Find an equation of the plane through the point (1, -4, 0) and perpendicular to the vector (5, 1, -4). Do this problem in the standard way or WebWork may not recognize a correct answer.
Answers
Answer:
x = = -5 ; y = -1 ; z = 4 \(\bigg | = 3 \bigg |\)
Step-by-step explanation:
The equation of the plane through (1,-4,0) is,
a(x-1) + b(y+4) + c(z+0) = 0 ....... (1)
Again the plane is perpendicular to the vector (5,1,-4)
So, the direction ratios of the normal to the plane is proportional to the direction ratios of the vector (5,1,-4)
So, a/(5) = b/(1) = c/(-4 )
Let,a/(5) = b/(1) = c/(-4 ) = k
So, a = 5k, b = k and c = -4k
So, from (1) we have,
(5k)(x-1) + (k)(y+4) + (-4k)(z+0) = 0
Thus;
-5(x-1) -(y+4) +4(z+0) = 0
So,
-5x +1 -y-4+4z+0 =0
-5x - y +4z -3 = 0
-5x - y +4z = 3
x = = -5 ; y = -1 ; z = 4 \(\bigg | = 3 \bigg |\)
Related Questions
Savannah buys a $40 gift card to her favorite smoothie shop. Each smoothie costs $4. She wants to have at least $10 left on her card at the end of this month. The inequality below relates x, the number of smoothies she could buy between now and the end of this month with her gift card balance. 40 minus 4 x greater-than-or-equal-to 10 Which best describes the number of smoothies Savannah can buy? She can buy from 0 to 3 smoothies, but no more. She can buy from 0 to 7 smoothies, but no more. She can buy from 0 to 8 smoothies, but no more. She can buy from 0 to 10 smoothies, but no more.
Answers
Answer:
0-7 bc 7×4 is 28 and 8×4 is 32, 32 is over the balance 28 is right on
Answer:She can buy from 0-7 smoothies, but no more.
Step-by-step explanation:i got it right
The formula for an account that earns
compound interest is Pt = P0 ⋅ (1 + r)
t
,
where Pt
represents the balance in the
account after t years, P0 represents the
initial amount of the deposit, and r
represents the interest rate.
Carrie is considering depositing $1480 into
an account that pays compound interest.
How much will be in her account if she
receives 1.9% compound interest for
10 years? Round to the nearest cent.
Answers
After 10 years with a Compound interest rate of 1.9%, the amount in Carrie's account will be approximately $1777.87.
The amount that will be in Carrie's account after 10 years with compound interest, we can use the formula Pt = P0 ⋅ (1 + r)^t.
Given:
P0 = $1480 (initial deposit)
r = 1.9% = 0.019 (interest rate as a decimal)
t = 10 (number of years)
Substituting these values into the formula, we get:
Pt = $1480 ⋅ (1 + 0.019)^10
Using a calculator, we can evaluate the expression inside the parentheses:
(1 + 0.019)^10 ≈ 1.201223
Now we can calculate the final amount in Carrie's account:
Pt ≈ $1480 ⋅ 1.201223
Pt ≈ $1777.87
Therefore, after 10 years with a compound interest rate of 1.9%, the amount in Carrie's account will be approximately $1777.87.
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6 / 29(1+2) is What??
Answers
Answer:5
Step-by-step explanation:
Identify the domain of the function shown in the graph.
A. X≥ 0
B. x < 0
C. 0
-8-84-2
D. x is all numbers.
10-
8
8.
4+
2+
y
-2-
4.
-8-
-10+
2
4 6 8 10 12
Answers
Answer:
A. \( x \geq 0\)
Step-by-step explanation:
The domain of a function is the set of \(x\)-values.
C
On Wednesday they made $5.50 How much does Zara get?
Please help?
Answers
Answer
Zara gets $5.50
Step-by-step explanation:
i need help can someone please help me
Answers
The measure of the angle m∠ZYX of the trapezoid is equal to 139°
What is a trapezoid?A trapezoid is a quadrilateral with two parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The adjacent angles of the trapezium are supplementary, so their sum is equal to 180°.
3x + 19 + x + 1 = 180°
4x + 20 = 180°
4x = 180 - 20 {collect like terms}
4x = 160
x = 160/4 {divide through by 4}
x = 40
m∠ZYX = 3(40) + 19 = 139°.
WXYZ is a trapezoid. Equation used to solve for x is (3x + 19) + (x + 1) = 180° because the angles m∠XYZ and m∠WXY are adjacent angles.
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A tunnel is shaped in the form of a semi-ellipse. The width of the tunnel is 20 feet and the height of the tunnel is 12 feet. A train is 10 feet wide and centered in the tunnel. Determine whether a 10-foot high train would have clearance to pass through. If so, by how much? If not, by how much? (Nearest inch.)
Answers
(x^2 / a^2) + (y^2 / b^2) = 1
where "a" is the horizontal radius (half of the width) and "b" is the vertical radius (half of the height).
In this case, we have:
a = 20/2 = 10 feet
b = 12/2 = 6 feet
We can assume that the train is centered in the tunnel, so we need to find the height of the semi-ellipse at the center (i.e., the value of "y" when "x" is 0).
Plugging in the values for "a" and "b", we get:
(0^2 / 10^2) + (y^2 / 6^2) = 1
Simplifying, we get:
y^2 / 36 = 1
y^2 = 36
y = ±6 feet
Therefore, the height of the semi-ellipse at the center is 6 feet.
To determine whether a 10-foot high train would have clearance to pass through, we need to check whether the height of the semi-ellipse at the sides is greater than or equal to 10 feet.
Plugging in the values for "a" and "b" and solving for "y" when "x" is 5 feet (half of the train's width), we get:
(5^2 / 10^2) + (y^2 / 6^2) = 1
Simplifying, we get:
y^2 / 36 = 0.75
y^2 = 27
y ≈ ±5.2 feet
Since the height of the semi-ellipse at the sides is about 5.2 feet, a 10-foot high train would not have clearance to pass through. The clearance is less than 5.2 - 5 = 0.2 feet (or about 2.4 inches).
Therefore, the train would not fit through the tunnel with 10 feet of clearance.
If f(x)= 5x + 40, what is f(x) when x = -5?
Answers
Answer:
f(x) = 15
Step-by-step explanation:
"If f(x)= 5x + 40, what is f(x) when x = -5?"
Substitute x for -5:
f(x) = 5x + 40
f(x) = 5(-5) + 40
f(x) = -25 + 40
f(x) = 15
2.13 Un recipiente de acero debe colocarse dentro de una excavación. Determine por trigonometría
a) la magnitud y la dirección de la fuerza P más pequeña para la cual la resultante R de las dos
fuerzas aplicadas en A sea vertical y b) la magnitud correspondiente de R.
Answers
Therefore, the force applied at point A such that the force applied is vertical is 1.84 kN. Now, let's find the magnitude of R.Corresponding magnitude of R is 3.97 m.
Given the following diagram;We need to determine the forces applied at point A such that a) the force applied is vertical and b) the corresponding magnitude of R.
For the given diagram, we can use trigonometry to find the required forces that are applied. We know that,Here, OA is the perpendicular drawn from point O on
AB.OA = OBcos(θ) = 4cos(25°) = 3.61m
Similarly, we can find the value of
OC.OC = OBsin(θ) = 4sin(25°) = 1.68m
Let's find the value of R first. We know that
R =\(\sqrt{ (OA^2 + OC^2)}R = √(3.61^2 + 1.68^2)R = 3.97m\)
Now, let's find the forces applied at point A such that the force applied is vertical. Here, the force applied is the horizontal component of the force at point A.Force at
A = OC/ OA * RForce at A = (1.68/3.61) * 3.97
Force at A = 1.84 kN (approx.)
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Can anyone help me with this question please?
Answers
Answer : -0.65
:)
Look at the graph below. Is it a function or not a function? Explain your reasoning.
Answers
2.93 km
Before the eruption of a volcano, the volcano was 2.93 kilometers
high. After the eruption, the volcano was 2.53 kilometers high
Use the bar diagram to find the difference in height of the volcano
before and after the eruption, in meters,
2.59 km
Click the icon to see the metric units of length
meters,
The difference in height of the volcano before and after the eruption is
(Type a whole number or a decimal)
Answers
Answer:
0.4
Step-by-step explanation:
A car traveled 81.6 mi in 1.6 hours.
Rate is found by dividing distance by time.
What is the rate in miles per hour?
Answers
Answer:
51
Step-by-step explanation:
81.6/1.6
Hope this helps. :)
what are 3 angles that are congruent to <4
Answers
Answer:
12,10,2
Step-by-step explanation:
Find the percent of change
8 feet to 10 feet
Answers
Answer:
10 feet is \(\frac{10}{8}\) or 1.25% of 8 feet.
Step-by-step explanation: :D
a rectangular auditorium seats 2244 people. The number of seats in each row exceeds the number of rows by 7. Find the number of seats in each row
Answers
Number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7. This can be obtained by assuming the value of number of seats in each row, forming quadratic equation and using quadratic formula to find root.
Find the number of seats in each row:
Here in the question it is given that,
a rectangular auditorium seats 2244 peoplenumber of seats in each row exceeds the number of rows by 7We have to find the number of seats in each row.
Let us assume that the number of seats in each row be x.
From the given statement, number of seats in each row exceeds the number of rows by 7, we can write that,
Number of seats in one row = Number of rows + 7
x = Number of rows + 7
⇒ Number of rows = x - 7
Total number of seats in the auditorium can be written as,
⇒ (Number of seats in one row)(Number of rows) = Total number of seats
(x)(x - 7) = 2244
x² - 7x = 2244
⇒ x² - 7x - 2244 = 0
By using quadratic formula we can find the root,
x = (-b ± √b² - 4ac)/2a
here in the question, a = 1, b = -7, c = -2244
√b² - 4ac = √(-7)² - 4(1)(-2244)
√b² - 4ac = √49 + 8976
√b² - 4ac = √9025
√b² - 4ac = 95
x = (-b ± √b² - 4ac)/2a
x = (7 ± 95)/2
x = 102/2 or x = -88/2
⇒ x = 51 or x = -44
Hence number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7.
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HALP PLAS NEED HALP PLESAAA
Answers
Answer:
the answer is 32
Step-by-step explanation:
ywwwww
Answer:
the answer is 32..... 32
How many ways to paint a house with 3 different colors from a pool of 12 distinct colors
Answers
Please help me needed this question asap
Answers
\(\pink{\underline{{\boxed{\bf{Question:: }}}}}\)
Select the names below of every young person aged 16, 17 or 18 who lives in wrexham.
\(\pink{\underline{{\boxed{\bf{Options:}}}}}\)
Eugene Smith❌Thomas Brown ✔️Paula Davis❌Tony AdamsAjit Singh✔️Su Ling ❌\(\pink{\underline{{\boxed{\bf{ Answer:}}}}}\)
The answer is Ajit Singh who's age is 18 and living in wrexham & Thomas Brown who's age is 17 and living in wrexham.
Other Notes:
Eugene Smith's age too is 18 but lives in Sutton.
Paula Davis too lives in Wrexham but her age is 20.
Tony Adam's age is 16 but lives in Ripely.
Su Ling's age is also 16 but lives in Dover.
\(\small{\underbrace{\overbrace{\color{Blue} {Hope \: It’ll \: Help \: You :)}}}}\)
jannie has 2 liters of orange squash she also has some empty cups One full Beach club holds 30 mL of orange squash jennine files as many cups as possible How much orange squash does janine have after filing as many cups as possible
Answers
Answer:
The question is a bit incorrect as there isnt mentioned how many cups are there.But if you meant how many 30ml cups can Jannie fill it would be 66.66 cups or 67/66 cups .
Step-by-step explanation:
If you would correct your answer I would try my best to give you the brainliest answer.
Calculate work by parts. 5x2-23)
Answers
Answer:
10-23= -13 is the answer
Answer:
think -13 is the answer
Fill in the blank 57.59 - ___=1.29
Answers
Answer: 57.59- 56.3=1.29
Step-by-step explanation:
57.59-x = 1.29
-x= 1.29-57.59
(—) -x= - 56.3
x=56.3
In ΔQRS, the measure of ∠S=90°, RS = 3.3 feet, and QR = 9.4 feet. Find the measure of ∠R to the nearest degree.
Answers
Answer:
69
Step-by-step explanation:
QUESTION 4 of 10: It is estimated that 32 patrons will attend an event for every $100 spent in advertising. If tickets cost $75, how much can a
promoter expect to increase sales if he spends $25,000 in advertising?
Answers
Answer:
$575000Step-by-step explanation:
Spend on advertising = $25000
32 patrons per $100
Number of patrons:
25000/100×32 = 8000Sales amount:
8000×$75 = $600000Increase in sales excluding advertisement cost:
$600000 - $25000 = $575000Answer:
$600,000
Step-by-step explanation:
$25,000 / 100 then 250 x 32 then 8,000 x 75 to get $600,000
Express the gross salary g of a person who earns per hour as a function of the number x of hours worked.
Answers
Answer:
Gross salary =G
Number of worked hours =x
Dollar per hour =$12
substitute the given data into the gross salary formula and simplify.
Gross salary = (number of worked hours)
G =(x) (12)
G =12x
Therefore, G(x) =12x
Hence the function is G(x) = 12x
megan buys a 2-quart bottle of juice for $2.56. What is the rate unit of the cost of the juice?
Answers
The rate unit of the cost of the juice bought by Megan is $1.28 per quart.
What is defined as the unitary method?The unitary method is a methodology that involves determining the value of a single unit and then calculating the value of the requisite number of units based on that value.The unitary method's formula is to obtain the price of a single unit and afterwards multiply that value by the number of components to get the required value.For the given question;
The price of 2-quart bottle of juice bought by Megan = $2.56.
For calculating the price of 1 bottle, simply divide the total cost by number of bottles.
Price of a single quart bottle = $2.56/2.
Price of a single quart bottle = $1.28 per quart.
Thus, the price of single quart bottle of juice is 1.28 per quart.
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Evaluate the function below for x = 2.
F(x) = x^4 + 6x2 + 3
Answers
Answer:
43
Step-by-step explanation:
NEED GEOMETRY HELP ASAP
Answers
Answer:
HJ > KP
Step-by-step explanation:
Form the figure attached,
Two triangles PKL and JGH have been given with HG ≅ KL and PL ≅ GJ
m∠HGJ = 90°
m∠KLP = 85°
Since m∠HGJ > m∠PLK
Therefore, measure of opposite sides of these angles have the same relation.
HJ > KP
The high school art teacher has 6 crayons with 61 boxes in each case. The elementary school art teacher has 9 cases of crayons 112 in each case. How many total boxes of crayons do both teachers have?
Answers
1. Collect Information.
High School Teacher: 9 cases of crayons + 52 boxes per case
Elementary School Teacher: 16 cases of crayons with 104 boxes per case
2. Multiply the number of cases by the boxes per case to get the number of boxes that each teacher has in total.
High School: 9 cases × 52 boxes = 468 boxes in total
Elementary School: 16 cases × 104 boxes = 1,664 boxes in total
3. State your answer.
The high school art teacher has 468 boxes in total and the elementary school art teacher has 1,664 boxes in total.
4. Is my answer reasonable?
Yes, my answer is reasonable for multiple reasons:
The elementary school art teacher had more cases and more boxes so it would only make sense that the total number of boxes which the elementary school art teacher has would be greater than the total number of boxes which the high school art teacher has.
Using common knowledge of 50 × 9 being equal to 450 (If this isn't common knowledge then remember that 5×9=45 and that you could just bring down the 0 from the 50 and the answer would be 450) you could tell that the answer would be a little more than 450 and knowing that 50×10=500 you would know that it would also be less than 500. 468 falls in between of 450 and 500 so my answer here is reasonable.
Using common knowledge of 16×100 being equal to 1,600 and 17×100=1,700 you could tell that the answer would be greater than 1,600 and less than 1,700. 1,664 falls in between of 1,600 and 1,700 so my answer here is reasonable.
solve this question please
Answers
Answer:
Step-by-step explanation:
a) 1.8 kg in grams is 1800 g
b) If 6 toys weigh 1800g; then 1 toy weighs 300 g(6:1)
c) If 1 toy weighs 300 g, 4 toys weigh 1200 g and you convert in kg which is 1.2 kg