The the value of constant proportionality k is 3 and the value of y is 42 when the value of x is 14.
Constant proportionality:
Constant proportionality means the ratio of two proportional values at a constant value.
Directly Proportional:
In direct proportion, if one quantity is increased or decreased then the other quantity increases or decreases, respectively.
Given,
Suppose that y is directly proportional to x.
And y = kx.
Here we need to find the value of k when the value of x = 10 and the value of y = 30.
And we also need to find the value of y when the value of x = 14.
First, we have to find the value of k by apply the given value of the equation,
=> 30 = k x 10
=> 30 /10 = k
=> k = 3
Now the value of y when the value of x = 14 and the value of k = 3,
Then
=> y = 3 x 14
=> y = 42.
Therefore, the value of constant proportionality k is 3 and the value of y is 42 when the value of x is 14.
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Which values are in the range of the function f(x) = -2x + 4 with a domain of (-6,0,6)
The range of the function is x∈[(-8 ,16)]
It is required to find the range.
What is function?A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given:
Since f(x) = -2x + 4 is linear, its limit values correspond to the limits imposed by the domain (in this case x∈[(-6 ,6)]
By put the value of x in the given function we get,
f(-6) = -2(-6) + 4
=12+4
=16
f(6) = -2*6 + 4
=-12+4
=-8
So the range is -8<x<16.
Therefore, the range of the function is x∈[(-8 ,16)]
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How many triangles can be made if one angle is 95° and another angle is acute?
A. 1
B.2
C. More than 2
D. None
Answer:
D. None Beacouse triangles are 3-sided not 2-sided.
Step-by-step explanation:
None
I'd like 75% of my order to be 3 cupcakes and the rest cookies.
How many cookies do I get?
Answer:
1 cookie
Step-by-step explanation:
75% = 75/100
75 and 100 are both divisible by 25, therfore the simplified verision is 3/4
[tex]\frac{75}{100} /\frac{25}{25} =\frac{3}{4}[/tex]
in order to get 100% we would need to:
3/4 + num of cookies = 4/4
re-arranged by subtracting 3/4 on bith sides:
num of cookie = 4/4 - 3/4
num of cookie = 1/4
meaning 1/4 of her orders is cookies
If f (x) = 3x - 1 and g (x) = x² + 1, find the following.
a) g(-4) + f(-2) =
b) f(1) - g(0) =
Will give brainliest and 5 star rating. Thank you. :)
The value of the functions are:
a. g(-4) + f(-2) = 24
b.. f(1) - g(0) = 1
What is a function?A function can be defined as an expression showing the relationship between two variables.
Given the functions;
f (x) = 3x - 1 g (x) = x² + 1g(-4); substitute the value of x as - 4 in g(x)
g(-4) = (-4)² + 1
g(-4) = 16 + 1
g(-4) = 17
f(-2); substitute the value of x as - 2 in f(x)
f(-2) = 3(-2) - 1
f(-2 = -7
a. g(-4) + f(-2) = 17 -(-7)
g(-4) + f(-2) = = 24
f(1) = 3(1) - 1
f(1) = 2
g(0) = (0)² + 1
g(0) = 1
b. f(1) - g(0) = 2 - 1
f(1) - g(0) = 1
Thus, the value of g(-4) + f(-2) and f(1) - g(0) are 24 and 1 respectively.
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How to get 5% of any number
______________________________________________________
Five percent is considered a half of 10 percent. So, to find 5% of a number, all you need to do is divide 10 percent of the number by 2.
Example: Let's find 5 percent of 230. You need to take 23 and divide it by 2, and you get 11.5.________________________________________________________
Hope this helps! If so, lmk! Thanks and good luck!
What is the sqaure root of 6475839
29
Write the answer in the blank.
What number is 260 more than 450?
Answer: 710
Step-by-step explanation:
260 + 450 = 710
Answer:
We are looking for a new number which is 260 more than 450.
We will get the new number by adding 260 to 450.
We write it down as:
450+260=710
And finally the solution for: What number is 260 more than 450?
is 710
All Done!
ram earns rs. 3500 in a week how much would he earn in 30 days?
Answer:15,000
Step-by-step explanation: 3500 divided by 7 because there are 7 days in a week= 500 and then 500 times 30 because of the thirty days
Answer:
Given the salary of Ram in 7days is rs.3500
Ram earns in a day = 3500 Divided By 7
= rs.500
Ram earns in 30 days = 500 Multiplied by 30
= rs.15,000
All Done!
a = 17.6 cm, b = 9.5 cm and c = 13.6 cm for the triangle shown below.
Answer: Click on this: a=13.6cm,b=9.5cm and c=2.6cm for the triangle show it has a step by step way
Step-by-step explanation:
At a coffee shop, the first 100 customers'
orders were as follows.
Small Medium Large
Hot
5
48
22
Cold
8
12
5
If one of these customers has purchased a
large drink, what is the probability that it is
cold?
P( hot| Large ) = [?]
Round to the nearest hundredth.
Answer:
so there is a 5% change of or ordering a large cold drink
Step-by-step explanation:
first add the total of all drinks
5+48+22+8+12+5=100
the amount of large drinks that are cold are 5
so there is a 5% change of ordering a large cold drink
The branch of statistical studies called descriptive statistics summarizes important aspects of a data set. True or false?.
Yes, The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.
Here,
We have to find the statement,
''The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.'' is true or not.
What is Descriptive statistics?
Descriptive statistics is a means of describing features of a data set by generating summaries about data samples.
Now,
The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.
Because : Descriptive statistics refers to the summary of important aspects of a data set.
Hence, The statement ''The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.'' is true.
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Under her cell phone plan, Caroline pays a flat cost of $54.50 per month and $5 per gigabyte. She wants to keep her bill at $74 per month. Write and solve an equation which can be used to determine gg, the number of gigabytes of data Caroline can use while staying within her budget.
To stay within budget, she must use 3.9 gigabytes.
Giving the following information:
Under her cell phone plan, Sofia pays a flat cost of $54.50 per month and $5 per gigabyte. She wants to keep her bill at $ 74 per month.
First, we need to establish the total cost formula:
Total cost= 54.5 + 5*x
x= number of gigabytes
Now, we isolate x:
74= 54.5 + 5x
19.5/5= x
3.9= x
To stay within budget, she must use 3.9 gigabytes
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Find the rate of change for each set of ordered pairs. What is
the average rate of change of all three sets?
(1, 15), (2, 12)
(-1,14), (3, 10)
(3,11), (5, 15)
Write your answer to the average rate of change as a fraction,
a/b.
Answer:
Find the rate of change for each set of ordered pairs. What is
the average rate of change of all three sets?
(1, 15), (2, 12)
(-1,14), (3, 10)
(3,11), (5, 15)
Write your answer to the average rate of change as a fraction,
a/b.
Step-by-step explanation:
Solve the inequality.
-2.5w<6.8
W>?
Answer:
-2.5w<6.8
-2.5w/-2.5<6.8/-2.5
w>-2.72
A bus ride costs P11 for the first 4 kilometers, and each additional integer kilometers adds P2.00 to the fare. Use a piecewise function to represent the jeepney fare in terms of the distance d in kilometers.
The function which represents the jeepney fare in terms of the distance(d) in kilometers is F = 2x ₊ 3.
Given a bus ride costs 11 pesos for first 4 kilometers.
2.00 pesos for each succeeding kilometer.
Function of Fare (F) in terms of distance (d).
Let F represent the total fare and d represent the distance in kilometers.
F = rate of fare × distance
rate = 11 for 4 km, and 2 for each km
rate = 11, if x ≤ 4,
rate = 2, if (x₋4), and x > 4
hence the equation is:
F = 11 pesos, if x ≤ 4,
F = 11 ₊ 2(x₋4), if x > 4
Simplify the above equation.
F = 11 ₊ 2x ₋ 8
F = 2x ₊ 3
Hence we derived the function in terms of distance as F = 2x ₊ 3
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the of a vector is the which that vector makes with
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
Find a general solution. show the steps of derivation. check your answer by substitution.y'=e^(2x-1)y^2
The general solution of the given equation is y² = 8x²Inx + cx².
Linear first order differential equation:A first-order linear differential equation is one that has the formula:
[tex]\frac{d y}{d x}+p(x) y=q(x)[/tex]
where p(x) and q(x) are continuous functions of x.
We begin by determining the integrating factor for the first-order linear differential equation.
I.F. = [tex]e^{\int p(x) d x}[/tex]
The solution to the first order linear differential equation is:
[tex]y \cdot e^{\int p(x) d x}=\int q(x) \cdot e^{\int p(x) d x} d x+c .[/tex]
Where c is the constant of integration.The solution to the first order linear differential equation is:
[tex]\int \frac{1}{x} d x=\ln x+c[/tex]
Where c is the constant of integration.So, given: [tex]y^{\prime}=\frac{\left(4 x^2+y^2\right)}{(x y)}[/tex]
The above differential equation can be written as:
[tex]\begin{aligned}&\frac{d y}{d x}=4 \frac{x}{y}+\frac{y}{x} \\&\frac{d y}{d x}-\frac{y}{x}=\frac{4 x}{y} \\&y \frac{d y}{d x}-\frac{y^2}{x}=4 x\end{aligned}[/tex]
Substitute, [tex]y^2=t, 2 y \frac{d y}{d x}=\frac{d t}{d x}[/tex].
[tex]\begin{aligned}&\frac{1}{2} \frac{d t}{d x}-\frac{t}{x}=4 x \\&\frac{d t}{d x}-\frac{2 t}{x}=8 x\end{aligned}[/tex]
Because this is a first-order linear differential equation, we must first determine the integrating factor:
[tex]\text { I. F. }=e^{-2 \int \frac{1}{x} d x}=e^{-2 \ln x}\\\text { I.F. } F=\frac{1}{x^2}[/tex]
As a result, the following is the general solution to the given IVP:
[tex]$$t \cdot(I . F .)=\int(I . F .) \cdot 8 x d x+c$$$t \cdot\left(\frac{1}{x^2}\right)=\int\left(\frac{1}{x^2}\right) \cdot 8 x d x+c$$t \cdot\left(\frac{1}{x^2}\right)=8 \int \frac{1}{x} d x+c$$t \cdot\left(\frac{1}{x^2}\right)=8 \ln x+c$$t=8 x^2 \ln x+c x^2$[/tex]
By reversing the value of t:
[tex]y^2=8 x^2 \ln x+c x^2[/tex]
We now test the solution by substituting [tex]y^2=8 x^2 \ln x+c x^2[/tex] it in the original differential equation.
[tex]\begin{aligned}&\frac{d}{d x}\left(y^2\right)=\frac{d}{d x}\left(8 x^2 \ln x+c x^2\right) \\&2 y \frac{d y}{d x}=16 x \ln x+8 x+2 c x \\&\frac{d y}{d x}=\frac{16 x \ln x+8 x+2 c x}{2 y} \\&\frac{d y}{d x}=\frac{8 x \ln x+4 x+c x}{y}\end{aligned}[/tex]
We calculated the value of [tex]y^2[/tex] and [tex]\frac{d y}{d x}[/tex] from the original differential equation:
[tex]\begin{aligned}&\frac{8 x \ln x+4 x+c x}{y}=\frac{4 x^2+8 x^2 \ln x+c x^2}{x y} \\&8 x \ln x+4 x+c x=8 x \ln x+4 x+c x .\end{aligned}[/tex]
Therefore, the general solution of the given equation is y² = 8x²Inx + cx².
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The complete question is given below:
For the following ODE, find a general solution, show the steps of derivation and check your answer by substitution.
[tex]y^{\prime}=\frac{\left(4 x^2+y^2\right)}{(x y)}[/tex]
in a sentence.
11) Kelsey has a $30 online gift voucher. She plans to buy as many books as she can. The cast of each book
is $3. There is also a single shipping charge of $2. How many books can she afford without spending more
than her gift voucher amount?
Answer:
Kelsey can buy 9 books.
Step-by-step explanation:
If Kelsey wants to buy as much books as possible with 30$, multiply 3$ by 9 (books) which is 27$.
30$-27$ is 3$ so she will have 3$ extra dollars to use for shipping. 2$ is the price for shipping so she will have an extra dollar.
I hope this was helpful! :) (Please rate/heart this if helpful)
A population has a mean = 79 and a standard deviation = 18. Find the mean and standard deviation of a sampling distribution of sampling means with sample size = 36.
The sampling distribution of sample means is a mean of 79 and a standard deviation of 3.
What is the standard deviation?The standard deviation mathematical and statistical analysis tool used to explain the diversity of treatments or values around the Mean is the standard deviation, which is also known as the square root of variance.
Given that,
Population mean, [tex]\bar{x}[/tex] = 79
Population standard deviation, σ = 18
Sample size, n = 36
We have to determine the mean and standard deviation of a sampling distribution of sample means.
Let X denotes a random variable distributed with a mean and standard deviation of 85 and 28 respectively.
Also, if a random sample of size n is drawn from the population, then the sample mean is denoted by [tex]\bar{x}[/tex].
The sampling distribution of sample means [tex]\bar{x}[/tex] is given by:
ц [tex]\bar{x}[/tex] = ц
σ [tex]\bar{x}[/tex] = σ/√n
Therefore, for the sample size n = 36, the sampling distribution of sample means [tex]\bar{x}[/tex] is obtained as:
ц [tex]\bar{x}[/tex] = 79
σ [tex]\bar{x}[/tex] = 18/√36 = 3
Hence, the required sampling distribution of sample means is mean of 79 and a standard deviation of 3.
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An inductive proof that p(n) is true for all n always starts with the base case. what is the base case?
The base case for which the inductive proof for p(n) is defined, is the smallest value of n for which p(n) is defined.
What is Mathematical Induction?Mathematical induction refers to a strategy for demonstrating a theorem's correctness by first demonstrating that, if it holds true in one particular situation, it will also hold true in all subsequent cases in the series.
Now,
The proof of mathematical induction is based upon showing the given expression true for one value, assuming that it will be true for some other value and finally proving that it will be true for all the values.The base case is the proof for which the expression is showed to be true in the beginning.In general cases, this initial value is 1 when the expression is defined for the values of variables belonging to Natural Numbers, i.e., the proof starts by showing that the given expression is true for the value of variable = 1.Hence, the base case for which the inductive proof for p(n) is defined, is the smallest value of n for which p(n) is defined.
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What is the scientific results to 5,97 X 1024 kg
The scientific results to 5.97 x [tex]10^{24}[/tex] kg is the Earth's mass.
What is the Earth's mass?The Earth has a mass of 5.9 sextillion tonnes, which is a significant amount of mass. The Earth's mass is approximately 5.97 x [tex]10^{24}[/tex] kg, with a standard error of 6 x [tex]10^{20}[/tex] kg. The mass of a planet is difficult to measure exactly due to its size, therefore this number has varied over time as we have developed better measuring techniques.Astronomers use the Earth's mass as a reference point when calculating the masses of other planets, including rocky terrestrial planets and exoplanets.To learn more about the Earth's mass visit:
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A college student is moving into a campus dormitory. The student rents a moving truck for $19.95 plus $.99 per mile. Before returning the truck, the student fills the tank with gasoline, which costs $65.32. The total cost is $144.67. How many miles did the student drive the truck?
The number of miles covered by the student is; 54.45 miles.
How many miles did the student cover?The college student in discuss incurs a total cost of $144.67.
On this note, the cost incurred over the miles covered can be determined as follows;
= $144.67 - $19.95 - $65.32
= $59.4
Hence, since the cost of one mile is $59.4, it follows that the number of miles covered is;
No. of miles = 54.9/0.99
= 54.45 miles.
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The midpoint of ABis M(-1, -4). If the coordinates of A are (-3, -7), what are the coordinates of B?
Given:
M(-1,-4) is the mid point of points a(-3, -7)
and B
To find:
Coordinates of B
Explanation:
Let (x, y) be the coordinates of B.
Since M is the midpoint of A and B,
M-A IB-EM
YM-YA-YB-YM
Substituting the values,
The x coordinate will be
-1-(-3)=-(-1)
-1+3=x+1
=2-1 x = 1
The y coordinate will beYM YAYB-YM
Substituting the values,
The x coordinate will be
- 1 - (- 3) = x - (- 1) - 1 + 3 = x + 1 x = 2 - 1 x = 1
The y coordinate will be
- 4 - (- 7) = y - (- 4) - 4 + 7 = y + 4 y = - 1
y = 7 - 8
Hence x=1, y = - 1
Final answer:
The coordinates of B are (1,-1)
Triangle ABC is a right triangle and cos(22.6o)=StartFraction b Over 13 EndFraction. Solve for b and round to the nearest whole number.
Triangle A B C is shown. Angle A C B is 90 degrees and angle C A B is 22.6 degrees. The length of hypotenuse A B is 13 centimeters, the length of A C is b, and the length of C B is a.
Which equation correctly uses the value of b to solve for a?
tan(22.6o) = StartFraction a Over 13 EndFraction
tan(22.6o) = StartFraction 13 Over a EndFraction
tan(22.6o) = StartFraction a Over 12 EndFraction
tan(22.6o) = StartFraction 12 Over a EndFraction
In the given triangle ABC right angled at C and [tex]AC = b[/tex] and [tex]CB = a[/tex], the equation using value of b used for solving for a will be [tex]tan(22.6degrees) = \frac{a}{12}[/tex].
According to the question statement, Triangle A B C is shown. Angle A C B is [tex]90[/tex] degrees and angle C A B is [tex]22.6[/tex] degrees. The length of hypotenuse A B is [tex]13[/tex] centimeters, the length of A C is b, and the length of C B is a.
We are supposed to find the equation using value of b used for solving for a.
Solution: Given,
[tex]AB = 13cm\\AC = b\\BC = a\\Angle BAC = 22.6degrees[/tex]
If hypotenuse is 13cm then value of b is either 5 or 12 as per Pythagorean Triplet. As there is no value such as 5 in the given options we take the value of [tex]b=12 cm[/tex].
[tex]cos(22.6degrees) = \frac{b}{13} =\frac{12}{13} \\sin(22.6degrees) = \frac{a}{13}\\[/tex]
Using the above two equations,
[tex]tan(22.6degrees)=\frac{a}{b} \\b=12\\tan(22.6degrees)=\frac{a}{12}[/tex]
Therefore option three "tan(22.6o) = StartFraction a Over 12 EndFraction" is the correct answer.
Pythagorean Triplet: If a, b and c are three sides of a right angled triangle, c being the hypotenuse then [tex]a^{2} +b^{2} =c^{2}[/tex] and a and b being either of the base and perpendicular.To learn more about Pythagoras theorem, click on the link given below:
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Answer: C tan (22.6)=a/12
Step-by-step explanation: edge 2023
Suppose the graph of y=x^2 is shifted left 6 units. Complete the modified equation: y=
please help
The equation of the modified graph is y = (x + 6)^2
How to complete the modified equation?The equation of the graph is given as
y = x^2
The graph is shifted to the left by 6 units
This is represented as:
(x, y) = (x + 6, y)
So, we have
y = (x + 6)^2
Hence, the equation of the modified graph is y = (x + 6)^2
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What is the ratio of protonated/deprotonated acetic acid at ph 1.8, 5.8, and 10.8?
The ratio of protonated/deprotonated acetic acid at the given pH is:
pH 1.8: 1000:1, pH 5.8: 1:10, pH 10.8: 1:1000000What is acetic acid?Acetic acid, also known as ethanoic acid, is a colorless liquid with a strong, vinegar-like odor. It is referred to as glacial acetic acid when it is pure (100% acetic acid). Acetic acid is a byproduct of fermentation that gives vinegar its distinctive aroma. Vinegar contains approximately 4-6% acetic acid in water. More concentrated solutions are available in laboratories, and glacial acetic acid is pure acetic acid containing only traces of water. Human Reactions: Acetic acid, in vapor form, is a severe irritant to the eyes, mucous membranes, upper respiratory tract, and skin. When acetic acid solutions of 80% or higher come into contact with the skin or eyes, they can be corrosive, causing severe burns to any exposed tissue.The protonated/deprotonated acetic acid pH 1.8, 5.8, and 10.8 ratios are 1000:1, 1:10, and 1:1000000, respectively.Therefore, the ratio of protonated/deprotonated acetic acid at the given pH is:
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The number 3465 is divisible by 11 and 5. Given that you change the position of two or more of these four digits, how many of the resulting numbers are divisible by 11 but not by 5?
Answer:
Divisible rule of 11
If the number of digits of a number is even, then add the first digit and subtract the last digit from the rest of the number
Divisible rule of 5
Divisibility by 5 is easily determined by checking the last digit in the number. If the last number is either 0 or 5, the entire number is divisible by 5.
First of all, the number 3456 is not divisible by 11 and 5.
But if we change position of digits then the numbers divisible by 11 are-
3564 / 11= 324
3465 / 11= 315
3465 / 5= 693
4356 / 11 = 396
4653 / 11 = 423
5346 / 11 = 486
5643 / 11 = 513
6534 / 11 = 594
6435 / 11 = 585
6435 / 5=1287
But the numbers 3465 and 6435 are also divisible by 5
So the numbers divisible by 11 but not with 5 are:
3564 , 4356, 4653, 5346, 5643 and 6534
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Find the area of the parallelogram with vertices k(2, 2, 1), l(2, 3, 3), m(6, 9, 3), and n(6, 8, 1).
Let [tex]\vec K,\vec L,\vec M,\vec N[/tex] be vectors pointing the vertices K, L, M, and N, respectively.
The side KL is parallel to and has the same length as the vector
[tex]\vec L - \vec K = (2\,\vec\imath + 3\,\vec\jmath + 3\,\vec k) - (2\,\vec\imath+2\,\vec\jmath+\vec k) = \vec\jmath + 2\,\vec k[/tex]
Similarly, the side KN is parallel and as long as
[tex]\vec N - \vec K = (6\,\vec\imath+8\,\vec\jmath+\vec k) - (2\,\vec\imath+2\,\vec\jmath+\vec k) = 4\,\vec\imath+6\,\vec\jmath[/tex]
These vectors have magnitudes
[tex]\|\vec L - \vec K\| = \sqrt{0^2 + 1^2 + 2^2} = \sqrt5[/tex]
[tex]\|\vec N - \vec K\| = \sqrt{4^2 + 6^2 + 0^2} = 2\sqrt{13}[/tex]
and their dot product is
[tex](\vec L - \vec K) \cdot (\vec N - \vec K) = 0\cdot4 + 1\cdot6+1\cdot0 = 6[/tex]
The parallelogram spanned by the vectors [tex]\vec L-\vec K[/tex] and [tex]\vec N-\vec K[/tex] has area equal to the magnitude of their cross product, for which we have the identity
[tex]\bigg\|(\vec L - \vec K) \times (\vec N - \vec K)\bigg\| = \|\vec L - \vec K\| \|\vec N - \vec K\| \sin(\theta) \\\\ \implies \text{area} = 2\sqrt{65} \, \sin(\theta)[/tex]
where [tex]\theta[/tex] is the angle between the sides KL and KN.
From the dot product identity, we have
[tex](\vec L - \vec K) \cdot (\vec N - \vec K) = \|\vec L - \vec K\| \|\vec N - \vec K\| \cos(\theta) \\\\ \implies 6 = 2\sqrt{65} \cos(\theta)[/tex]
Then
[tex]\cos(\theta) = \dfrac3{\sqrt{65}} \implies \sin(\theta) = \sqrt{1-\cos^2(\theta)} = 2\sqrt{\dfrac{14}{65}} \\\\ \implies \text{area} = 2\sqrt{65} \cdot 2\sqrt{\dfrac{14}{65}} = \boxed{4\sqrt{14}}[/tex]
Im stuck can someone help?
Answer:
- p / 2
Step-by-step explanation:
4 / -8 = - 1/2
p^3 / p^2 = p
- 1/2 * p = - p / 2
Sharon is twice as old as Brain. In 5 years, the sum of their ages will be 25 years. Find their present ages.
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Answer:
Brian is 5, and Sharon is 10
Step-by-step explanation:
CURRENT AGES:
Let b = Brian's age
Let 2b = Sharon's age
5 YEARS FROM NOW:
b + 5 = Brian's age
2b + 5 = Sharon's age
The sum will be 25
b + 5 + 2b + 5 = 25
3b + 10 = 25
3b = 15
b = 5
So Brian is 5, and Sharon is 10
