The scale drawing car length is 3 cm. If the scale is 1cm:4ft, what is the actual car length?

Answer:

x=13 and y=sqrt338

Step-by-step explanation:

so basically the opposite of one of the 45 degrees is 13 so the other 45 degrees is 13 too and you find pythagorean theorem of the other one

A. The size of the tower bounded by the plane z = 0 and the paraboloid z = 1 - x² - y² can be calculated using a double integral in polar coordinates. B. Differential equation models can be 1. free-falling stone, 2. spring vertical displacement C. The rate of change of temperature at the origin in the direction of the unit vector u = (3,-5) can be determined by T = r² + s².

A. To calculate the size of the tower bounded by the plane z = 0 and the paraboloid z = 1 - x² - y², we can use a double integral in polar coordinates. By expressing the paraboloid equation in polar coordinates, we can set up the integral and evaluate it to find the size of the tower.

B. Differential equation models are mathematical representations used to describe various real-life phenomena. For the given examples:

The free-falling stone can be modeled using Newton's second law and the concept of acceleration due to gravity.

The vertical displacement of a spring can be described using Hooke's law and the properties of springs.

Kirchhoff's Second Law, also known as the voltage law, can be used to model the behavior of electrical circuits.

Newton's Law of Cooling is a differential equation that describes the rate of change of temperature of an object as it loses heat to its surroundings.

Growth and decay phenomena, such as population growth or radioactive decay, can be modeled using exponential or logarithmic functions.

C. To calculate the rate of change of temperature at the origin in the direction of the unit vector u = (3,-5), we need to find the gradient of the temperature function T = r² + s². The gradient represents the direction of the steepest increase in a function. By computing the gradient at the origin and taking the dot product with the unit vector u, we can determine the rate of change of temperature in the desired direction.

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(5+2.5+2.5 Marks) A. Use double integral and polar coordinates to calculate the size of a tower bounded by the plane z = 0 and the paraboloid z = 1 - x² - y² B. Design a differential equation model for the following real-life phenomena: 1. free-falling stone, 2. spring vertical displacement, 3. Kirchoff's Second Law for the circuit, 4. Newton's Law of Cooling, and 5. Growth and Decay. C. The external body temperature in the r-s plane is T = r² +s². Calculate the rate of change of temperature at the origin in the direction of the unit vector u = (3,-5).

Answer:

Step-by-step explanation:

Therefore , the solution of the given problem of expression comes out to be  =C3 by using this formula, the spreadsheet is instructed to show the value in column C3.

Mathematical processes like multiplying, dividing, addition, and subtracting are essential. Combining them would result in the following phrase: An equation, some information, and a mathematical function Values, variables, and functions, such as additions, subtractions, multiplications, and divisions, are the building blocks of a statement of truth. Words and sentences can be contrasted and compared.

Here,

Simply type the following formula into the formula bar to show the value of cell 3 in a chosen cell:

=C3

By using this formula, the spreadsheet is instructed to show the value in column C3.

You can change "C3" to the complex number of the cell whose value you want to show.

Make sure the formula is written in the proper cell and that the cell reference is accurate.

The formula would then calculate and display a value from the designated cell in the chosen cell after you hit the Enter key.

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Answer:

\(\frac{25}{32}\)

Step-by-step explanation:

Rode here on the bus

Now you're one of us

It was magic hour

Counting motorbikes

On the turnpike

One of Eisenhower's

Live your life on a merry-go-round

Who starts a fire just to let it go out?

(dreams tonite lol)

Answer:

All of them are rational except for 0.0100100010001, root50, and pi

rational = no forever decimal these are the ones that arent rational

Hope this helps plz hit the crown :D

To solve the expression -25 x (84/21) + (-3) x (-6), follow these steps:

Step 1: Perform the division inside the parentheses.
(84/21) = 4

Step 2: Replace the terms and rewrite the expression.
-25 x (4) + (-3) x (-6)

Step 3: Perform the multiplications.
-25 x 4 = -100
-3 x -6 = 18

Step 4: Rewrite the expression and perform the addition.
-100 + 18

Step 5: Calculate the final result.
-100 + 18 = -82

Your answer is -82.

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Answer:

Plato answer.

Answer:

(−3, −2) (−2, −1) (−1, −2) (−1, −4)

Angle of Rotation (CCW)    

90°   (2, −3) (1, −2) (2, −1) (4, −1)

180°  (3, 2) (2, 1)  (1, 2)         (1, 4)

270° (−2, 3) (−1, 2) (−2, 1) (−4, 1)

360° (−3, −2) (−2, −1) (−1, −2) (−1, −4)

Answer:

yellow = red - 3 and green = yellow x 2 and red = yellow + 3

or

green= (red-3) x 2

Step-by-step explanation:

Three fewer yellow than read is the same as saying red -3

twice as many green as yellow is the same as yellow x 2

if green is yellow x 2 you can substitute yellow for the equation to find yellow

you can flip the equation for yellow around by doing inverse operations. To have the equation equal red you need to move the three by doing its inverse. The opposite of subtraction is addition so you'd add 3 to each side, getting rid of the -3 and isolating the red to make the equation red=yellow+3

The breadth of your books are perpendicular to the length because they meet at right angles.

The shape of a book is a rectangle. A rectangle has four enclosure. This means they are formed by 4 lines.

The opposite sides are equal in length.

The sides of the book has a pair of breadth and a pair of length.

The breadth and length are straight lines.

When this straight line meets, it forms a right angle(90 degrees). This means the breadth and the length are perpendicular to each other.

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a) The evaporation rate per square foot of surface area (in gal/A) is equals to the 1/12 gal/A.

b) The thirty-three gallons of water will evaporate from a pool of 200 square feet.

We have, Area of a pool = 200 square feet

and we have to determine quantity of water evaporate from a pool in gallons. For this, first we have to calculate the evaporation rate. Let's assume y = gallons of water and

x = surface area in square foot

From the data, dy/dx = (50-25) / (400-100)

=> dy/dx = 1/12

The above equation means that for every 12 square feet surface there is 1 gallons water of evaporation will happen. So, similarly for 100 square feet = 100/12 gallons water

=> 8.33 gallons

But for 100 square feet 25 gallons of evaporation will happen.

=> 25 - 8.33 = 16.67

b) Now we will calculate quantity of water will evaporate from a pool of 200 square feet. As we know, 1 gallon for 12 square feet, so number of gallons for 200 square foot = 200/12

= 16.66

Now we add 16.67 for answer that is 16.66+ 16.67 = 33.33 ~ 33 gallons of water. Hence, required value is 33 gallons.

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Complete question:

Water evaporates from a swimming pool at an approximately constant rate of 25 gallons of water for a pool with a surface area of 100 square feet to 50 gallons for a pool with a surface area of 400 square feet.

(a) What is the evaporation rate per square foot of surface area (in gal/A?)? Round to the nearest hundredth. gal/

(b) How many gallons of water will evaporate from a pool of 200 square feet? Round to the nearest gallon. X gal Need Help? Read Submit Answer

Answer:

12 cups

If the size of the bag decreased by 20%, so will the number of cups held.

Number of cups held before the change = 15 cups

If the number of cups held after the 20% reduction in the size of the bag

= (100 - 20)% × 15

=80% × 15

= 12 cups

The new bags will hold 12 cups.

Step-by-step explanation:

(a) The slope of the line through P and Q is -2.

(b) The equation of the line through R parallel to the line through P and Q is y = -2x + 11.

(c)

(a) The slope of the line through points P(3, -2) and Q(2, 0) can be calculated using the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

Substituting the coordinates of P and Q:

slope = (0 - (-2)) / (2 - 3) = 2 / (-1) = -2

Therefore, the slope of the line through P and Q is -2.

(b) To find the equation of the line through point R(4, 3) parallel to the line through P and Q, we can use the slope-intercept form:

y = mx + b

Since the line is parallel to the line through P and Q, it will have the same slope of -2. Substituting the coordinates of point R:

3 = -2(4) + b

Simplifying:

3 = -8 + b

b = 3 + 8 = 11

Therefore, the equation of the line through R parallel to the line through P and Q is y = -2x + 11.

(c) The line through Q(2, 0) perpendicular to the line through P and Q will have a slope that is the negative reciprocal of -2. The negative reciprocal of -2 is 1/2. Using the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

Substituting the coordinates of point Q and the slope:

y - 0 = 1/2(x - 2)

Simplifying:

y = 1/2x - 1

Therefore, the equation of the line through Q perpendicular to the line through P and Q is y = 1/2x - 1.

To find the break-even point for the manufacturer, we need to determine the number of items (x) that need to be produced and sold to cover the daily operational cost. The break-even point occurs when the revenue equals the cost. The revenue per item is $3.75 and the cost per item is $2.50. So, the equation for break-even is:

Revenue = Cost

3.75x = 2.50x + 500

Subtracting 2.50x from both sides and simplifying:

1.25x = 500

x = 500 / 1.25

x = 400

Therefore, the break-even point is when 400 items are produced and sold. The coordinates of the break-even point would depend on the context of the problem and the units used for the x and y-axis.

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Statistical tools are deemed to fail because people have a poor understanding of the scientific method

The given statement is false

1. Statistical tools are designed to analyze and interpret data systematically.
2. These tools can be effective when used correctly and within the context of the scientific method.
3. A poor understanding of the scientific method may lead to incorrect usage of statistical tools, but this does not mean the tools themselves are deemed to fail.
4. The effectiveness of statistical tools depends on the user's knowledge, application, and interpretation.
5. Proper education and training can improve the understanding of the scientific method and the appropriate use of statistical tools.


Statistical tools are not deemed to fail because of people's poor understanding of the scientific method. Instead, it is the incorrect usage and interpretation of these tools that may lead to unreliable results. Improving knowledge of the scientific method and proper application of statistical tools can enhance their effectiveness.

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Answer: 3 votes

Step-by-step explanation:

3 votes were in Tucker's favour, because 10% of 15 is 1.5, 1.5 x 8 is 12.

Answer:

x=9/4,x=-9/4

Step-by-step explanation:

16x^2−81=0

Step 1: Add 81 to both sides.

16x^2−81+81=0+81

16x^2=81

Step 2: Divide both sides by 16.

16x^2/16 = 81/16

x^2 = 81/16

Step 3: Take square root.

x = ±√81/16

x=2.25,x=−2.25

Convert to fraction form.

x=9/4,x=-9/4

The simplest form of the given algebraic expression √(250c³/9d⁶) is; 5c * (√10c)]/3d³

We are given the algebra problems as;

√(250c³/9d⁶)

Now 250c³ can be broken down into 250 = 25c² × 10c

Thus, we now have;

√(250c³/9d⁶) = [√(25c²) * (√10c)]/√9d⁶

When we breakdown the above expression, we have;

5c * (√10c)]/3d³

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Answer:

the answer is a

Step-by-step explanation:

i got it right

\((y + 1)(y + 12)\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\( {y}^{2} + 13y + 12 \\ = {y}^{2} + 12y + 1y + 12 \\ taking \: common \: factor \: from \: the \: two \: pairs \\ = y(y + 12) + 1(y + 12) \\ = (y + 1)(y + 12)\)

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}\)

A single song may be downloaded for $0.35. Adjusting the solution c = 0.35s yields the answer because c/s = 0.35.

An equation is an mathematical statement that uses an equal sign to express the relationship across two or more objects, such as variables or integers. Equations can be used to represent relationships between physical, chemical, and other sorts of events as well as to solve mathematical problems. An equation in mathematics is a claim made regarding the equivalence of two expressions. A assertion claiming two expressions equal equal is what an equation is, in other words.

This indicates that each music download costs $0.35. Consequently, it costs $0.35 to buy a single song.

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Therefore, the nerf reaches its maximum height at 1.75 seconds after it is launched.

In mathematics, a function is a rule that assigns to each element in a set (called the domain) exactly one element in another set (called the range). The domain and range can be any set, including numbers, and the function itself can be a formula, a graph, or described in words. Functions are widely used in various fields of mathematics, science, and engineering to describe relationships between variables and analyze data.

Here,

It looks like there is a mistake in the function definition provided, as it is missing an independent variable. Assuming the correct function is:

h(t) = -16t² + 56t + 142

To find the time at which the nerf reaches its maximum height, we need to find the vertex of the parabolic function defined by h(t). The x-coordinate of the vertex gives us the time at which the maximum height is reached.

The x-coordinate of the vertex is given by:

t = -b/2a

where a = -16 and b = 56. Substituting these values, we get:

t = -56 / 2(-16) = 1.75

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Tthe area enclosed by the lemniscate is 4 units squared.

The lemniscate is symmetric about the x-axis and y-axis, so we can find the area in the first quadrant and multiply it by 4.

In polar coordinates, the equation of the lemniscate can be written as:

r^2 = 4cos(2θ)

Squaring both sides, we get:

r^4 = 16cos^2(2θ)

Converting to Cartesian coordinates, we have:

x^2 + y^2 = 16cos^2(2θ)

Using the identity cos(2θ) = (1/2)(cos^2θ - sin^2θ), we can simplify the equation to:

x^2 + y^2 = 8(cos^4θ - cos^2θsin^2θ)

Multiplying both sides by r, we get:

r^2 = 8r(cos^4θ - cos^2θsin^2θ)

Substituting x = rcosθ and y = rsinθ, we get:

x^2 + y^2 = 8(x^2 - xy + y^2)(x^2 + y^2)

Simplifying, we get:

x^4 - 2x^2y^2 + y^4 = (1/8)

This is the equation of a quartic curve, which is symmetric about the x-axis and y-axis.

To find the area enclosed by the lemniscate in the first quadrant, we can integrate over the range 0 ≤ θ ≤ π/4:

A = 4 ∫[0,π/4] ∫[0,r(θ)] r dr dθ

where r(θ) = 2√cos(2θ).

Evaluating the integral, we get:

A = 4 ∫[0,π/4] ∫[0,2√cos(2θ)] r dr dθ

= 4 ∫[0,π/4] (1/2)(2√cos(2θ))^2 dθ

= 4 ∫[0,π/4] 2cos(2θ) dθ

= 4[sin(π/2) - sin(0)]

= 4

Therefore, the area enclosed by the lemniscate is 4 units squared.

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Answer:

the answer would be y^6/x^2

Step-by-step explanation:

so (Y) to the sixth power over (X) to the second power

Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

Answer:

A: she will earn 450$ interest

B:the balance will be 7950$

hope that helps

Step-by-step explanation:

If it took 49 sec for 1.0L of helium to effuse through a pin hole, it would take 98 sec for 1.0L of methane, CH4, to effuse under identical conditions. So, correct option is e.

The rate of effusion of a gas is inversely proportional to the square root of its molar mass. Therefore, we can use Graham's law of effusion to compare the effusion rates of different gases.

The molar mass of helium (He) is approximately 4 g/mol, and the molar mass of methane (CH₄) is approximately 16 g/mol.

According to Graham's law, the ratio of the effusion rates of two gases is given by the square root of the ratio of their molar masses:

Effusion rate of helium / Effusion rate of methane = √(Molar mass of methane / Molar mass of helium)

Plugging in the values:

Effusion rate of helium / Effusion rate of methane = √(16 g/mol / 4 g/mol) = √4 = 2

Therefore, the effusion rate of methane is two times slower than the effusion rate of helium.

If it took 49 seconds for 1.0L of helium to effuse, it will take 49 seconds multiplied by 2, which is 98 seconds or 1 minute and 38 seconds, for 1.0L of methane to effuse under identical conditions.

So, correct option is e.

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Complete question is:

It took 49 sec for 1.0L of helium to effuse through a pin hole. How long will it take for 1.0L of methane, CH4, to effuse under identical conditions? a) 196 s

b) 75 s

c) 25 s

d)12 s

e) 98s

The side of the square of each block = 2 feet

Given,

Shelly sews a square blanket that has an area of 144 square feet.

and,  it has 36 square blocks, each the same size.

To find the approximate length of each side of a block

Now, According to the question:

36 square blocks of same size. We need to find the area of each square block. so we divide = area / square blocks

= 144/ 36

= 4

The area of each square = 4 square feet

We know that

Area of square = side ^2

Side ^2 = 4

side = \(\sqrt{4}\)

Side = 2

Hence, The side of the square of each block = 2 feet

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The value of x is 81 .  double x = 5 4 * 3 / 2 .

What is a linear equation?

     x = 54 * 3/2

      x  = 27 * 3

     x = 81

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Answer: x= 67.5 feet

Step-by-step explanation:

Answer:

The answer is G. 5/3

Step-by-step explanation:

I used the elimination process and multiplied the second equation by three which allowed me to cancel out the positive and negative three y's.

6x+3y=13

(3x-y=4)*3

6x+3y=13

9x-3y=12

6x+9x=15x

13+12=25

15x=25

15x/15=25/15

By dividing, the fifteens on the left cancel out leaving:

x=1.66667 or 1 2/3 = 5/3

I hope this helps. :)