PLEASE ANSWER ASAP!!!
Equation in the picture
Solve for r in the equation in the picture. You must use the LCD (Least Common Denominator) to simplify. You can also use cross products to solve.
Must show work
A. r = 19
B. r = 21
C. r = 25
D. r = 30
any unrelated answer will be reported
Answers
Answer:
r = 19
Step-by-step explanation:
( r-5) /2 = ( r+2) /3
The least common denominator is 6
3/3 *( r-5) /2 = ( r+2) /3 * 2/2
3( r-5) /6 = 2( r+2) /6
Since the denominators are the same, the numerators are the same
3( r-5) = 2(r+2)
Distribute
3r -15 = 2r+4
Subtract 2r from each side
3r-2r -15 = 2r+4-2r
r-15 =4
Add 15 to each side
r-15+15 = 4+15
r = 19
Related Questions
What is the true solution to the equation below? 2 in e in2×-in e in 10×= in 30 A x=30 B x=75 C x=150 D x=300
Answers
Answer:
Option B.
Step-by-step explanation:
Let as consider the given equation:
[tex]2\ln e^{\ln 2x}-\ln e^{\ln 10x}=\ln 30[/tex]
It can be written as
[tex]2(\ln 2x)-(\ln 10x)=\ln 30[/tex] [tex][\because \ln e^a=a][/tex]
[tex]\ln (2x)^2-(\ln 10x)=\ln 30[/tex] [tex][\because \ln a^b=b\ln a][/tex]
[tex]\ln \dfrac{4x^2}{10x}=\ln 30[/tex] [tex][\because \ln \dfrac{a}{b}=\ln a-\ln b][/tex]
[tex]\ln \dfrac{2x}{5}=\ln 30[/tex]
On comparing both sides, we get
[tex]\dfrac{2x}{5}=30[/tex]
Multiply both sides by 5.
[tex]2x=150[/tex]
Divide both sides by 2.
[tex]x=75[/tex]
Therefore, the correct option is B.
Answer:
b x=75
Step-by-step explanation:
A 95% confidence interval indicates that:
A. 95% of the intervals constructed using this process based on samples from this population will
include the population mean
B. 95% of the time the interval will include the sample mean
C. 95% of the possible population means will be included by the interval
D. 95% of the possible sample means will be included by the interval
Answers
95% interval would be 95% of the population mean.
The answer should be:
A. 95% of the intervals constructed using this process based on samples from this population will
include the population mean
Answer:
A
Step-by-step explanation:
A 95% confidence interval indicates that 95% of the intervals constructed using this process based on samples from this population will
include the population mean
Find the equation of the para bola that has zeros of x = -2 and x = 3 and a y-intercept of (0,-30)
Answers
Answer:
y = 5x^2-5x-30
Step-by-step explanation:
A parabola with x-intercepts at (-2,0) and (3,0) has the equation
y = a(x+2)(x-3)
where a is to be determined.
We know that it passes through the point (0,-30), so
-30 = a(0+2)(0-3) = -6a
Therefore solve for a to get
a = 5
y = 5(x+2)(x-3)
y = 5(x^2-x+6)
y = 5x^2-5x-30
A soup can has a height of 4 inches and a radius of 2.5 inches. What's the volume of soup in cubic inches that would fill one soup can? Question 3 options: A) 62.8 in3 B) 125.7 in3 C) 78.5 in3 D) 314 in3
Answers
Answer:
C. 78.5 in^3
Step-by-step explanation:
A soup can is in the shape of a cylinder. The volume of a cylinder can be found using the following formula:
[tex]v=\pi r^2h[/tex]
We know that the height is 4 inches and the radius is 2.5 inches.
r= 2.5 in
h= 4 in
[tex]v=\pi (2.5in)^2*4in[/tex]
Evaluate the exponent.
[tex](2.5 in)^2=2.5 in*2.5in=6.25 in^2[/tex]
[tex]v=\pi *6.25 in^2*4 in[/tex]
Multiply 6.25 in^2 and 4 in.
[tex]6.25 in^2*4 in=25 in^3[/tex]
[tex]v=\pi*25 in^3[/tex]
Multiply pi and 25 in^3.
[tex]v=78.5398163 in^3[/tex]
Round to the nearest tenth. The 3 in the hundredth place tells us to leave the 5 in the tenth place.
[tex]v=78.5 in^3[/tex]
78.5 cubic inches can fill one soup can.
A regression analysis between sales (y in $1000) and advertising (x.in dollars) resulted in the following equation: ỹ= 30,000 + 4x
The above equation implies that an:________
a. increase of $l in advertising is associated with an increase of $4 in sales.
b. increase of $4 in advertising is associated with an increase of $4000 in sales.
c. increase of $1 in advertising is associated with an increase of $34,000 in sales.
d. increase of $1 in advertising is associated with an increase of $4000 in sales.
Answers
Answer:
Correct answer is option d. increase of $1 in advertising is associated with an increase of $4000 in sales.
Step-by-step explanation:
Given the equation of regression analysis is given as:
[tex]y= 30,000 + 4x[/tex]
where [tex]x[/tex] is the cost on advertising in Dollars.
and [tex]y[/tex] is the sales in Thousand Dollars.
To find:
The correct increase in sales when there is increase in the advertising cost.
Solution:
Suppose there is an increase of [tex]\$1[/tex] in the advertising cost.
Let the initial cost be [tex]x[/tex] then the cost will be [tex](x+1)[/tex].
Initial sales
[tex]y= 30,000 + 4x[/tex] ....... (1)
After increase of $1 in advertising cost, final cost:
[tex]y'= 30,000 + 4(x+1)\\\Rightarrow y' = 30,000+4x+4\\\Rightarrow y' = 30,004+4x ..... (2)[/tex]
Subtracting (2) from (1) to find the increase in the sales:
[tex]y'-y=30004+4x-30000-4x = 4[/tex]
The units of sales is Thousand Dollars ($1000).
So, increase in sales = [tex]4 \times1000 = \bold{\$4000}[/tex]
So, correct answer is:
d. increase of $1 in advertising is associated with an increase of $4000 in sales.
Find the measure of a.
A. 60
B. 57
C. 40
D. 80
Answers
Answer:
Option (C)
Step-by-step explanation:
Since angle 'a' is the inscribed angle of the given triangle
Therefore, angle measure of the intercepted arc will be equal to the double of the inscribed angle.
x = 2a ⇒ a = [tex]\frac{x}{2}[/tex]
By the tangent-chord theorem,
"Angle between a chord and tangent measure the half of the angle measure of intercepted minor arc"
[tex]\frac{x}{2}[/tex] = 40°
Therefore, a = [tex]\frac{x}{2}[/tex] = 40°
Option (C) will be the answer.
If x=64 &y=27 Evaluate x½-y⅓÷y-x⅔
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
-191/162
▹ Step-by-Step Explanation
Answer:
-191/162
Step-by-step explanation:
Substitute the numbers for the variables:
64 1/2 - 27 1/3 ÷ 27 - 64 2/3
Convert the mixed numbers to improper fractions:
129/2 - 82/3 * 1/27 - 194/3
Multiply the improper fractions:
129/2 - 82/81 - 194/3
= -191/162
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
1. Which word best describes how you feel when working on a math assessment? ( point)
bored
excited
anxious
confident
Answers
Answer:
math is really a difficult subject for me. sometimes i feel confident when i get my answers correct, but sometimes i feel bored when i dnt get my answer. Sometimes i feel anxious , sometimes i feel excited to solve the problems.
Learn more:
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Timothy invested $2,000 in an account earning 3.5% annual interest that is compounded continuously. How long will it take the investment to grow to $3,500?
Answers
Answer: 16 years
Step-by-step explanation:
The exponential function for continuous growth is given by :-
[tex]P=Ae^{rt}[/tex]
, where A = initial amount, r= rate of growth and t = time.
As per given , we have
A= $2,000, =r 3.5%=0.035 and P= $3500
put these vales in equation , we get
[tex]3500=2000e^{0.035t}\\\\\Rightarrow\ \dfrac{3500}{2000}=e^{0.035t}\\\\\Rightarrow\ 1.75=e^{0.035t}[/tex]
Taking log on both sides , we get
[tex]\ln 1.75=0.035t\\\\\Rightarrow\ t=\dfrac{\ln1.75}{0.035}=\dfrac{0.560}{0.035}=16[/tex]
Hence, it will take 16 years to grow to $3,500.
What are the roots for x?
Answers
Answer:
B
Step-by-step explanation:
Use the quadractic equation, x=-b+or-sqrtb^2-4ac/2a, then simplify.
I'm really sorry that it looks messy, I don't know how to make my text look better :(
Jan. 2 Purchased merchandise on account from Nunez Company, $20,000, terms 3/10, n/30. (Lily uses the perpetual inventory system.)
Feb. 1 Issued a 9%, 2-month, $20,000 note to Nunez in payment of account.
Mar. 31 Accrued interest for 2 months on Nunez note.
Apr. 1 Paid face value and interest on Nunez note.
July 1 Purchased equipment from Marson Equipment paying $10,000 in cash and signing a 10%, 3-month, $63,600 note.
Sept. 30 Accrued interest for 3 months on Marson note.
Oct. 1 Paid face value and interest on Marson note.
Dec. 1 Borrowed $22,800 from the Paola Bank by issuing a 3-month, 8% note with a face value of $22,800.
Dec. 31 Recognized interest expense for 1 month on Paola Bank note.
Answers
Assume that random guesses are made for multiple-choice questions on a test with choices for each question, so that there are n trials, each with probability of success (correct) given by p. Find the probability of no correct answers
Answers
Complete Question
Assume that random guesses are made for 7 multiple-choice questions on a test with 5 choices for each question, so that there are n=7 trials, each with probability of success (correct) given by p=0.20. Find the probability of no correct answers.
Answer:
The probability is [tex]P(X = 0 ) = 0.210[/tex]
Step-by-step explanation:
From the question we are told that
The number of trial is n = 7
The probability of success is p = 0.20
Generally the probability of failure is
[tex]q = 1- 0.20[/tex]
[tex]q = 0.80[/tex]
Given that this choices follow a binomial distribution as there is only two probabilities i.e success or failure
Then the probability is mathematically represented as
[tex]P(X = 0 ) = \left n} \atop {}} \right. C_0 * p^{0} * q^{n- 0}[/tex]
[tex]P(X = 0 ) = \left 7} \atop {}} \right. C_0 * (0.2)^{0} * (0.8)^{7- 0}[/tex]
Here [tex]\left 7} \atop {}} \right. C_0 = 1[/tex]
=> [tex]P(X = 0 ) = 1 * 1* (0.8)^{7- 0}[/tex]
=> [tex]P(X = 0 ) = 0.210[/tex]
PLS HELP:Find the side length, C.
Round to the nearest tenth.
Answers
Answer:
[tex]\huge\boxed{c = 14.9}[/tex]
Step-by-step explanation:
Using Cosine Rule
[tex]c^2 = a^2 + b^2 -2abCosC[/tex]
Where a = 11 , b = 7 and C = 110
[tex]c^2 = (11)^2+(7)^2-2(11)(7)Cos 110[/tex]
[tex]c^2 = 121+49-154 (-0.34)\\c^2 = 170+52.7\\c^2 = 222.7[/tex]
Taking sqrt on both sides
c = 14.9
Kim is earning money for a trip. She has saved and she earns per hour babysitting. The total amount of money earned (y) after (x) number of hours worked is given by the equation . How many hours will she need to work in order to earn for her trip?
Answers
Answer:
what is the amount of money Kim earn per hour of babysitting? Also I need to know how much trip cost to find out how many hours she need to work.
Step-by-step explanation:
5. What is the solution of the following linear system?
y= 3x + 1
2y = 6x + 2
O A. (5,-2)
OB. (34)
C. Infinitely many solutions
D. No solution
Answers
Answer:
C. Infinitely many solutions
Step-by-step explanation:
First, simplify the second equation by dividing it by 2
2y = 6x + 2
y = 3x + 1
Now, we can see that both equations are the same, both y = 3x + 1.
Since they are the same line, this means that there are infinitely many solutions.
So, the correct answer is C.
Identify the decimals labeled with the letters A, B, and C on the scale below. Letter A represents the decimal Letter B represents the decimal Letter C represents the decimal
Answers
There are [tex]10[/tex] divisions between $3.2$ and $3.3$
so that means each division is $\frac{3.3-3.2}{10}=0.01$
A is the 3rd division after $3.2$, So A is $3.2+3\times0.01=3.23$
similarly, C is 3 division behind $3.2$ so it will be $3.17$
and B is $3.34$
A represents the decimal 3.23
B represents the decimal 3.34
C represents the decimal 3.17
Calculating the decimal values:We can see that there are 10 divisions between 3.2 and 3.3.
The difference between the two points for 10 divisions is 3.3 -3.2 = 0.1 unit.
Therefore, one division will be equal to 0.1/10 = 0.01 unit
So, point A is 3 divisions after 3.2, thus
A = 3.2 + 0.01×3
A = 3.23
Similarly,
B = 3.3 + 0.01×4
B = 3.34
And,
C = 3.2 - 0.01×3
C = 3.17
Learn more about decimals:
https://brainly.com/question/548650?referrer=searchResults
I will rate you brainliest Select the best description of what the LCM of a set of polynomials is. a.It is the quotient of all the factors of the polynomials. b.It is the common numerator of a rational expression. c. It is the product of the prime factors that are either unique to or shared by the polynomials. d. It is all the polynomials in the set.
Answers
Answer:
C. It is the product of the prime factors that are either unique to or shared by the polynomials.
Step-by-step explanation:
LCM of polynomials is:
=> Finding the factors of all the numbers and variable in the expression
=> Next, we multiply the unique numbers and the variable of the expression to find the LCM.
So, C is the correct answer.
The LCM of a set of polynomials is the product of the prime factors that are either unique to or shared by the polynomials.
What is LCM of polynomial?To find the lowest common multiple (L.C.M.) of polynomials, we first find the factors of polynomials by the method of factorization and then adopt the same process of finding L.C.M.
Example : The L.C.M. of 4a2 - 25b2 and 6a2 + 15ab.
Factorizing 4a2 - 25b2 we get,
(2a)2 - (5b)2, by using the identity a2 - b2.
= (2a + 5b) (2a - 5b)
Also, factorizing 6a2 + 15ab by taking the common factor '3a', we get
= 3a(2a + 5b)
L.C.M. is 3a(2a + 5b) (2a - 5b)
According to the question
The LCM of a set of polynomials is
is the product of the prime factors that are either unique to or shared by the polynomials.
(from above example we can see that )
Hence, It is the product of the prime factors that are either unique to or shared by the polynomials.
To know more about LCM of polynomial here :
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# SPJ2
Find the values of x which satisfy the following inequation:
x3 – x² <12x
Answers
Answer:
x< -3 and 0 < x < 4
Step-by-step explanation:
x^3 – x² <12x
Subtract 12x from each side
x^3 -x^2 - 12x< 0
Factor
x( x^2 -x-12) <0
Factor
x( x-4) ( x+3) < 0
Using the zero product property
x=0 x=4 x=-3
We have to check the signs regions
x < -3
-( -) (-) < 0 True
-3 to 0
-( -) (+) < 0 False
0 to 4
+( -) (+) < 0 True
x>4
+( +) (+) < 0 False
The regions this is valid is
x< -3 and 0 < x < 4
Suppose log subscript a x equals 3, log subscript a y equals 7, and log subscript a z equals short dash 2. Find the value of the following expression. log subscript a open parentheses fraction numerator x cubed y over denominator z to the power of 4 end fraction close parentheses
Answers
Answer:
24Step-by-step explanation:
Given the following logarithmic expressions [tex]log_ax = 3, log_ay = 7, log_az = -2[/tex], we are to find the value of [tex]log_a(\frac{x^3y}{z^4} )[/tex]
[tex]from\ log_ax = 3, x = a^3\\\\from\ log_ay = 7,y = a^7\\\\from\ log_az = -2, z = a^{-2}[/tex]Substituting x = a³, y = a⁷ and z = a⁻² into the log function [tex]log_a(\frac{x^3y}{z^4} )[/tex] we will have;
[tex]= log_a(\frac{x^3y}{z^4} )\\\\= log_a(\dfrac{(a^3)^3*a^7}{(a^{-2})^4} )\\\\= log_a(\dfrac{a^9*a^7}{a^{-8}} )\\\\= log_a\dfrac{a^{16}}{a^{-8}} \\\\= log_aa^{16+8}\\\\= log_aa^{24}\\\\= 24log_aa\\\\= 24* 1\\\\= 24[/tex]
Hence, the value of the logarithm expression is 24
ASAP Two points ___________ create a line. A. sometimes B. always C. never D. not enough information
Answers
Answer: B. Always
Explanation:
Two points always create a line. The correct answer is option B.
What is a line?
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.
If there are two points A(x₁,y₁) and B(x₂,y₂) then the distance between the two points will be the length of the line. The formula to calculate the distance is given as below:-
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Therefore, the two points always create a line. The correct answer is option B.
To know more about lines follow
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A la propiedad fundamental de las proporcionas, comprueba si las siguientes son o no hay elementos a) 5/7 a 15/21 b) 20/7 a 5/3 c) 16/8 a 4/2
Answers
Answer:
fucuvucybycych tcy bic ttx TV ubtx4 cub yceec inivtxr xxv kb
Step-by-step explanation:
t tcextvtcbu6gt CNN tx r.c tct yvrr TV unu9gvt e tch r,e xxv t u.un4crcuv3cinycycr xxv yctzrctvtcrzecycyvubr xiu nyfex tut uhyh
Why is f (x) = (3x + 1/3)^2 + 8/9 not the vertex form of f (x)
not the vertex form of f (x) = 9x^2 +2x +1?
O The expression has a constant outside of the squared term.
O Some of the terms are fractions instead of integers.
O The expression is not the product of two binomials.
O The variable x has a coefficient.
Answers
Answer:
The Variable has a coefficient.
Step-by-step explanation:
Please help. I’ll mark you as brainliest if correct!
Answers
Answer: x= -1, z=2, y= -4
Step-by-step explanation:
System of equations:
-5x - 4y - 3z= 15 +
-10x + 4y + 6z= 6
-15x + 3z = 21 ------> 3 (-5x + z) = 7.3
-5x + z = 7
now,
-10x + 4y + 6z= 6
2(-5x + z) + 4y + 4z = 6
14 + 4y + 4z = 6
7 + 2y + 2z = 3
2y + 2z= -4
y+z=-2
Now we were using the equation: 20x + 4y + 4z = -28
20x + 4(y+z) = 20x -8= - 28
20 x = -20
x= -1
With this we can find y and z
X=-1
-5x + z = 7
z= 2
y+z=-2
y=-4
Finally we have: x= -1, z=2, y= -4
I hope this can help you.
Thank you
In a local university, 10% of the students live in the dormitories. A random sample of 100 students is selected for a particular study. Carry answer to the nearest ten-thousandths. (Bonus Question)
a. What is the probability that the sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178?
b. What is the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025?
Answers
Answer:
a
[tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]
b
[tex]P( X >0.025 ) = 0.99379[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.10[/tex]
The sample size is [tex]n = 100[/tex]
Generally the standard error is mathematically represented as
[tex]SE = \sqrt{\frac{ p (1 - p )}{n} }[/tex]
=> [tex]SE = \sqrt{\frac{ 0.10 (1 - 0.10 )}{100} }[/tex]
=> [tex]SE =0.03[/tex]
The sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178
[tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} < \frac{ X - 0.10}{SE} < \frac{ 0.178 - 0.10}{0.03} )[/tex]
Generally [tex]\frac{ X - 0.10}{SE} = Z (The \ standardized \ value \ of X )[/tex]
[tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} <Z < \frac{ 0.178 - 0.10}{0.03} )[/tex]
[tex]P( 0.172 < X < 0.178 ) = P (2.4 <Z < 2.6 )[/tex]
[tex]P( 0.172 < X < 0.178 ) = P(Z < 2.6 ) - P (Z < 2.4 )[/tex]
From the z-table
[tex]P(Z < 2.6 ) = 0.99534[/tex]
[tex]P(Z < 2.4 ) = 0.9918[/tex]
[tex]P( 0.172 < X < 0.178 ) =0.99534 - 0.9918[/tex]
[tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]
the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025 is mathematically evaluated as
[tex]P( X >0.025 ) = P (\frac{ X - 0.10}{SE} > \frac{ 0.0025- 0.10}{0.03} )[/tex]
[tex]P( X >0.025 ) = P (Z > -2.5 )[/tex]
From the z-table
[tex]P (Z > -2.5 ) = 0.99379[/tex]
Thus
[tex]P( X >0.025 ) = P (Z > -2.5 ) = 0.99379[/tex]
A person collected $700 on a loan of $600 they made 5 years ago. If the person charged simple interest, what was the rate of interest? The interest rate is %. (Type an integer or decimal rounded to the nearest hundredth as needed.)
Answers
Answer:
Rate= 3 1/3%
Or Rate= 3.33%
Step-by-step explanation:
Final amount collected= $700
Initial amount given out= $600
Interest made= Final amount - initial amount
Interest made= $700-$600
Interest made= $100
Type of interest rate = simple
Number of years = 5
PRT/100= interest
R=(100*interest)/(PT)
R= (100*100)/(600*5)
R= 10000/3000
R= 10/3
R= 3 1/3%
Or R= 3.33%
Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. (If the vector field is not conservative, enter DNE.) F(x, y) = (3x2 − 2y2)i + (4xy + 4)j
Answers
In order for F to be conservative, there must be a scalar function f such that the gradient of f is equal to F. This means
[tex]\dfrac{\partial f}{\partial x}=3x^2-2y^2[/tex]
[tex]\dfrac{\partial f}{\partial y}=4xy+4[/tex]
Integrate both sides of the first equation with respect to x :
[tex]f(x,y)=x^3-2xy^2+g(y)[/tex]
Differentiate both sides with respect to y :
[tex]\dfrac{\partial f}{\partial y}=-4xy+\dfrac{\mathrm dg}{\mathrm dy}=4xy+4\implies\dfrac{\mathrm dg}{\mathrm dy}=8xy+4[/tex]
But we assume g is a function of y, which means its derivative can't possibly contain x, so there is no scalar function f whose gradient is F. Therefore F is not conservative.
In this problem, since the condition of equal derivatives does not apply, the vector field is not conservative.
A vector field can be described as:
[tex]F = <P,Q>[/tex]
It is conservative if:
[tex]\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x}[/tex]
In this problem, the field is:
[tex]F = <3x^2 - 2y^2, 4xy + 4>[/tex]
Then:
[tex]P(x,y) = 3x^2 - 2y^2[/tex]
[tex]\frac{\partial P}{\partial y} = -4y[/tex]
[tex]Q(x,y) = 4xy + 4[/tex]
[tex]\frac{\partial Q}{\partial x} = 4y[/tex]
Since [tex]\frac{\partial P}{\partial y} \neq \frac{\partial Q}{\partial x}[/tex], the field is not conservative.
A similar problem is given at https://brainly.com/question/15236009
Find a vector equation and parametric equations for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5.
Answers
The normal vector to the plane x + 3y + z = 5 is n = (1, 3, 1). The line we want is parallel to this normal vector.
Scale this normal vector by any real number t to get the equation of the line through the point (1, 3, 1) and the origin, then translate it by the vector (1, 0, 6) to get the equation of the line we want:
(1, 0, 6) + (1, 3, 1)t = (1 + t, 3t, 6 + t)
This is the vector equation; getting the parametric form is just a matter of delineating
x(t) = 1 + t
y(t) = 3t
z(t) = 6 + t
The vector equation for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5 is v =(1+t)i + (3t)j + (6+t)k
The parametric equations for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5
x(t) = 1+ty(t) = 3tz(t) = 6+tThe parametric equation of a line through the point A(x, y, z) perpendicular to the plane ax+by+cz= d is expressed generally as:
A + vt where:
A = (x, y, z)
v = (a, b, c) (normal vector)
This can then be expressed as:
s = A + vt
s = (x, y, z) + (a, b, c)t
Given the point
(x, y, z) = (1,0,6)
(a, b, c) = (1, 3, 1)
Substitute the given coordinate into the equation above:
s = (1,0,6) + (1, 3, 1)t
s = (1+t) + (0+3t) + (6+t)
The parametric equations from the equation above are:
x(t) = 1+t
y(t) = 3t
z(t) = 6+t
The vector equation will be expressed as v = xi + yj + zk
v =(1+t)i + (3t)j + (6+t)k
Learn more here: brainly.com/question/12850672
Michelle is 7 years older than her sister Joan, and Joan is 3 years younger than their brother Ryan. If the sum of their ages is 64, how old is Joan?
16
22
18
19
Answers
Answer:
(C) 18
Step-by-step explanation:
We can create a systems of equations. Assuming [tex]m[/tex] is Michelle's age, [tex]j[/tex] is Joan's age, and [tex]r[/tex] is Ryan's age, the equations are:
[tex]m = j + 7[/tex]
[tex]j = r-3[/tex]
[tex]m+j+r = 64[/tex]
We can use substitution, since we know the "values" of m and j.
[tex](j+7)+(r-3)+r = 64\\(j+7)+(2r-3)=64\\2r + j + 4 = 64\\2r + j = 60\\\\[/tex]
[tex]r = 21, j = 18[/tex]
So we know that Joan is 18 years old.
Hope this helped!
A ship leaves the port of Miami with a bearing of S80°E and a speed of 15 knots. After 1 hour, the ship turns 90° toward the south. After 2 hours, maintain the same speed. What is the bearing to the ship from port?
Answers
Answer:
The bearing is N 55.62° W
Step-by-step explanation:
ship leaves the port of Miami with a bearing of S80°E and a speed of 15 knots.
It then turns 90° towards the south after one hour.
Still maintain the same speed and direction for two hours.
The bearing is just the angle difference from the ship current location to where it started.
Let the speed be km/h
Distance covered in the first round
= 15*1
= 15km
Distance covered in the second round
=15*2
= 30 km
Angle at C = (90-80)+90
Angle at C = 10+90= 100
Let the distance between the port and the ship be c
C²= a² + b² -2abcos
C²= 15²+30²-2(15)(30)cos 100
C²= 225+900+156.28
C²= 1281.28
C= 35.8 km
Using sine formula
30/sin x= 35.8/sin 100
30/35.8 * sin 100 = sinx
0.838*0.9848= sin x
0.8253= sin x
Sin ^-1 0.8253 = x
55.62° = x
The bearing is N 55.62° W
Original price of a soda: $800 tax 7% selling price: $
Answers
Answer:
$856
Step-by-step explanation:
Find 7% of $800 and then add it to $800
