Area between curves questions

Thus, the closest area of the blue painted region (square - circle) on teh canvas is 7.7 sq. ft.

A circle is an a double shape made up of a collection of points that are spaced regularly apart from one another (called the radius) on a plane. The fixed point is referred to as the circle's origin or centre, and the defined distance between each point and the origin is referred to as the radius.

Given data:

Area of painted region  = Area of square - Area of circle  

Area of painted region = side² - π*r²

Area of painted region = 6² -  3.14*3²

Area of painted region = 36 -  28.26

Area of painted region = 7.74

Thus, the closest area of the blue painted region (square - circle) on teh canvas is 7.7 sq. ft.

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The point (2,3) and  (2,-5) both lie on the circle with center (-1,-1) and radius 5.

In geometry, a circle is a closed shape consisting of all points in a plane that are a fixed distance (called the radius) from a given point (called the center). The circle is one of the most basic geometric shapes, and it has many important properties.

In this case, we have a circle with center (-1,-1) and radius 5, so its equation is:

(x + 1)² + (y + 1)² = 5²

We also know that the point (2,b) lies on this circle, so we can substitute x = 2 and y = b into the equation to get:

(2 + 1)² + (b + 1)² = 5²

9 + (b + 1)² = 25

Subtracting 9 from both sides, we get:

(b + 1)² = 16

b + 1 = ±4

Solving for b in each case, we get:

b = -1 ± 4

Therefore, the possible values of b are:

b = 3 or b = -5

So the point (2,3) and the point (2,-5) both lie on the circle with center (-1,-1) and radius 5.

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Answer: x times 3

Step-by-step explanation:

marks up the electric stove's wholesale price 10%. Ignoring tax, how much would he

pay for the electric stove at this store?

$0

(b)

Joe then looks at the electric stove in a department store that marks up the electric stove's wholesale price 30%.

But because of a customer loyalty program, he would receive a 20% discount off the in-store price. Ignoring tax,

how much would he pay for the electric stove at this store?

$0

(C)

Select the true statement.

Hours, h Total Cost

1 14

2 18

3 22

4 26

Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this case, leveling generates b + 7 rather than another algorithm that could divide 12 into two parts, evaluate the information provided by y + 7, and generate y + 7.

Here,

To find the total cost of renting the golf clubs for h hours, we can use the expression:

Total Cost = 10 + 4h

We can use this expression to complete the table as follows:

Hours, h Total Cost

1 10 + 4(1) = 14

2 10 + 4(2) = 18

3 10 + 4(3) = 22

4 10 + 4(4) = 26

Therefore, the completed table is:

Hours, h Total Cost

1 14

2 18

3 22

4 26

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Step-by-step explanation:

The answers to the given numerical expressions are:

(12-5)^2 + (-18) x 4 = 49 + (-72) = -23

4^3 + (15-3) ÷ 2 = 64 + 6 = 70

The required Lagrangian form of the polynomial p2(x) is given by

 [(x - x1) × (x - x2) / (x0 - x1) × (x0 - x2)] × y0 + [(x - x0) × (x - x2) / (x1 - x0) × (x1 - x2)] × y1 + [(x - x0) × (x - x1) / (x2 - x0) × (x2 - x1)] × y2

The Lagrangian form of the interpolating polynomial p2(x) corresponding to the data in the table is,

p2(x) = L0(x) × y0 + L1(x) ×y1 + L2(x) ×y2

where Li(x) for i = 0,1,2 are the Lagrange basis polynomials defined by,

L0(x) = (x - x1) × (x - x2) / (x0 - x1) × (x0 - x2)

L1(x) = (x - x0) × (x - x2) / (x1 - x0) × (x1 - x2)

L2(x) = (x - x0) × (x - x1) / (x2 - x0) × (x2 - x1)

Substituting the values of xi and yi from the table, we get,

p2(x)

= [(x - x1) × (x - x2) / (x0 - x1) × (x0 - x2)] × y0 + [(x - x0) × (x - x2) / (x1 - x0) × (x1 - x2)] × y1 + [(x - x0) × (x - x1) / (x2 - x0) × (x2 - x1)] × y2

Note that the indices of xi and yi in the Lagrange basis polynomials correspond to the indices of the data points in the table.

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The given question is incomplete, I answer the question in general according to my knowledge:

Write the Lagrangian form of the interpolating polynomial p2 corresponding to the data in the table below

x0   y0

x1    y1

x2   y2

Answer: After each half-life, the amount of radioactive isotope will be reduced to half its previous amount. Therefore, after 5 half-lives, the amount remaining will be:

155 grams / 2^5 = 4.84 grams (rounded to two decimal places)

So, after 5 half-lives, approximately 4.84 grams of the radioactive isotope will be left.

Step-by-step explanation:

Answer:

perimeter =the circumference around the semicircle

22/7×34/2

=53.43cm

area = (22/7×17^2)/2

454.14cm^2

Answer :

Step-by-step explanation :

Question :

Find the perimeter and area of the semicircle.

Given : Diameter = 14 cm

Radius = 14/2 = 7 cm

Solution :

Perimeter of semicircle = πr + d

[tex]\longrightarrow \: \: \dfrac{22}{7} \times 7 + 14 \\ \\ \longrightarrow \: \: 22 + 14 \\ \\ \longrightarrow \: \: 36 \: cm \\ [/tex]

Area of semicircle = 1/2 πr²

[tex]\longrightarrow \: \: \dfrac{1}{2} \times \dfrac{22}{7} \times {(7)}^{2} \\ \\ \longrightarrow \: \: \frac{22}{14} \times 7 \times 7 \\ \\ \longrightarrow \: \: \frac{1078}{14} \\ \\ \longrightarrow \: \: 77 \: {cm}^{2} \\ \\ [/tex]

Answer:

Answer:8.85cm

Step-by-step explanation:

we need to use sinuses theorem:

[tex]\frac{13.5}{sin90} =\frac{x}{sin41} \\sin90=1\\13.5 =\frac{x}{sin41} \\\\13.5*sin41=x\\sin41=0.65\\x=8.85[/tex]

After answering the provided question, we can state that Therefore, the parallelograms measure of angle C is 63°.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two sets of parallel sides. A parallelogram is a type of quadrilateral in which both sets of opposite sides are parallel and equal. Parallelograms are classified into four types, three of which are unique. The four different shapes are parallelograms, squares, rectangles, and rhombuses. A quadrilateral is a parallelogram when it has two sets of parallel sides. The opposing sides and angles of a parallelogram are both the same length. The interior angles on the same side of the horizontal line are also angles. 360 degrees is the total number of interior angles.

Since ABCD is a parallelogram, opposite angles are congruent. Therefore,

m∠A = m∠C

13x - 41 = 6x + 15

7x = 56

x = 8

m∠C = 6(8) + 15 = 63

Therefore, the measure of angle C is 63°.

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Answer:

M = 1/8t - 223.05

Step-by-step explanation:

Answer:

a and b are equivalent.

c, d and e are not equivalent.

So, 2 equivalent expression for c and are,

c.

( i ) 2 ( x + 2 )

( ii ) ( 4x + 8 ) / 2

d.

( i ) 3x + 16

( ii ) ( 6x + 32 ) / 2

Step-by-step explanation:

a.

2 ( x + 4 )

= 2 ( x ) + 2 ( 4 )

= 2x + 8

b.

8 + 2x can also be written as 2x + 8.

d.

3 ( x + 4 ) + ( 4 + x )

= 3 ( x ) + 3 ( 4 ) + 4 + x

= 3x + 12 + 4

= 3x + 16

Answer:

A and B

Step-by-step explanation:

2(x+4)

2 + x = 2x

2 x 4 = 8

8 + 2x or 2x + 8

the solution to the equation -4(y - 2) = 12 is y = -1.

How to solve?

(1.) -3x - 5 = 16

To solve for x, we need to isolate the variable on one side of the equation. We can start by adding 5 to both sides:

-3x - 5 + 5 = 16 + 5

-3x = 21

Next, we can divide both sides by -3 to get the value of x:

x = -7

Therefore, the solution to the equation -3x - 5 = 16 is x = -7.

(2.) -4(y - 2) = 12

To solve for y, we can start by simplifying the left side of the equation by distributing the -4:

-4y + 8 = 12

Next, we can isolate y by subtracting 8 from both sides:

-4y + 8 - 8 = 12 - 8

-4y = 4

Finally, we can solve for y by dividing both sides by -4:

y = -1

Therefore, the solution to the equation -4(y - 2) = 12 is y = -1.

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Complete question:

Solve the following equations and show your work or explain your reasoning:

(1.) -3x - 5 = 16

(2.) -4(y - 2) = 12

Most times, questionnaire, which involves list of questions or items. are  used to gather data from respondents about their attitudes, experiences, or opinions. It helps to collect quantitative and/or qualitative information.

Please provide accurate information to the best of your knowledge. Your personal information will not be disclosed.

Thank you for your participation.

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Answer:

34%

Step-by-step explanation:

80+10 = 90 (The number of people who do not like meat on their pizzas

Add all the numbers (150+25+80+10) = 265

You do # of people who don't like meat on their pizzas / # of total people

90/265 = 0.339622642

When rounded (Since they're asking for per cent which is 100 because 100 cents make 1 dollar) it will be 0.34 because 0.34 is in it's hundredth place

0.34 x 100(because it is per-cent)

Gives you 34%

Answer:

[tex] \sqrt[4]{16x {}^{4} } [/tex]

a) The scale of the drawing is 1 in. 3 ft.

b) the scale of the new​ drawing is 1 inch = 4 feet.

What is proportion?

The size, number, or amount of one thing or group as compared to the size, number, or amount of another. the proportion of boys to girls in our class is three to one.

Part 1: The scale of the drawing is 1 in. 3 ft.

Part 2: To find the scale of the new​ drawing, we can set up a proportion using the scale of the original drawing:

1 inch : 3 feet = x inches : 1 foot

Simplifying this proportion, we get:

1/3 = x/12

Multiplying both sides by 12, we get:

x = 4

So the scale of the new​ drawing is 1 inch = 4 feet.

In the new scale​ drawing, a length of 4 inches represents an actual length of 16 feet (since 1 inch represents 4 feet).

Hence, a) The scale of the drawing is 1 in. 3 ft.

b) the scale of the new​ drawing is 1 inch = 4 feet.

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Answer:

Yes, I can help you simplify that expression.

Starting with the expression:

p(p-2) x (2/p)

You can simplify it by first multiplying the terms in the first set of parentheses:

p(p-2) = p^2 - 2p

Then you can rewrite the second term as a fraction with a common denominator of p:

2/p = 2p/p^2 = 2/p^2

Now the expression becomes:

(p^2 - 2p) x (2/p^2)

Next, you can factor out a 2 from the first set of parentheses:

2p(p - 1) x (2/p^2)

Finally, you can simplify the expression by canceling out the p in the second fraction:

2(p - 1)

So the simplified expression is 2(p - 1).

The piecewise function for f(x) is f(x) = x - 2, x ≥ 2; -x + 2, x < 2, So the correct answer is option C.

In mathematics, a function is a rule that assigns each element of a set (called the domain) to a unique element of another set (called the range). Functions are a fundamental concept in mathematics and are used to describe relationships between variables, as well as to model and solve a wide range of mathematical problems.

A function is typically denoted using a letter such as "f", and is defined by an equation or formula that specifies how the input (or domain) values are transformed into output (or range) values. For example, the function "f(x) = 2x + 1" assigns each input value "x" to an output value equal to twice the input value plus one.

The absolute value function f(x) = |x - 2| can be written as a piecewise function by separating it into two cases:

Case 1: x - 2 ≥ 0 or x ≥ 2

In this case, the expression inside the absolute value bars becomes x - 2, so f(x) = x - 2.

Case 2: x - 2 < 0 or x < 2

In this case, the expression inside the absolute value bars becomes -(x - 2) = -x + 2, so f(x) = -x + 2.

Therefore, the piecewise function for f(x) is:

f(x) =

x - 2, x ≥ 2

-x + 2, x < 2

So the correct answer is option C.

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Answer: Hope this helps ;)

Step-by-step explanation:

Answer:$

28 dollars

Step-by-step explanation:

Answer:

$57.14

Step-by-step explanation:

It should be noted that 768 hand-held color televisions can be sold at $320 per television.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

It should be noted that to find the number of hand-held color televisions sold at $320 per television, we need to substitute p = 320 into the supply model or demand model and solve for N.

Using the supply model:

N = 2.4p = 2.4(320) = 768

Therefore, at a price of $320 per television, the supplier is willing to produce 768 hand-held color televisions per week.

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The fastest speed at which you can go around the curve without the book sliding is equal to 4.43 m/s.

According to Newton's Second law of motion, the centrifugal force which acts on a physical object that is moving around a curve in the x-direction (x-coordinate) and y-direction (y-coordinate) is modeled by the following mathematical equations:

∑Fx = Fc = mv²/r (x-direction)

∑Fy = Fmax = n - W = mg = 0

Fmax = μmg

Where:

Generally speaking, the maximum speed of a physical object would be attained when its static friction is maximum. Therefore, we would have the following:

Fmax = μmg = mV²/r

Making V the subject of formula, we have:

Maximum speed, V = √μgr

Maximum speed, V = √(0.2 × 9.8 × 10)

Maximum speed, V = 4.43 m/s.

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Sam had 21 hits, and Jessica had 42 hits

A linear equatiοn is a mathematical equatiοn that can be written in the fοrm οf "ax + b = c", where "a", "b", and "c" are cοnstants and "x" is the variable being sοlved fοr. Linear equatiοns describe a straight line relatiοnship between variables.

Let's use variables tο represent the number οf hits that Jessica and Sam had.

Let's say that Sam had x hits.

Accοrding tο the prοblem, Jessica had dοuble the amοunt οf hits Sam had, sο Jessica had 2x hits.

Tοgether, they had 63 hits, sο we can write an equatiοn:

x + 2x = 63

Simplifying the equatiοn:

3x = 63

Dividing bοth sides by 3:

x = 21

Sο Sam had 21 hits, and Jessica had dοuble that amοunt, οr 42 hits.

Therefοre, Sam had 21 hits, and Jessica had 42 hits

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This question cannot be answered

Please post the diagram/chart.

Answer: there should be a diagram but where is it

Step-by-step explanation:

The solution to the homogenous equation is M = c₁e⁻(ⁿ² + √[n(n+1)n] + c₂e⁻(ⁿ²-√[n(n+1)n

To solve the second order differential equation:

d²M/dn² + 2n (dM/dn) = n

We can use the method of undetermined coefficients. First, we assume a particular solution of the form M = An + B, where A and B are constants to be determined. We then find the first and second derivatives of M:

dM/dn = A

d²M/dn² = 0

Substituting these into the differential equation, we get:

0 + 2n(A) = n

Solving for A, we find:

A = 1/2

So the particular solution is:

M = (1/2)n + B

To find B, we can substitute the particular solution into the original differential equation:

d²M/dn² + 2n (dM/dn) = n

0 + 2n(1/2) = n

So the homogeneous solution is:

Mh = C1n + C2

where C1 and C2 are constants to be determined. The general solution is the sum of the homogeneous and particular solutions:

The solution to the homogenous equation is;

M = c₁e⁻(ⁿ² + √[n(n+1)n] + c₂e⁻(ⁿ²-√[n(n+1)n

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Answer:

2/3 is not equal to 60%

Step-by-step explanation:

2/3 of is equal to 66.6%

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{Question reads..}[/tex]

[tex]\rm{Suzanna \ says \ that \ \dfrac{2}{3} \ and\ 60\% \ are \ equal.\ Is\ she \ correct?}\\\\\rm{Justify \ your \ thinking.}[/tex]

[tex]\huge\textsf{Let us make the problem easier to solve}[/tex]

[tex]\mathtt{\dfrac{2}{3} = 2\div 3 = 0.666667}\\\\\mathtt{ 0.666667\times100 = 66.67\%}\\\\\mathtt{\dfrac{2}{3} \approx 66.67\%}\\\\\\\\\mathtt{\dfrac{2}{3}\neq 60\%}[/tex]

[tex]\huge\text{Is she correct? Justify your thinking.}[/tex]
[tex]\huge\boxed{\mathtt{No, \she\ is \ incorrect\ because\ \dfrac{2}{3}\ is}}\\\\\huge\boxed{\mathtt{equivalent\ to\ approximately \ 66.67\%}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

55ft2

Step-by-step explanation:

Find the area of the added rectangle

-23 - -21 = 2ft

12-7 = 5ft

A=bh = 2ft x 5ft = 10ft^2

add old area and new area

45ft^2 + 10ft^2 = 55ft^2

Answer:

55 ft2

Step-by-step explanation:

Since the x values are -21 and -23, it shows that they are 2 points away from eachother. They y values are 7 and 12 so they are 5 points away from eachother. Multiply 2 x 5 = 10 which is the area of the new garden. Since the old garden is 45 square feet, add 10 + 45 to get 55 square feet total.

Option B. 5 and one-third units. The value of a in triangle XYZ is 5 and two-thirds units. This is found using the Pythagorean theorem twice and solving for a.

To find the value of a, we can use the Pythagorean theorem in triangles WZY and WYX as follows:

In triangle WZY:

[tex]c^2 = 3^2 + (a + 4)^2[/tex]

In triangle WYX:

[tex]b^2 = 4^2 + a^2[/tex]

Since angle ZWX is a right angle, we can use the Pythagorean theorem in triangle ZWX as follows:

[tex]ZWX^2 = ZW^2 + WX^2[/tex]

We know that ZW = c and WX = b, so we have:

[tex]a^2 + b^2 = c^2[/tex]

Substituting[tex]c^2[/tex] in terms of a and simplifying, we get:

[tex]a^2 + b^2 = 25 + (a + 4)^2[/tex]

Expanding and simplifying, we get:

[tex]a^2 + b^2 = a^2 + 8a + 41[/tex]

Subtracting [tex]a^2[/tex] from both sides, we get:

[tex]b^2 = 8a + 41[/tex]

Substituting [tex]b^2[/tex] in terms of a in the equation [tex]a^2 + b^2 = c^2[/tex], we get:

[tex]a^2 + 8a + 41 = c^2[/tex]

Substituting[tex]c^2[/tex] in terms of a from the equation for triangle WZY, we get:

[tex]a^2 + 8a + 41 = 9 + (a + 4)^2/16[/tex]

Expanding and simplifying, we get:

[tex]16a^2 + 128a + 656 = 9a^2 + 50a + 97[/tex]

Simplifying further, we get:

[tex]7a^2 + 78a - 559 = 0[/tex]

Using the quadratic formula, we get:

[tex]a = (-78 ± sqrt(78^2 + 4(7)(559))) / 14[/tex]

a = (-78 ± sqrt(49379)) / 14

Since a represents a length in a triangle, it must be positive. Therefore, we have:

a = (sqrt(49379) - 78) / 14 ≈ 6.67

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Triangle X Y Z is shown. Angle Z W X is a right angle. An altitude is drawn from point W to point Y on side Z X to form a right angle. The length of W Y is 4, the length of Y X is a, the length of Z Y is 3, the length of Z W is c, and the length of W X is b.

What is the value of a?

A. 5 units

B. 5 and one-third units

C. 6 and two-thirds units

D. 7 units

Hope this answer helps.