Answers
If 70.7 tons is within the acceptable range for the car's capacity, then the randomly selected car's weight would not necessarily indicate an issue with the loading mechanism.
It is difficult to determine if the loading mechanism is overfilling the cars based solely on one randomly selected car with a weight of 70.7 tons. Without more data and a comparison to the expected weight capacity of the cars, it is not possible to make an accurate assessment of the loading mechanism's performance.
It is important to gather additional data and analyze trends over time to determine if there is an issue with overloading. If 70.7 tons is within the acceptable range for the car's capacity, then the randomly selected car's weight would not necessarily indicate an issue with the loading mechanism.
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Write the quotient and remainder when we divide (x^3 -4x^2 + 2x + 5) by (x - 2)
Answers
Answer:
Step-by-step explanation:
Sorry I can't explain how it is done. It is very difficult to explain on paper.
Help please. thank you
Answers
Your dividing by 30
your 180 (which is degrees) is
radians. As the cosine function is periodic with period 2 we get
Carla has a rectangular garden in her backyard. The width of the garden is 9 meters. The area of the garden is 360 square meters. What is the length of the garden? Show your work.
Answers
Answer:
l = 40 m
Step-by-step explanation:
The formula for area of a rectangle is
A = lw, where
A is the area in square units,l is the length,and w is the widthStep 1: Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):
360 = 9l
Step 2: Divide both sides by 9 to solve for l
(360 = 9l) / 9
40 m = l
Optional Step 3: We can check our answers by checking that the product of 40 and 9 is 360
40 * 9 = 360
360 = 360
If an inflatable ball with a volume of 96pi loses air until its radius is half of its original size, what is the new volume?
Answers
The new volume of the inflatable ball after the radius becomes half of the original one is 16π.
The original volume of the ball is given as 96π
The radius then becomes half of its original size which means if the radius of the ball is 'r' then the new radius becomes 'r/2'.
The formula for the volume of the ball is equal to, where 'r' is the radius of the ball. (4/3)π X r³
With this the original volume of the ball is
(4/3)π X r³
and the new volume of the ball after it's halved is
V₂ = (4/3)π X (r/2)³
After simplification
V₂ = (4/3)π X (r³/8)
The new volume of the ball is:
V₂ = (1/6) X πr³
So the new volume is (1/6) of the original volume. We can calculate this as
V₂ = (1/6) X 96π
= 16π
Therefore, the new volume of the inflatable ball is 16π.
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Two liters of the Gatorade cost $3.98. How much do 8 liters cost?
Answers
Answer:
$15.92
Step-by-step explanation:
We Know
2 liters of Gatorade cost $3.98
How much do 8 liters cost?
We take
3.98 x 4 = $15.92
So, 8 liters cost $15.92
can someone please help:)? I will appreciate it
Answers
Answer:
y = 6
Step-by-step explanation:
.
11.1 divide by 0.01 is equal to ?
Answers
step by step explanation:
6 gardeners can plant 18 trees in 30 minutes. How many gardeners would it take to plant 45 trees in 45 minutes
Answers
It would take 10 gardeners to plant 45 trees in 45 minutes.
Rule of ThreeIt's a math tool for solving problems about proportion. You can relate more than 2 variables and from the proportion, it's possible to find an unknown number.
The question gives:
6 gardeners can plant 18 trees in 30 minutes.
? gardeners can plant 45 trees in 45 minutes.
6 gardeners can plant \(\frac{18\; tree}{30\; min}=\frac{3}{5}\) trees/min. You can calculate the second rate from \(\frac{45\; tree}{45\; min}=\frac{1}{1}=1\) tree/min.
Write the previous text information in form of proportion.
6 gardeners ----------- 3/5 trees/min
x gardeners ----------- 1 tree/min
Then, applying cross multiplication:
\(\frac{3x}{5}=6\\ \\ 3x=30\\ \\ x=10\)
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(6 - 4) × 9
sjjdcnjcbdc
Answers
Answer:
18
Step-by-step explanation:
(2) x 9
18
That's it
Byeeeee
Here is a polygon. A scaled copy of the polygon is created using a scale factor of 1/2. What are the new side lengths in the copy?
Answers
Answer:
3 by 4
Step-by-step explanation:
Given the dimension of the polygon as 6 by 8
If the scale factor is 1/2, the new side length is gotten by multiplying both dimensions by 1/2 as shown:
For the side length 6:
New length = 1/2 * 6 = 3
For the side length 8:
New length = 1/2 * 8
New length = 4
Hence the new side lengths in the copy is 3 by 4
Solve for X in the attached picture.
Answers
Answer:
x=20
Step-by-step explanation:
aro now if a I am rite but a try mai best
Please help!!!
4. Graph the quadratic y=x²-2x-5 below
Answers
The vertex of the function is -6.
The domain of the function is {real numbers}.
The range of the function is y ≥ -6.
What are the domain and range of the function?The range and domain of the function is calculated as follows;
y = x² - 2x - 5
From the graph of the function, the range of the function includes y values;
range = y ≥ -6
From the graph of the function, the domain of the function includes x values;
domain = real numbers.
The vertex of the graph is -6.
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the value of x which makes 2/3(1/4x-2)=1/5(4/3x-1)
PLEASE ANSWER ASAP 45 POINTS !!!
Answers
Answer:
x= -34/3
Step-by-step explanation:
just solve by multiplying both sides by 15, then distribute 10 and 3 through the parenthesis, multiply both sides by 2, move the variable to the left side and change the sign, move the constant and change the sign, combine like terms, calculate the sum, and finally divide both sides by -3
HELP PLEASE SO I CAN MOVE ON
find the measure of the indicated angle to the nearest degree
Answers
Answer:
16
Step-by-step explanation:
\( \tan(x) = \frac{13}{46} \)
\( \tan {}^{ - 1} ( \frac{13}{46} ) = 16\)
PLEASE HELP !!!!!!! A group of 1,254 people is going on a boat tour if each boat holds 8 people how many boats will they need ?
Answers
We need to round up to the next full number because we are unable to equation have a fraction of a boat. The organization will thus require 157 boats to hold the entire 1,254 persons.
What is equation?Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.
We may divide the total number of persons by the capacity of each boat to determine the number of boats required to hold a party of 1,254 individuals:
8 individuals per boat times 1,254 passengers is 156.75 boats.
We need to round up to the next full number because we are unable to have a fraction of a boat. The organization will thus require 157 boats to hold the entire 1,254 persons.
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Suppose that a particular brand of 5 inch candles has an average life of 27 hours with a standard deviation of six hours. If all possible samples of 4 candles were selected in the average life of the samples was determined, what would the mean of the distribution of the sample means be?
5
3
4
27
Answers
The mean of the distribution of sample means would be 27 hours, which is the same as the average life of the candles.
This is because the sample means would be expected to be centered around the population mean.
The standard deviation of the distribution of sample means (also known as the standard error of the mean) can be calculated using the formula:
standard deviation of sample means = standard deviation of population / square root of sample size
In this case, the standard deviation of sample means would be:
6 / square root of 4 = 3
So the answer is 3.
So, the mean of the distribution of the sample means would be 3. Your answer: 3.
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HELP! BRainliest +20
A function f is defined such that 8f(x)=f(\(\frac{1}{8}\)x) for all values of x, and f(4) = 24. What is the value of f(32) ?
Answers
The value of f(32) is 3
What is a Function ?A function is a mathematical statement used to relate two variables .
It is given that
8f(x) = f((1/8)x)
It is also given that
f(4) = 24
now to determine the value of f(32)
8 * f(32) = f((1/8) *32)
8 * f(32) = f(4 )
f(32) = 24 /8 = 3
Therefore the value of f(32) is 3
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Find the sum of 6x^2-3 and 8x^2–5x-1
Answers
By grouping like terms and taking common factors, we will see that the addition of the polynomials gives:
(6x^2 - 3) + (8x^2 - 5x - 1) = 14x^2 - 5x - 4
How to find the sum of the polynomials?Here we want to add two polynomials:
6x^2 - 3
And
8x^2 - 5x - 1
To make that addition, we just need to group like terms and take common factors.
We start with:
(6x^2 - 3) + (8x^2 - 5x - 1)
Grouping like terms we will get:
(6x^2 + 8x^2) + (-5x) + (-3 - 1)
Now we can simplify that, so we will get:
(6 + 8)*x^2 - 5x - 4
14x^2 - 5x - 4
That is the addition of the polynomials.
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Pls, answer for 20 points asap. I really need this
Answers
Its B then A
Step-by-step explanation:
Answer:
You helped me so it's B and A mark me brainliest please
Step-by-step explanation:
Find the value of the monomial: 3x^2y for x=1, y=9
Answers
Answer:
Step-by-step explanation:
3x^2y
3(2)^2(9)
6^18= 101 559 956 668 416
Answer:
387,420,489 is the answer to the monomial.
Step-by-step explanation:
3x^2y = 3(1)^2(9) when the variables are replaced.
3(1) = 3
2(9) = 18
3^18 = 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3
3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 387,420,489
Therefore, 387,420,489 is the answer to the monomial.
Hope this helps! :D