I
really need thorough explanations of the questions, I would be very
appreciated.
Definitely giving likes.
Especially the fifth one please :), thank you.
1. Find an equation for the line which passes through the origin and is parallel to the planes 2x-3y + z = 5 and 3x+y=2= -2. 2. Find an equation for the plane which passes through the points (0,-1,2),

Answer: $570

Step-by-step explanation: 10% of 800 is 80, so we add 80 + 150. That is equal to 230, we then subtract that amount from the original cost. SO: 800-230 = 570

The parametric equations for the tangent line to the curve at the point (5/3, 5, 4) are x(t) = -6.708t + 14.036, y(t) = 3.536t + 1.932, and z(t) = -8.986t + 12.97.

To find the tangent line to the curve at the given point, we first need to find the value of t that corresponds to the point.

We can do this by setting the x, y, and z equations equal to the given coordinates and solving for t:

10 cos(t) = 5/3

10 sin(t) = 5

8 cos(2t) = 4

Solving the first equation for cos(t) and the second equation for sin(t), we get:

cos(t) = 1/6

sin(t) = 1/2

Using the identity cos^2(t) + sin^2(t) = 1, we can find the value of cos(2t):

cos^2(t) + sin^2(t) = 1

cos^2(t) + (1-cos^2(t)) = 1

2cos^2(t) = 1

cos(2t) = 2cos^2(t) - 1 = -11/18

So the value of t that corresponds to the point (5/3, 5, 4) is t = arctan(2) ≈ 1.107.

Now, to find the parametric equations for the tangent line, we need to find the derivative of each component function with respect to t. We have:

x'(t) = -10 sin(t)

y'(t) = 10 cos(t)

z'(t) = -16 sin(2t)

Evaluating these at t = arctan(2), we get:

x'(arctan(2)) = -10 sin(arctan(2)) ≈ -6.708

y'(arctan(2)) = 10 cos(arctan(2)) ≈ 3.536

z'(arctan(2)) = -16 sin(2arctan(2)) ≈ -8.986

So the parametric equations for the tangent line are:

x(t) = 5/3 - 6.708(t - arctan(2))

y(t) = 5 + 3.536(t - arctan(2))

z(t) = 4 - 8.986(t - arctan(2))

Simplifying, we get:

x(t) = -6.708t + 14.036

y(t) = 3.536t + 1.932

z(t) = -8.986t + 12.97

Therefore, the parametric equations for the tangent line to the curve at the point (5/3, 5, 4) are x(t) = -6.708t + 14.036, y(t) = 3.536t + 1.932, and z(t) = -8.986t + 12.97.

To know more about derivative click here

brainly.com/question/29096174

#SPJ11

Answer: The given expression can be factorized as (2k - 3)(k² - 1) using the difference between squares.

Step-by-step explanation: To factorize the given expression using the difference between squares, we need to identify terms that can be written as the square of some other term.

We can rewrite the expression as:

(2k³ - 3k²) - (2k - 3)

Now, we can factor out the common terms from each bracket:

k²(2k - 3) - 1(2k - 3)

We can see that both brackets have a common factor of (2k - 3), which we can factor out:

(2k - 3)(k² - 1)

Therefore, the given expression can be factorized as (2k - 3)(k² - 1) using the difference between squares.

The equation will be written as (42/2) = 21.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the quotient of a number, 2, and 21 is 42. The equation of the quotient will be written as,

42 / 2 = 21

Here the value 42 when divided by 2 will give 21.

Therefore, the equation will be written as (42/2) = 21.

To know more about an expression follow

https://brainly.com/question/28416731

#SPJ1

Answer:

17

Step-by-step explanation:

f(x) = 2x+7

Let x =5

f(5) = 2*5 +7

     = 10+7

    = 17

Answer:

c = 8

Step-by-step explanation:

A slope of a line is the change in y coordinate with respect to the change in x coordinate. y=3x-22  is equation in point-slope form of the line through each pair of points" (9,5) and ( 8,2).

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

The slope intercept form of a line is y=mx+b

where m is the slope and b is y intercept.

slope of a line passing through two points is given by

m=y₂-y₁/x₂-x₁

(9,5) and ( 8,2)

x₁=9, y₁=5, x₂=8,y₂=2

Plug in the values to get the slope.

m=2-5/8-9

m=-3/-1

m=3

The equation of line is given by y-y₁=m (x-x₁)

y-5=3(x-9)

y-5=3x-27

y=3x-27+5

y=3x-22

Hence y=3x-22  is equation in point-slope form of the line through each pair of points" (9,5) and ( 8,2).

To learn more on slope of line click:

https://brainly.com/question/14511992

#SPJ1

Answer:

\({ \boxed{ \sf{Actual \: profit \: = \: Rs \: 78}}}\)

\( \boxed{ \sf{Selling \: price \: = \: Rs \: 1638}}\)

Step-by-step explanation:

Finding the selling price of a fan ( SP ) :

\( \boxed { \sf{SP = \frac{CP(100 + profit \: \%)}{100} }}\)

\( \sf{↦ \: SP \: = \frac{1560(100 + 5)}{100} }\)

\( \sf{↦SP = \frac{1560 \times 105}{100}} \)

\( \sf{↦ \: SP = \frac{163800}{100} }\)

\( ↦ \boxed{ \sf{SP = Rs \: 1638}}\)

Now, We have :

Finding the actual profit :

\( \boxed{ \sf{Actual \: profit \: = \: Selling \: price \: - \: Cost \: price}}\)

\( \sf{↦ \: Actual \: profit \: = \: Rs \: 1638 - \: Rs\: 1560}\)

\( \boxed{ \sf{↦ \: Actual \: profit \: = \: Rs \: 78}}\)

We're done !

Hope I helped!

Best regards! :D

~TheAnimeGirl

Both solutions satisfy the original equation. As a result, there are no extraneous solutions in this case.

To determine the number of extraneous solutions in the given equation, let's simplify it step by step:

Step 1: Let's find the common denominator for the two fractions on the left side of the equation. The common denominator is (2m + 3)(2m - 3).

Step 2: Apply the common denominator to both fractions:

[(2m)(2m - 3)]/[(2m + 3)(2m - 3)] - [(2m)(2m + 3)]/[(2m + 3)(2m - 3)] = 1

Step 3: Simplify the numerators:

\([4m^2 - 6m - 4m^2 - 6m]/[(2m + 3)(2m - 3)] = 1\)

[-12m]/[(2m + 3)(2m - 3)] = 1

Step 4: Cancel out common factors:

-12m = (2m + 3)(2m - 3)

\(-12m = 4m^2 - 9\)

Step 5: Rearrange the equation:

\(4m^2 + 12m - 9 = 0\)

Step 6: Solve the quadratic equation using factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

\(m = (-b ± √(b^2 - 4ac))/(2a)\)

For our equation, a = 4, b = 12, and c = -9. Substituting these values:

m = (-(12) ± √((12)^2 - 4(4)(-9)))/(2(4))

m = (-12 ± √(144 + 144))/(8)

m = (-12 ± √288)/8

m = (-12 ± 12√2)/8

Simplifying further:

m = (-3 ± 3√2)/2

So, we have two potential solutions for m:

m = (-3 + 3√2)/2  and  m = (-3 - 3√2)/2

Now we need to check if these solutions satisfy the original equation. Let's substitute these values back into the equation:

For m = (-3 + 3√2)/2:

[(2(-3 + 3√2))/(2(-3 + 3√2) + 3)] - [(2(-3 + 3√2))/(2(-3 + 3√2) - 3)] = 1

Simplifying this equation, we find that it holds true.

For m = (-3 - 3√2)/2:

[(2(-3 - 3√2))/(2(-3 - 3√2) + 3)] - [(2(-3 - 3√2))/(2(-3 - 3√2) - 3)] = 1

Simplifying this equation, we also find that it holds true.

Therefore, both solutions satisfy the original equation. As a result, there are no extraneous solutions in this case.

To know more about solutions check the below link:

https://brainly.com/question/29174899

#SPJ4

Answer:

4 nights

Step-by-step explanation:

12 centimeters over 3 nights

12 divided by 3 is 4

Each night she knitted 4 centimeters of the scarf

The next night she will knit  more centimeters 12 + 4 = 16

So she would take 4 nights to knit a total of 16 centimeters

As a result, the two phrases are logically equal. The two formulations are not logically identical, as we can see. The two formulations are not logically identical, as we can see.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms.

Here,

(a) The first statement can be expressed as:

(~j -> (l v ~r))

The second statement can be expressed as:

((r ^ ~l) -> j)

To determine whether the two expressions are logically equivalent, we can use truth tables. A truth table is a method for checking the validity of logical equivalences by comparing the truth values of the two expressions for all possible combinations of inputs.

Truth table for (~j -> (l v ~r)) and ((r ^ ~l) -> j):

j l r (~j -> (l v ~r)) ((r ^ ~l) -> j)

T T T T T

T T F T T

T F T F F

T F F T T

F T T T T

F T F T T

F F T T T

F F F T T

Since both expressions have the same truth values for all possible combinations of inputs, we can conclude that the two expressions are logically equivalent.

(b) The first statement can be expressed as:

(j -> ~l)

The second statement can be expressed as:

(~j -> l)

Truth table for (j -> ~l) and (~j -> l):

j l (j -> ~l) (~j -> l)

T T T F

T F T T

F T T T

F F T T

Since the expressions have different truth values for some combinations of inputs, we can conclude that the two expressions are not logically equivalent.

(c) The first statement can be expressed as:

((r v ~l) -> j)

The second statement can be expressed as:

(j -> (r ^ ~l))

Truth table for ((r v ~l) -> j) and (j -> (r ^ ~l)):

j l r ((r v ~l) -> j) (j -> (r ^ ~l))

T T T T T

T T F T T

T F T T T

T F F T T

F T T T F

F T F T F

F F T T F

F F F T T

Since the expressions have different truth values for some combinations of inputs, we can conclude that the two expressions are not logically equivalent.

We can conclude that the two expressions are logically equivalent. We can conclude that the two expressions are not logically equivalent. We can conclude that the two expressions are not logically equivalent.

To know more about expression,

https://brainly.com/question/30091997

#SPJ1

Answer:

C

Step-by-step explanation:

Simple physics

Answer:

try decrease the temperature of juice in glass B by 10 °C

Step-by-step explanation:

the only one that makes sense to me... sorry if im wrong

Answer:

you can but dont touch anything inside i did when i was a kid and electrocuted myself.

Step-by-step explanation:

careful. i dont recomend using it though

Answer:

that happed to me i still use the outlet sometime but i wouldn't take any chances

Step-by-step explanation:

By definitions of volume and flow rate, it will take a time of 10 minutes to fill the tank to a height of 50 centimeters.

Herein we find the case of a rectangular tank being filled with water at constant flow are, which is dimensionally speaking, volume by time. We know that dimensions of the tank are described in centimeters, whereas flow rate is described in liters per minute. Please notice that a liter is equal to 1000 cubic centimeters:

t = [(80 cm) · (60 cm) · (50 cm) · (1 L / 1000 cm³)] / (24 L / min)

t = 10 min

By definitions of volume and flow rate, it will take a time of 10 minutes to fill the tank to a height of 50 centimeters.

To learn more on filling processes: https://brainly.com/question/13310861

#SPJ1

Answer:

4

Step-by-step explanation:

15x+20 = 40 +10x

x = 4

Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

Answer:6528

Since there are 2 tires, both of which are $130,056 you would need to divide by 2 to get the price of the tires separately.

Answer:

$23

Step-by-step explanation:

50 + 19 is 69, and since Justin wants to divide the money into 3 parts. Just divide the total (69) by 3, to get 23. So, Justin will put $23 into the three of the accounts.

Answer:

Step-by-step explanation:

yes

Answer:

I think of having 81inches

20 students are selected at random from each grade level, of random sampling within each stratum.

A random sample from each grade level, the survey plan ensures that each grade level is represented in the sample, and that the sample is likely to be representative of the entire school population.

The survey plan described in the question is a combination of two different sampling techniques:

stratified sampling and random sampling.

Stratified sampling involves dividing the population into subgroups, or strata, based on certain characteristics that are relevant to the research question.

The population is divided by grade level, which is likely to be a relevant factor when it comes to determining student support for the student-council president.

The purpose of stratified sampling is to ensure that each subgroup is represented in the sample in proportion to its size in the population.

This helps to minimize sampling bias and increase the precision of the estimates obtained from the sample.

Once the population is divided into subgroups, random sampling is used to select a sample from each stratum.

Random sampling involves selecting individuals from the population in such a way that each individual has an equal chance of being selected.

This helps to ensure that the sample is representative of the population and that any estimates obtained from the sample are unbiased.

In this survey plan, 20 students are selected at random from each grade level, which is an example of random sampling within each stratum.

By selecting a random sample from each grade level, the survey plan ensures that each grade level is represented in the sample, and that the sample is likely to be representative of the entire school population.

Overall, the survey plan described in the question is a good example of how different sampling techniques can be combined to obtain a representative sample of a population.

By using stratified sampling to divide the population into subgroups and random sampling to select individuals from each subgroup, the survey plan helps to minimize sampling bias and increase the precision of the estimates obtained from the sample.

For similar questions on random

https://brainly.com/question/251701

#SPJ11

For the ratios of the angles;

Sine, cosine, and tangent are trigonometric functions used to calculate the ratios of the sides of a right triangle. The side opposite the right angle is called the hypotenuse, while the other two sides are called the adjacent and opposite sides.

Let the hypotenuse be X

Angle A;

Sine A= D/X

Cos A = M/X

Tan A = D/M

Angle B;

Sin B = M/X

Cos B = D/X

Tan B = M/D

The e angle in question may be measured in radians or degrees.

Learn more about right triangle ratios:https://brainly.com/question/20367690

#SPJ1

Answer:

(-infinity, -2) ∪ (-3, infinity).

Step-by-step explanation:

To solve this compound inequality, we need to first solve each inequality separately. For the first inequality, 4(z+1) > -4, we can distribute the 4 to get 4z + 4 > -4. Then, we can subtract 4 from both sides to get 4z > -8. Finally, we can divide both sides by 4 to get z > -2.

For the second inequality, 2z - 4 < -10, we can add 4 to both sides to get 2z < -6. Then, we can divide both sides by 2 to get z < -3.

Now that we have solved both inequalities, we need to consider their intersection. Since the inequalities are joined by the "or" operator, the solution is the union of the solutions to each inequality. In interval notation, this is represented as the union of the intervals (-infinity, -2) and (-3, infinity).

Therefore, the solution to the compound inequality in interval notation is (-infinity, -2) ∪ (-3, infinity).

Answer:

$2,400

Step-by-step explanation:

3 tons equals 6000 pounds

6000*0.40= $2,400

The simplified expression is u^(3) - v^(3).

To perform the indicated operation on the algebraic expressions, we need to multiply each term in the first expression by each term in the second expression and then simplify the resulting expression.

Step 1: Multiply each term in the first expression by each term in the second expression:

(u)(u^(2)) + (u)(uv) + (u)(v^(2)) - (v)(u^(2)) - (v)(uv) - (v)(v^(2))

Step 2: Simplify the resulting expression by combining like terms:

u^(3) + u^(2)v + uv^(2) - u^(2)v - uv^(2) - v^(3)

Step 3: Simplify further by canceling out terms that are equal but opposite in sign:

u^(3) - v^(3)

Therefore, the simplified expression is u^(3) - v^(3).

Learn more about simplified expressions here:

brainly.com/question/403971#

#SPJ11