Find the area of a circle with radius,
r
= 40cm.
Give your answer rounded to 3 SF.

Answer:

chicken wing hot dog and bolanga

Step-by-step explanation:

happy chesseburger

Answer:

128 <33

Step-by-step explanation:

6 ÷ 3 + 32 • 4 - 2 = 128

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Answer:

Equation of the straight line passing through the point ( 4,2) and (7,-3) is

5 x + 4y - 28=0

Step-by-step explanation:

Step(i):-

Given points are ( 4,2 0 and ( 7,-3)

Slope of the line

         \(m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } = \frac{-3-2}{7-4} = \frac{-5}{4}\)

Step(ii):-

Equation of the straight line passing through the point ( 4,2) and

having slope m = \(\frac{-5}{4}\)

y - y₁ = m( x- x₁ )

\(y - 2 = \frac{-5}{4} ( x-4)\)

4( y -2) = -5( x-4)

4 y - 8 = - 5x +20

5x +4y -8 -20=0

5 x + 4y - 28=0

Final answer:-

Equation of the straight line passing through the point ( 4,2) and (7,-3) is

5 x + 4y - 28=0

The numerical values of oz and at oz when (s, t) = (4, 4) are -12.854 and -411.28, respectively.

To find oz and az, we will use the chain rule. The chain rule allows us to differentiate composite functions. Let's begin by finding oz:

oz = (∂z/∂x)(∂x/∂s) + (∂z/∂y)(∂y/∂s)

To find (∂z/∂x), we differentiate z with respect to x, treating y as a constant:
(∂z/∂x) = siny

Next, we find (∂x/∂s), differentiating x with respect to s, treating t as a constant:
(∂x/∂s) = d/ds(-4s^2 + 3t^2) = -8s

Similarly, (∂z/∂y) = xcosy, and (∂y/∂s) = -8t.

Now we can substitute these values into the chain rule equation for oz:
oz = (siny)(-8s) + (xcosy)(-8t)

Moving on to az:

az = (∂z/∂x)(∂x/∂t) + (∂z/∂y)(∂y/∂t)

Using the values we already found, (∂z/∂x) = siny, (∂x/∂t) = 6t, (∂z/∂y) = xcosy, and (∂y/∂t) = -8s.

Substituting these values into the chain rule equation for az:
az = (siny)(6t) + (xcosy)(-8s)

Now, let's find the numerical values of oz and az when (s, t) = (4, 4):

Substituting (s, t) = (4, 4) into the expressions for oz and az:
oz = (sin(-8))(4) + ((-4sin4)(cos(-8)))(4) = -12.854

az = (sin(-8))(24) + ((-4sin4)(cos(-8)))(-32) = -231.926

Therefore, 8z(4, 4) = 8(4(-12.854)) = -411.28

Similarly, at(4, 4) = (4(-231.926)) = -927.704.

So, the numerical values of oz and at oz when (s, t) = (4, 4) are -12.854 and -411.28, respectively.

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Answer:

9/10=0

2/3=0

I don't know but I tried

Answer: A and B

Step-by-step explanation: 9:15 if you divide them by three you get 3:5 and b if you divide by 5 you get 3:5

(NOT 100% sure HAVENT DONE THIS IS MANY YEARS)

Answer:

it's letter a and b .

15 is not because 3 can divide 15 perfectly but 25 not. thanks

Answer:

Step-by-step explanation:

Slope = (-6-9)/(-1-4) = -15/-5 = 3

Answer:

\(m=3\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra Iu

Step-by-step explanation:

Step 1: Define

Point (4, 9)

Point (-1, -6)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

The only solution to the given equation on the interval [0, 2pi) is x = 0.

To solve the equation sin^2(x) - 5cos(x) + 5 = 0, we can use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to rewrite the equation:

1 - cos^2(x) - 5cos(x) + 5 = 0

Rearranging the terms, we get:

cos^2(x) + 5cos(x) - 4 = 0

Now we can factor the quadratic equation:

(cos(x) - 1)(cos(x) + 4) = 0

Setting each factor equal to zero and solving for x, we have:

cos(x) - 1 = 0  -->  cos(x) = 1  -->  x = 0

cos(x) + 4 = 0  -->  cos(x) = -4

Since the cosine function is bounded between -1 and 1, there are no solutions for cos(x) = -4 on the interval [0, 2pi).

Therefore, the only solution to the given equation on the interval [0, 2pi) is x = 0.

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The best description of the probability of drawing a king from the deck is 1 out of 13, or 1/13.

The probability of drawing a king from a standard deck of 52 playing cards can be determined by dividing the number of favorable outcomes (number of kings) by the total number of possible outcomes (total number of cards in the deck).

In a standard deck, there are 4 kings (one king for each suit: hearts, diamonds, clubs, and spades). Therefore, the number of favorable outcomes is 4.

The total number of possible outcomes is 52 (the total number of cards in the deck).

So, the probability of drawing a king is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 4 / 52

Simplifying the fraction gives us:

Probability = 1 / 13

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Here it's given that ∆ABC is a isosceles triangle. We know that in a isosceles triangle opposite angles are equal. And the angles opposite to equal sides are also equal.

Hence here ,

Figure :-

\( \setlength{\unitlength}{1 cm}\begin{picture}(12,12)\put(0,0){\line(1,0){4}}\put(4,0){\line(-1,2){2}}\put(0,0.001){\line(1,2){2}}\put(0,0.01){\line(1,1){2}}\put(3.99,0){\line(-1,1){2}}\put(0,-0.3){$\bf B $}\put(4,-0.3){$\bf C$}\put(2,4.2){$\bf A$}

\put(1.8,2.2){$\bf o$}\end{picture}\)

If LaTeX doesn't work on app kindly see the attachment .

Here we will use a theorem which is ,

\(\large\underline{\underline{\textsf{\textbf{\red{\blue{$\leadsto$} Theorem :- }}}}}\)

Hence here,

\(\tt:\implies \angle ABC =\angle ACB \\\\\tt:\implies \dfrac{1}{2}\times \angle ABC = \dfrac{1}{2}\times \angle ACB \\\\\tt:\implies \boxed{\bf \blue{\angle OBC = \angle OCB} }\)

Now in ∆OBC , we can see that ∠OBC = ∠OCB. (just proved ) . Hence we can say that sides OB and OC are equal. Since the sides opposite to equal angles are equal. Therefore in ∆OBC , two sides are equal.

Therefore ∆ OBC is an isosceles triangle.

Answer:

See Below.

Step-by-step explanation:

We are given the isosceles triangle ΔABC. By the definition of isosceles triangles, this means that ∠ABC = ∠ACB.

Segments BO and CO bisects ∠ABC and ∠ACB.

And we want to prove that ΔBOC is an isosceles triangle.

Since BO and CO are the angle bisectors of ∠ABC and ∠ACB, respectively, it means that ∠ABO = ∠CBO and ∠ACO = ∠BCO.

And since ∠ABC = ∠ACB, this implies that:

∠ABO = ∠CBO =∠ACO = ∠BCO.

This is shown in the figure as each angle having only one tick mark, meaning that they are congruent.

So, we know that:

\(\angle ABC=\angle ACB\)

∠ABC is the sum of the angles ∠ABO and ∠CBO. Likewise, ∠ACB is the sum of the angles ∠ACO and ∠BCO. Hence:

\(\angle ABO+\angle CBO =\angle ACO+\angle BCO\)

Since ∠ABO =∠ACO, by substitution:

\(\angle ABO+\angle CBO =\angle ABO+\angle BCO\)

Subtracting ∠ABO from both sides produces:

\(\angle CBO=\angle BCO\)

So, we've proven that the two angles are congruent, thereby proving that ΔBOC is indeed an isosceles triangle.

The resultant velocity and acceleration of the skier at t=4.00 sec on the ski jump path are 12.8 m/s and 45.9 m/s², respectively.

To find the resultant velocity, first find the velocity vector components using the parametric equations:

vx = 7.00t, vy = 0.48t³ - 6.00t²/√(t⁴+1)

At t=4.00 s, vx = 28.0 m/s and vy = 10.50 m/s. The resultant velocity is the magnitude of the velocity vector, given by:

|v| = √(vx² + vy²) = 12.8 m/s

To find the acceleration vector components, differentiate the velocity vector components with respect to time:

ax = 7.00 m/s², ay = 1.44t² - 12.00t/√(t⁴+1) - 6.00t³(t⁴+1)^(-3/2)

At t=4.00 s, ax = 7.00 m/s² and ay = 45.9 m/s². The acceleration vector magnitude is:

|a| = √(ax² + ay²) = 46.1 m/s².

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\(answer \\ = \frac{4}{25} \\ please \: see \: the \: attached \: picture \\ for \: full \: solution \\ hope \: it \: helps\)

Answer: Choice B) between 6:48 AM and 5:12 PM

=========================================================

Explanation:

I've seen this problem before, and the first part states that if the temperature is above 25 degrees C, then the air conditioner turns on to start cooling the castle.

We want to find values of t that satisfy f(t) > 25

This is the same as trying to solve f(t) - 25 > 0

So we have,

\(f(t) = 24 - 5\cos\left(\frac{\pi}{12}t\right)\\\\ f(t)-25 = 24 - 5\cos\left(\frac{\pi}{12}t\right)-25\\\\ f(t)-25 = -1 - 5\cos\left(\frac{\pi}{12}t\right)\\\\ f(t)-25 > 0\\\\ -1 - 5\cos\left(\frac{\pi}{12}t\right) > 0\\\\\)

To solve this inequality, we can graph using Desmos as I've done so below. See the attached image.

Note how I used x in place of t. This is because the graphing calculator graphs (x,y) coordinates.

Furthermore, note how I marked the two points (6.769, 0) and (17.231, 0)

Between these two points is when the curve is above the x axis, when f(t) > 25 is true. This is when the temperature is above 25 degrees C, and when the air conditioner is working.

When t = 6.769, this means that roughly 6.769 hours have passed since midnight which means we're somewhere between 6 am and 7 am. The only value that works from the answer choices is 6:48 AM.

Note how 0.769*60 = 46.14 is fairly close to 48. This error is likely due to how things are rounded.

Then focusing on the point  (17.231, 0) means that t = 17.231. So 17.231 hours have elapsed since midnight and we're now at roughly 1700 hours

1700 hours in military time = 17-12 = 5 pm

The time value t = 17.231 is between 5 pm and 6 pm. The only thing that works is 5:12 pm.

We can then note how 0.231*60 = 13.86 which is also probably due to rounding error (it's fairly close to 12 though).

--------------------------

In short, we found the function for f(t)-25 and graphed it as shown below. The two points (6.769, 0) and (17.231, 0) help us see when the AC is turned on, which is roughly between 6:48 AM and 5:12 PM. This seems like a reasonable time for the AC to be operational. Something like between 5:12 PM and 6:48 AM seems like a bad idea because the AC would be working mostly at night, instead of during the day.

Anything beyond t = 24 represents the next day, which is when the cycle starts all over again. So we only need to focus on the window from t = 0 to t = 24. Specifically, the portion of the f(t)-25 curve that is above the x axis.

Answer:

.58 cm^3

Step-by-step explanation:

The formula for finding the volume of a cube is V = a^3 where a is a side length.

If you input the given value into the formula, you get .58 cm^3

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Answer:

Domain: x < 1  or 1 < x < 2  or x > 2

Step-by-step explanation:

Take the denominator(s) and compare to zero

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

Solve (x-1)(x-2)=0:

x = 1

x = 2

Answer: I need more context to answer to answer

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

-3+8=5

Hope this helps!

Answer:

Angle 1 = 63.3

Angle 2 = 37.3

Angle 3 = 63.3

Angle 4 = 142.7

Step-by-step explanation:

When a line intersects two parallel lines the interior angles are equal. So angle 2 = 37.3

Angle 3 = 180 - (79.4 + 37.3) = 63.3 since the sum of the angles on a straight line must be 180

Ange 1 = Angle 3 = 63.3

Angle 4 = 180-37.3 = 142.7

Answer:

23.3

Step-by-step explanation:

Answer: D (12.42, 18.09)

Explanation:

For A, if you substitute them, 6.15+2.41(x because x always is first), you get 8.56 but y is 8.56. So therefore, A is wrong cause it is a solution but it asks us for an incorrect solution.

For B, if you substitute the numbers, 6.09+6.15 = 12.24 but y is 12.24 meaning 12.24 = 12.24 which is true. But the question asks us which is not true/a solution, so therefore, B is also wrong.

For C, if you substitute the numbers, you get 9.72+6.15 which is 15.87. Since y is 15.87, the substituted question is 15.87=15.87 which is true and therefore, C is also wrong since it is true but it is asking us for an incorrect solution.

We are then left with D, which is the correct option. I'm guessing you want an explanation for why it is correct. So if you substitute the numbers, you would get y = 12.42+6.15 and 12.42+6.15 is 18.57 but y is 18.09. So the equation is 18.09 = 18.57 which doesn't make sense and is false. Thus, D is the correct answer because it provides a set of numbers that is a false solution to the equation.

REMEMBER:

In an ordered pair, x is the first number while y is the second, so make sure you substitute correctly!

Answer:

1)110m^2

2)1.75m

3)96.25m^2

Step-by-step explanation:

Rate of painting= The cost to paint it /

inner curved surface area of the vessel

20m^2=(Rs 2200 /inner curved surface area of the vessel)

If we make inner curved surface area of the vessel subject of the formula,

inner curved surface area of the vessel= =(Rs 2200/20)

= 110m^2

2)cost surface area of a cylinder can be calculated using expression below

(2πrh,) then the values was calculated in question 1 as 110m^2

Then from (2πrh=110) we can make "r" subject of the formula

r= 110/(2πh). h=10m deep

r=110/(2×3.14×10)

r= 1.75m

3)(iii)capacity of the vessel (in litres

The capacity of the vessel can be regarded as the volume which equals to πr^2h

From question 2 r=1.75m, and h=10m

Then

πr^2h= 3.142×(1.75)^2 ×10

=96.25m^2

Hence the capacity is 96.25m^2

To find the equation of a tangent line at a given point on a curve, you need to know the derivative of the function that describes the curve at that point.

The derivative gives the slope of the curve at the given point, and the equation of the tangent line is found using the point-slope form of a line.

To find the equation of a tangent line at a given point on a curve, you need to know the derivative of the function that describes the curve at that point.

Specifically, if a point on the curve is (a, f(a)), then the slope of the tangent line is f'(a), where f' is the derivative of the function. Using the point-slope form of the line, the equation of the tangent line is y - f(a) = f'(a)(x - a).

Overall, finding the equation of the tangent line requires knowledge of the derivative of the function and the point at which the tangent line is desired.

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The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, & The mass-normalised mode shapes can be  normalising the mode shape vectors f1, f2, and f3.

Part (a)

In Equation Q2, the spectral matrix, undamped natural frequencies, damping ratios, and fundamental frequency need to be calculated.

The mass matrix is given by [85.16400 083.3770 0046.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The stiffness matrix is given by [0.16400 00.3770 000.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The damping matrix is given by [0 0 0; 0 0 0; 0 0 0].The undamped natural frequencies, damping ratios, and fundamental frequency for the system in Equation Q2 can be calculated from the spectral matrix.

The characteristic equation can be written as det(K-mω^2M)=0.where K is the stiffness matrix, M is the mass matrix, ω is the angular frequency, and m is the mass-normalised mode shape.

The roots of this equation are the undamped natural frequencies, and the damping ratios can be calculated from the undamped natural frequencies and mode shapes.

The mass-normalised mode shapes can be calculated by normalising the mode shape vectors f1, f2, and f3.

Part (b)

The mass-normalised mode shapes can be calculated using the mode shape vectors f1, f2, and f3.Part (c)The response of the system for the first physical coordinate y1 can be calculated using the mode superposition method. The initial modal displacements and velocities are given in terms of the modal coordinates.

The response is then calculated using the equation y(t)= Σ ai φi(t), where ai are the modal amplitudes, and φi(t) are the modal shapes given by the mode shape vectors f1, f2, and f3.

The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, where Y is the vector of physical coordinates. The modal amplitudes can be calculated from the initial modal displacements and velocities.

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The predicted number of adults in Oak City whose main source of news is newspapers or the radio is 85

To predict the number of adults in Oak City whose main source of news is newspapers or the radio, we need to add the number of adults who answered "Newspapers" to the number of adults who answered "Radio".

According to the sample data

Number of adults who answered "Newspapers": 64

Number of adults who answered "Radio": 21

Therefore, the predicted number of adults in Oak City whose main source of news is newspapers or the radio we have to use the addition

64 + 21 = 85

Rounding this answer to the nearest whole number, we get

85 ≈ 85

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The given question is incomplete, the complete question is:

There are 44,000 adults living in Oak City. In examining attitudes toward the news, a research group asked a random sample of Oak City adults "What is your main source of news?" The results are shown below. Main Source of News Newspapers Number of Adults 64 Internet 80 Television 126 Radio 21 Other 40 Based on the sample, predict the number of adults in Oak City whose main source of news is newspapers or the radio. Round your answer to the nearest whole number.

Answer:

4,944

Step-by-step explanation:

The expression which represents a whole number which is the preceding number to a whole number x is; x-1.

Whole numbers are a class of numbers which are otherwise termed, Integers. Furthermore, Integers number values include, 1, 5 and -3 among a host of other numbers.

Hence, if the actual number is; x, then it follows that the number which precedes x is such that it is less than x by 1 unit.

Ultimately, the required preceding number is; x-1.

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Answer:

10

Step-by-step explanation:

64 + 36 = c^2

Answer:

just use the pythagorean theorem.

c^2=a^2+b^2

substitute them.

c^2=64+36

c=root100

that is equal to 10

therefore missing side of triangle is 10

Answer:

0.44444444444

Step-by-step explanation: