help me with this equation

The maximum error in the calculated surface area is 24.19cm² and the relative error is 0.0132.

Given that the circumference of a sphere is 76cm and error is 0.5cm.

The formula of the surface area of a sphere is A=4πr².

Differentiate both sides with respect to r and get

dA÷dr=2×4πr

dA÷dr=8πr

dA=8πr×dr

The circumference of a sphere is C=2πr.

From above the find the value of r is

r=C÷(2π)

By using the error in circumference relation to error in radius by:

Differentiate both sides with respect to r as

dr÷dr=dC÷(2πdr)

1=dC÷(2πdr)

dr=dC÷(2π)

The maximum error in surface area is simplified as:

Substitute the value of dr in dA as

dA=8πr×(dC÷(2π))

Cancel π from both numerator and denominator and simplify it

dA=4rdC

Substitute the value of r=C÷(2π) in above and get

dA=4dC×(C÷2π)

dA=(2CdC)÷π

Here, C=76cm and dC=0.5cm.

Substitute this in above as

dA=(2×76×0.5)÷π

dA=76÷π

dA=24.19cm².

Find relative error as the relative error is between the value of the Area and the maximum error, therefore:

\(\begin{aligned}\frac{dA}{A}&=\frac{8\pi rdr}{4\pi r^2}\\ \frac{dA}{A}&=\frac{2dr}{r}\end\)

As above its found that r=C÷(2π) and r=dC÷(2π).

Substitute this in the above

\(\begin{aligned}\frac{dA}{A}&=\frac{\frac{2dC}{2\pi}}{\frac{C}{2\pi}}\\ &=\frac{2dC}{C}\\ &=\frac{2\times 0.5}{76}\\ &=0.0132\end\)

Hence, the maximum error in the calculated surface area with the circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm is 24.19cm² and the relative error is 0.0132.

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Answer:

Step-by-step explanation:

The general equation we use for ballistic motion is ...

  \(h(t)=\frac{1}{2}gt^2+v_0t+h_0\)

where g is the acceleration due to gravity, v₀ is the initial upward velocity, and h₀ is the initial height.

The values of g commonly used are -32 ft/s², or -4.9 m/s². Units are consistent when the former is used with velocity in ft/s and height in feet. The latter is used when velocity is in m/s, and height is in meters.

_____

Dwayne throws a ball with an initial velocity of 73 feet/second. Dwayne holds the ball 5 feet off the ground before throwing it. (h = -16t^2 + 73t + 5)

A watermelon falls from a height of 5 feet to splatter on the ground below. (h = -16t^2 + 5)

Marcella shoots a foam dart at a target. She holds the dart gun 1.5 meters off the ground before firing. The dart leaves the gun traveling 73 meters/second. (h = -4.9t^2 + 73t + 1.5)

Greg drops a life raft off the side of a boat 1.5 meters above the water. (h = -4.9t^2 + 1.5)

_____

Additional comment on these scenarios

The dart and ball are described as being launched at 73 units per second. Generally, we expect launches of these kinds of objects to have a significant horizontal component. However, these equations are only for vertical motion, so we must assume the launches are straight up (or that the up-directed component of motion is 73 units/second).

Answer:

30feet

Step-by-step explanation:

I don't know the requirement to get full mark but can work through the equation but:

The man is creating a small triangle as information about the small triangle is given. The small triangle is a miniature size of the bigger triangle. So,

let x be the height of the tree

6/4=x/20

6/4*20=x

x=30 feet

Answer:

-59 im pretty sure

The number of bowling games played for $34 is 8

The  mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by linear equation y = 3.50x + 6.00

We are given that total money spent is $34

The number of bowling  games played is assumed to be x

Now, we have substitute the value of y in the linear equation to get number of bowling  games played

34 = 3.50x +6.00

34 - 6 = 3.50 x

28 = 3.5x

x = 28/ 3.5

x = 8

So, the number of bowling games played for $34 is 8

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Answer:

Total earnings = $80,425

Step-by-step explanation:

Commission = Sale Price × Commission %

Commission = $950,000 × .0275                         2.75% as a decimal is .0275

Commission = $26,125

Total earnings = Base salary + Amount of Commission

Total earnings = $54,300 + $26,125

Total earnings = $80,425

Answer: x = 136.4 minutes

Step-by-step explanation:

x = (100/22)(30) minutes = 136.4 minutes

Answer: B is incorrect

we can find the angle beside the angle ( 4x -2 ) which will be 180° - (4x -2) =     ( 182 -4x )°           ...................................as lies on a straight line summing up 180°

now we can find x°

by

3x + 6 + ( 182 -4x )° = 180° .............both sides sum up to 180°

3x - 4x - 188 = 180°

-x° = 180 - 188°

-x = -8

x = 8°

We can thus confirm the x value will be 8° and B is wrong and A correct.

Option A (Verification)

Check:

The statement given is true because when we compare the LHS and the RHS, which are equal, it will give us the value of x.

Option B (Verification)

The statement given is false because 4x - 2 and 3x + 6 equal each other and, if added, it won't give 180. Hence, Option B is our answer.

We can now conclude that Option B is the answer.

Hoped this helped.

\(BrainiacUser1357\)

It will take to reach their first stop in 5 hours 43 minutes.

How to solve word problems?

Solve word puzzles on a regular basis, teach students how to solve problems, Model or visualise the issue, Make that they specify the question at hand, Take the numbers off, Select the appropriate action for the circumstance.

Speed = Distance/ time

Distance / Speed = Time

= 350 mi / 70 mph

= 5.7142 hours

= 0.7142 hours

≈ 60(0.7142)

≈ 5 hours 43 minutes

Hence, The trip takes 5 hours and 43 minutes to reach their first stop.

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Answer:

⦿ seven and seven-thousandths

Step-by-step explanation:

7.007

The leftmost 0 is in the tenths place.

The next zero to the right is in the hundredths place.

The rightmost 7 is in the thousandths place.

The rightmost 7, in the thousandths place, has a value of seven thousandths.

The leftmost 7 has a value of 7 since it's in the ones place.

The number is

seven and seven-thousandths

In ∆JKL and ∆MLK

Hence

∆JKL≅∆MLK(Side-Angle-Side)

by SAS property of congruency of triangles, ΔJKL and ΔMLK are congruent.  

Given that :

JK ≅ ML

∠JKL ≅ ∠MLK

To Prove: △JKL ≅ MLK

Proof:

We know that corresponding angles formed by transversal line are congruent.

Hence ∠JKL = ∠ MLK ...(i)

Now consider triangles ΔJKL and triangles  ΔMLK

JK = LM  {Given}  , This means that Line JK is Congruent to Line LM. Two congruent lines means they are equal. Thus; JK = LM.

∠JKL = ∠ MLK { Using (i) }

KL = KL  {common sides}

Hence by SAS property of congruency of triangles, ΔJKL and ΔMLK are congruent.  

Hence proved.

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Answer: The rate at which the angle between the string and the horizontal is decreasing when 300ft of string has been let out is -25/√35 rad/s, which is approximately -4.22 rad/s (rounded to two decimal places).

We are given that a kite is 50ft above the ground and moves horizontally at a speed of 6ft/s. We are to determine the rate at which the angle between the string and the horizontal is decreasing when 300ft of string has been let out. We know that the kite is 50ft above the ground and is connected to a person on the ground via a string.

The horizontal distance from the person to the kite is changing as the kite moves. Let this distance be x. The length of the string is given by L, so we have:x2+502=L2...(1)

Differentiating both sides with respect to t, we obtain: \(2xdxdt=2LdLdt=>dxdt=(L/x)(dLdt)\)

Recall that the length of the string is given by L=300ft, while x can be obtained from the right triangle with hypotenuse L and one leg equal to 50ft.

Using equation (1) above, we have:\(x2+502=3002\\= > x=√(3002−502)\\=√(90000−2500)\\=√87500\\=50√35ft\)

We now need to find the angle between the string and the horizontal. Let θ be this angle. Then:

\(tan θ=50/x=50/(50√35)=1/√35\\Cos θ=1/√(1+tan2θ)=√35/√36=√35/6\)

Therefore, sin θ=50/6 and cos θ=√35/6

Differentiating cos θ with respect to time t, we have: \(d(cos θ)dt=d(cos θ)/dθ*dθ/dt=-sin θ*(dθ/dt)\)

Recall that sin θ=50/6, so we need to find dθ/dt when L=300ft.

Differentiating equation (1) with respect to time t, we obtain: \(2xdxdt+2*50*0=2LdLdt=>dxdt=(L/x)(dLdt)\)

Plugging in L=300ft and x=50√35ft, we get: \(dxdt=(300/(50√35))(dL/dt)=(6/√35)ft/s\)

Finally, we have:\(d(cos θ)dt=-sin θ*(dθ/dt)=-(50/6)*(dx/dt)=-(50/6)*(6/√35)=-25/√35 rad/s\)

Therefore, the rate at which the angle between the string and the horizontal is decreasing when 300ft of string has been let out is -25/√35 rad/s, which is approximately -4.22 rad/s (rounded to two decimal places).

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Answer:

8 3/14 total pages

Step-by-step explanation:

3 + 4 = 7

5/7 + 1/2 = 10/14 + 7/14 = 17/14 = 1 3/14

7 + 1 3/14 = 8 3/14

Answer:

Range:  

{ − 1 ,  0 ,  4 ,  9 }

brainliest pls :D

Answer:

x=4.4

Step-by-step explanation:

9x+2 = 4x+ 24

5x+2 = 24

5x = 22

5x/5 = 22/5

x=4.4

i got one solution scream at me if im wrong

Answer: missing side length = 12.5

Step-by-step explanation:

1. Identify what equation to use

there are 2 side lengths, and no Pythagorean triples present therefore using the Pythagorean theorem a^2+b^2=c^2 would be a good approach

2. plug in numbers

knowing the missing side length is the hypotonus we can plug 6 and 11 for a and b: 6^2+11^2=c^2

3. Solve equation

6^2+11^2=c^2

36+121=c^2

157=c^2

12.52=c | to cancel square (^2) you must square root the number

12.5=c | round

Answer:

70

Step-by-step explanation:

Its 70 because you see the degree is 110 so try to subtract 180 degrees by 110 and you get 70 so it's the answer

The commission of the agent is 196000

From the question, we have the following parameters that can be used in our computation:

Commission percentage = 7%

Earnings = 2.8 million

Using the above as a guide, we have the following:

Commission = 7% * Earnings

Substitute the known values in the above equation, so, we have the following representation

Commission = 7% * 2.8 million

Evaluate

Commission = 196000

Hence, the commission is $196000

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The one that has the most circles in a group :D

Answer:

As Per Given Information

we have been asked to determine the consine ratio of ∠K .

\( \bf \: cos \: k = \cfrac{Base}{Hypotenuse} \)

with respect to ∠K .

substitute the given value & let's solve it for k .

\( \longrightarrow\sf \: cos \: k \: = \cfrac{30}{50} \\ \\ \\ \longrightarrow\sf \: cos \: k \: = \cfrac{ 3\cancel0}{5 \cancel0} \\ \\ \\ \longrightarrow\sf \: cos \: k \: = \cfrac{3}{5} \)

Therefore,

Your answer is (c) 3/5

Answer:

x = 24

x = 20

Step-by-step explanation:

x/3 - 2 = 6

Add 2 to both sides

x/3 = 8

multiply both sides by 3

x = 24

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

x/5 +1 = 5

Subtract 1 from both sides

x/5 = 4

multiply both sides by 5

x = 20

Answer:

1. add two both sides and then multiply by 3 each side to get to the answer of 24.

Check: 24/3 = 8 - 2 = 6

2. x/5 + 1 = 5

subtract 1 from each side and then multiply by 4 on each side to get to the result of 20.

check: 20/5 is 4 + 1 = 5

Brainlist please :)

The interval of systolic blood pressure that represents the middle 95% of males is from 94 to 126.

Explain interval

An interval is a set of real numbers that lie between two endpoints. It can be represented as a closed interval, which includes both endpoints or an open interval, which excludes them. Intervals can also be half-open, including one endpoint but not the other. Intervals are used in a variety of mathematical concepts, including calculus, linear algebra, and set theory.

According to the given information

We can calculate the interval of systolic blood pressure that represents the middle 95% of males as follows:

Lower limit = mean - 2 * standard deviation = 110 - 2 * 8 = 94

Upper limit = mean + 2 * standard deviation = 110 + 2 * 8 = 126

So, the interval of systolic blood pressures that represent the middle 95% of males is from 94 to 126.

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Answer:

Slope is 2

Step-by-step explanation:

\(Slope=\frac{y_2-y_1}{x_2-x_1}\\\\Slope=\frac{4-(-2)}{-1-(-4)}\\ \\Slope=\frac{4+2}{-1+4}\\\\Slope=\frac{6}{3}\\ \\Slope=2\)

Thus, the slope of the line is 2.

Answer:

see attachment.  Slope is 2

Step-by-step explanation:

Explained in the attachment.

Answer:

Step-by-step explanation:

d

It is likely that jed will select a button with one hole because 14/73> 1/2 .

Given,

22 buttons have two holes .

14 buttons have one whole .

37 buttons have four holes .

Now probability of selection in random cases,

Total number of buttons = 73 .

Probability that a button having one whole is selected = 14/73

Probability that a button having two whole is selected = 22/73

Probability that a button having four whole is selected = 37/73

Thus 14/73> 1/2 hence the probability that jed will choose a button with one whole is more .

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the total cost for birch plywood needed to cover a room with a width of 23 feet and a length of 25 feet would be $432.

Now, For the total cost of birch plywood needed for the room, we first need to determine the area of the room.

Hence, We get;

A = 23 x 25

A = 575 square feet.

Assuming that the birch plywood comes in 4 x 8 sheets, we can calculate how many sheets we need by dividing the total area by the area of a single sheet as;

= 575 sq. ft. / (4 ft. x 8 ft.)

= 18 sheets

So, you will need 18 sheets of birch plywood to cover the entire room.

Now, The total cost of the plywood is,

18 sheets x $24 per sheet = $432

Therefore, the total cost for birch plywood needed to cover a room with a width of 23 feet and a length of 25 feet would be $432.

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Answer: AC is congruent to PR.

Step-by-step explanation:

Letter A takes the corresponding position as letter P, and letter C takes the corresponding position as letter R in the given congruence statement.

Answer:

Explanation:

To make q the subject of provided equation p equal to 6q +7, rewrite the equation in terms of q as q=(p+7)/6.

To write an equation in the subject of a specified variable, isolate this variable at one side of the equation using the mathematical operations.

The expression given in the problem is,

\(p=6q +7\)

This equation need to be written as the subject of q. Subtract 7 both side of the equation to do this,

\(p+7=6q +7-7\\p+7=6q\)

Divide both side of equation with number 6.

\(\dfrac{p+7}{6}=q\)

Rewrite the equation as,

\(q=\dfrac{p+7}{6}\)

Thus, to make q the subject of provided equation p equal to 6q +7, rewrite the equation in terms of q as q=(p+7)/6.

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