An implicit equation for the plane passing through the point (5,0,5) that is perpendicular to the line l(t)=⟨3,−1−5t,−1−2t⟩ is
The implicit equation for the plane passing through the point (5,0,5) that is perpendicular to the line l(t)=⟨3,−1−5t,−1−2t⟩ is 3x - 5y - 2z = 20.
Explanation:To find the equation of the plane passing through the point (5,0,5) and perpendicular to the line l(t)=⟨3,−1−5t,−1−2t⟩, we need to find the normal vector of the plane. The normal vector is the direction vector of the line, which is (3, -5, -2). Using the formula for the equation of a plane in standard form, which is ax + by + cz = d, and substituting the coordinates of the point and the normal vector, we get 3x - 5y - 2z = 20
as the implicit equation for the plane.
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Emmanuel read 150 pages in 5 hours. How long would it take him to read 230 pages?
Suppose the tank is 10 ft high and has radius 2 ft and the circular hole has radius ! in. if the tank is initially full, how long will it take to empty?
Lizzy and Ella sold 10 boxes of cookies for $55.50. How much does each box of cookies cost? Show all your work and explain how you got your answer.
Charlie has the utility function u(xa, xb) =xaxb.his indifference curve passing through 32 applesand 8 bananas will also pass through the point where he consumes 4 apples and
Final answer:
To find the indifference curve passing through 32 apples and 8 bananas, we can set up a system of equations and solve for the relationship between apples and bananas. The indifference curve will also pass through the point where Charlie consumes 4 apples and 2 bananas.
Explanation:
An indifference curve represents a set of choices that have the same level of utility. In this case, Charlie's utility function is u(xa, xb)=xaxb. To find the indifference curve passing through 32 apples and 8 bananas, we can set up a system of equations. If we plug in these points into the utility function, we get 32a*8b=4a*xb. Solving for b, we find that b=1/2a. This means that for every amount of apples, Charlie wants to consume half as many bananas to maintain the same level of utility. Therefore, the indifference curve passing through 32 apples and 8 bananas will also pass through the point where he consumes 4 apples and 2 bananas.
Gunther is buying baseballs in bags of 10 he has 40 baseballs but needs a total of 70 baseballs for throwing practice.
Big Louie's Pizza house sells a 12 inch square pan pizza for $3.95 and a 24-inch square pan pizza for $14.95 which pizza is a better deal explain clearly how you know
The 24-inch pizza is a better deal because it costs slightly less per square inch compared to the 12-inch pizza.
Explanation:To determine which pizza is a better deal, we need to compare their prices per square inch. First, let's find the area of the 12-inch pizza. The formula to find the area of a square is side length squared, so the area of the 12-inch pizza is 12 x 12 = 144 square inches. Now, we can divide the price of the 12-inch pizza by its area to find the price per square inch: $3.95 / 144 = $0.0274 per square inch.
Next, let's find the area of the 24-inch pizza. The area of the 24-inch pizza is 24 x 24 = 576 square inches. Now, we can divide the price of the 24-inch pizza by its area to find the price per square inch: $14.95 / 576 = $0.0259 per square inch.
Comparing the prices per square inch, we can see that the 24-inch pizza is a better deal, as it costs slightly less per square inch compared to the 12-inch pizza.
(sinx-1)(sinx+cos^2x) multiply and simplify
Find the slope and y-intercept of the following line
-7x+7y=-17
find the Factor of 6x 2 - 17x + 5.
Answer:
Step-by-step explanation:
[tex]6x^2-17x+5[/tex]
This can be written as
[tex]6x^2-15x-2x+5[/tex]
Because -15-2=-17 and also (-15)(-2)=30
so now we have two pairs
[tex](6x^2-15x)+(-2x+5)[/tex]
Take out GCF from each pair
[tex]3x(2x-5)-1(2x-5)[/tex]
since (2x-5) is now the common factor so final factored form
[tex](3x-1)(2x-5)[/tex]
Solve for a 6(a+3)=18+6a
The equation 6(a+3) = 18+6a is an identity after canceling out like terms on both sides, which implies that the solution for 'a' is all real numbers.
To solve for a in the equation 6(a+3) = 18+6a, we begin by expanding the left side of the equation:
6a + 18 = 18 + 6a
We notice that there are terms on both sides of the equation that can be cancelled out. The 6a on the left side can be subtracted from both sides, as well as the constant 18.
After cancelling out these terms, we are left with:
0 = 0
This equation suggests that the original equation is an identity, meaning that the value of a can be any real number, as the original equation holds true for all values of a.
All the digits are odd. The last two digits add to make ten. The first and last digits add to make eight. The first two digits add to make twelve. What is the number?
The number that fits all the given criteria is 3955, where all digits are odd, the last two add to 10, the first and last to 8, and the first two to 12.
To find a number where all digits are odd, the last two digits add up to make ten, the first and last digits add up to eight, and the first two digits add up to twelve, we can use a process of elimination and reasoning.
The last two digits must be 5 and 5 because these are the only odd digits that add up to 10.The first and last digit must be 3 and 5 respectively because these add up to 8.Since the first digit is 3 and we need the first two digits to add to 12, the second digit has to be 9.Therefore, the number is 3955.
Josiah went to the local barber to get his hair cut. It cost $18 for the haircut. Josiah tipped the barber 15%. What was the total cost of the haircut including the tip
The total cost of the haircut including the tip is $20.70. 18*15%=2.70+18=20.7.
Hope this helps:)
Answer:
$20.70
Step-by-step explanation:
Turn the % to a decimal.
15%= 15/100 = 0.15
Multiply the total and decimal.
18.00 x 0.15
= 2.70
Add the total to the sum.
18.00 + 2.70
= 20.70
(hope it helped please vote and say thanks <3)
what is 3×4-14+4=? It's one of my math class questions
Complex numbers are often used when dealing with alternating current (AC) circuits. In the equation V = IZ, V is voltage, I is current, and Z is a value known as impedance. If V = 1+i and Z=2-i, find I. Please do this quickly!!
Final answer:
The current I in the AC circuit equation V = IZ is found by complex division and is equal to 1/5 + 3/5i when V = 1+i and Z=2-i.
Explanation:
To find the current I in the equation V = IZ where V = 1+i and Z=2-i, we need to solve for I using complex division. This process involves conjugating the denominator and then performing standard multiplication of complex numbers.
Step-by-step solution:
Write down the given values in the equation: V = 1+i, Z = 2-i.Use the formula I = V / Z.Conjugate the denominator Z, which gives 2+i.Multiply the numerator and denominator by the conjugate of the denominator:So, I = (1+i) * (2+i) / ((2-i) * (2+i)).Simplify both numerator and denominator: numerator becomes 2 + 3i + i^2, and the denominator becomes 4 - i^2.Substitute i^2 with -1 and simplify: numerator becomes 2+3i-1, and the denominator becomes 4+1.The final result is I = (1+3i) / 5.Divide both the real and imaginary parts by 5: I = 1/5 + 3/5i.Therefore, the current I is 1/5 + 3/5i.
Find three consecutive odd integers whose sum is 279. N + 2 and n + 4 represent the other two numbers
divide 279 by 3
279 / 3 = 93
93-2 = 91
first number = 91
N +2 = 91 +2 = 93
N+4 = 91 +4 = 95
91 + 93 +95 =279
Thomas earns x dollars each week walking his neighbor’s dog. He also earns $10 allowance each week. Which expression represents the amount of money Thomas has earned after 4 week select each correct statments
Pythagoras was born about 582 BC. Isaac Newton was born in 1643
AD. How many years apart were they born.?
Complete the given table
The sum of two numbers is 99. If three times the smaller number is subtracted from the larger number, the result is 19. Find the two numbers.
A truck with 32-inch diameter wheels is traveling at 60 mi/h. Find the angular speed of the wheels in rad/min. How many revolutions per minute do the wheels make?
The angular speed of the wheel is 3960 rad/min and the revolutions per minute is 630 rpm.
The velocity of the truck is 60 mph. We need to convert this speed to inches per minute.
1 mile = 63360 in, 1 hour = 60 minutes
Hence:
60 mph = (60 mile * 63360 in/mi) / (1 hr * 60 min/hr) = 63360 in/min
The diameter = 32 in, hence radius = 32/2 = 16 in
The angular speed = 63360 in/min ÷ 16 in = 3960 rad/min
Revolution per minute = 3960 rad/min ÷ 2π = 630 rpm
Hence the angular speed of the wheel is 3960 rad/min and the revolutions per minute is 630 rpm.
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The wheels make approximately 52.55 revolutions per minute.
To find the angular speed of the wheels in radians per minute, we first need to find the linear speed of a point on the edge of the wheel.
The formula to calculate the linear speed (v) is given by:
[tex]\[ v = r \times \omega \][/tex]
Where:
- v is the linear speed,
- r is the radius of the wheel, and
- [tex]\( \omega \)[/tex] is the angular speed in radians per second.
Given that the diameter of the wheels is 32 inches, the radius (r ) is half of the diameter, so [tex]\( r = \frac{32}{2} = 16 \)[/tex] inches.
We are given the speed of the truck, v = 60 mi/h. To convert this to inches per minute, we need to convert miles to inches and hours to minutes:
[tex]\[ 60 \text{ miles/h} = 60 \times 5280 \text{ inches/60 minutes} = 5280 \text{ inches/minute} \][/tex]
Now, we can rearrange the formula to solve for [tex]\( \omega \):[/tex]
[tex]\[ \omega = \frac{v}{r} \][/tex]
Substituting the known values:
[tex]\[ \omega = \frac{5280 \text{ inches/minute}}{16 \text{ inches}} \]\[ \omega = 330 \text{ radians/minute} \][/tex]
So, the angular speed of the wheels is 330 radians per minute.
Now, to find the number of revolutions per minute (rpm), we need to convert the angular speed from radians per minute to revolutions per minute. Since [tex]\( 2\pi \)[/tex] radians is equal to one revolution, we have:
[tex]\[ \text{Revolutions per minute (rpm)} = \frac{\omega}{2\pi} \][/tex]
Substituting the value of [tex]\( \omega \):[/tex]
[tex]\[ \text{rpm} = \frac{330}{2\pi} \]\[ \text{rpm} \approx \frac{330}{6.28} \approx 52.55 \][/tex]
So, the wheels make approximately 52.55 revolutions per minute.
To the nearest ten thousand , the population of Vermont was estimated to be about 620,000 in 2008. What might have been the exact population of Vermont in 2008?
The statement given is
The population of Vermont was estimated to be about 620,000 in 2008.
Exact population of Vermont in 2008
= 615,000 ≤ A number between ≤ 620,000
=[615000, 620000]
solve q+12-2(q-22)>0
The solution to the given inequality problem is;
q < 56
We are given the equation;
q + 12 - 2(q - 22) > 0
Step 1; Using distributive property, distribute 6 to the numbers inside the bracket to get;
q + 12 - 2q + 44 > 0
Step 2; Combining similar terms on the left side and simplifying gives us;
56 - q > 0
Step 3; Using addition property of equality, add q to both sides;
56 - q + q > 0 + q
q < 56
Thus, the final solution is q < 56
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5.14 grater than 5.041
A eighteen-sided die is rolled three times. In how many ways can this happen?
Number of ways it can happen is 5832.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
We have eighteen-sided die is rolled three times.
When the die is first rolled, there are 18 possibilities of outcomes.
Again when the die is rolled, again there are 18 possibilities.
In the third rolling also, there are 18 possibilities.
Each die has 18 possibilities of numbers for a number for the other die.
Total number of sets = 18 × 18 × 18
= 5832
Hence the total number of ways that the numbers can be formed is 5832.
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The width of a rectangle is 3 inches less than twice the length. If the length of the rectangle is represented by L, write an algebraic expression to represent the width
The width of the rectangle is 3 inches less than twice the length, which is represented by L. The algebraic expression for the width is W = 2L - 3.
The width of a rectangle is described in the problem as being 3 inches less than twice the length of the rectangle. If the length of the rectangle is denoted by L, the algebraic expression to represent the width (W) can be written as:
W = 2L - 3
To clarify, this expression means that whatever the length L is, you would double it (that's the 2L part), and then subtract 3 inches to find the width of the rectangle.
Does this graph show a function?
please help me differentiate this
A curve is defined by the parametric equations
x=t^2 and y=t^3
show that the equation of the tangent to the curve at the point P (p^2, p^3) is
2y-3px+p^3=0
Jed has 25 toy cars. Kai has 32 you cars. Ken has fewer cars than either Jed or Kai. How many cars might Ken have?
The possible range of numbers of cars Ken might have is 0 ≤ Ken ≤ 24.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Jed has 25 toy cars.
Kai has 32 you cars.
Since Ken has fewer cars than either Jed or Kai, the maximum number of cars Ken could have is 24 (if both Jed and Kai give him one car each).
The minimum number of cars Ken could have is 0 (if both Jed and Kai have more cars than Ken).
So the possible range of numbers of cars Ken might have is 0 ≤ Ken ≤ 24.
Hence, the possible range of numbers of cars Ken might have is 0 ≤ Ken ≤ 24.
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G find an equation of the sphere with center (3, −10, 4) and radius 5. (x−3)2+(y+10)2+(z−4)2=25 use an equation to describe its intersection with each of the coordinate planes. (if the sphere does not intersect with the plane, enter dne.)