Find the length of an arc of circle of radius 7cm which subtends an angle 84 at the center of the circle

Answer:

4

Step-by-step explanation:

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Step-by-step explanation:

[tex]y' + y = y^2[/tex]

We can rewrite the differential equation above as

[tex]\dfrac{dy}{dx} + y = y^2[/tex]

[tex]dy = (y^2 - y)dx[/tex]

or

[tex]\dfrac{dy}{y^2 -y} = dx[/tex]

We can rewrite the left side of the equation above as

[tex]\dfrac{dy}{y^2-y}=\dfrac{dy}{y(y-1)}= \left(\dfrac{1}{y-1} - \dfrac{1}{y} \right)dy[/tex]

We can the easily integrate this as

[tex]\displaystyle \int \left(\dfrac{1}{y-1} - \dfrac{1}{y} \right)dy = \int dx[/tex]

or

[tex]\displaystyle \int \dfrac{dy}{y-1} - \int \dfrac{dy}{y} = \int dx[/tex]

This will then give us

[tex]\ln |y-1| - \ln |y| + \ln |k| = x[/tex]

where k is the constant of integration. Combining the terms on the left hand side, we get

[tex]\ln \left|\dfrac{k(y-1)}{y} \right| = x[/tex]

or

[tex]\dfrac{y-1}{y} = \frac{1}{k}e^x[/tex]

Solving for y, we get

[tex]y= \dfrac{1}{1- \frac{1}{k} e^x}=\dfrac{k}{k-e^x}[/tex]

We know that [tex]y(0)= \frac{1}{3}[/tex], so when we substitute [tex]x=0[/tex], we find that [tex]k = -\frac{1}{2}[/tex].

Therefore, the final form of the solution to the differential equation above is

[tex]y = \dfrac{1}{1+2e^x}[/tex]

Answer:

ASA

Step-by-step explanation:

..................

To prove ABC = ADC, We use ASA triangle postulate.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

The similarity of triangles on the other hand is when the corresponding angles are equal but the corresponding sides are not equal but they have the same common ratio.

From the given diagram a quadrilateral ABCD is given,

Line segment AC divides quadrilateral ABCD into two triangles namely

ABC and ADC, and both have a common side AC.

m∠BAC ≅ m∠DAC and m∠BCA ≅ m∠DAC.

Therefore, Triangle ABC and ADC are congruent by ASA, with two angles and a side included between them.

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Answer:

j = 9.65

Step-by-step explanation:

[tex]\frac{8}{cos(34)}[/tex] = j

j = 9.649743588... (round as needed)

Answer:

ur mom

Step-by-step explanation:

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Answer:

[tex] \dfrac{(x - 2)^2}{(x - 1)^2} [/tex]

Step-by-step explanation:

[tex] \dfrac{x^2 + x - 6}{x^2 - 6x + 5} \div \dfrac{x^2 + 2x - 3}{x^2 - 7x + 10} = [/tex]

[tex] = \dfrac{x^2 + x - 6}{x^2 - 6x + 5} \times \dfrac{x^2 - 7x + 10}{x^2 + 2x - 3} [/tex]

[tex] = \dfrac{(x + 3)(x - 2)}{(x - 1)(x - 5)} \times \dfrac{(x - 5)(x - 2)}{(x - 1)(x + 3)} [/tex]

[tex] = \dfrac{(x + 3)(x - 2)(x - 5)(x - 2)}{(x - 1)(x - 5)(x - 1)(x + 3)} [/tex]

[tex] = \dfrac{(x - 2)(x - 2)}{(x - 1)(x - 1)} [/tex]

[tex] = \dfrac{(x - 2)^2}{(x - 1)^2} [/tex]

Answer:

Last month the grocery store sold 578.88 gallons of ice cream and 632.8 pounds of broccoli.

Step-by-step explanation:

Since a grocery store manager notices that this month her store sold a total of 521 gallons of ice cream, which represents a decrease of 10% from last month, and on the other hand, her store sold 791 pounds of broccoli this month, which It represents an increase of 25% from last month, to determine how much ice cream and broccoli did the store sell last month, the following calculation must be performed:

Ice cream = 100 - 10 = 90

90 = 521

100 = X

100 x 521/90 = X

52,100 / 90 = X

578.88 = X

Broccoli = 100 + 25 = 125

125 = 791

100 = X

100 x 791/125 = X

79,100 / 125 = X

632.8 = X

Therefore, last month the grocery store sold 578.88 gallons of ice cream and 632.8 pounds of broccoli.

Answer:

1/6x1/2=1/12

Step-by-step explanation:

Answer:

It should be 33 degrees!

Step-by-step explanation:

This can be found out when we realize that all complimentary degrees add up to 90!

Answer:

33 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

In order to write the equation of the line perpendicular to the given line, we first have to know what the slope of the given line is, and there's no way to tell by looking at it in its current form, which is standard. We need to solve that equation for y to determine the slope of that line. Solving for y:

[tex]-3y=-4x+5[/tex] and

3y = 4x - 5 (just change all the signs so our y term isn't negative anymore...yes, you're "allowed" to do that!) and

[tex]y=\frac{4}{3}x-\frac{5}{3}[/tex] So we can see now that the slope of this line is 4/3. That means that the perpendicular slope is -3/4. Passing through the given point (3, 5):

[tex]y-5=-\frac{3}{4}(x-3)[/tex]* and

[tex]y-5=-\frac{3}{4}x+\frac{9}{4}[/tex] and

[tex]y=-\frac{3}{4}x+\frac{9}{4}+\frac{20}{4}[/tex] so

[tex]y=-\frac{3}{4}x+\frac{29}{4}[/tex]** and, in standard form:

4y = -3x + 29 and

3x + 4y = 29***

* : point-slope form

** : slope-intercept form

*** : standard form

Answer:

Diameter(line going across the circle that you've given) = 6 in

Radius(half of diameter) = 3 in

Circumference(the perimeter of the circle) = 18.85 in

Area = 28.27^2

Step-by-step explanation:

In order to find the circumference, you will need to first find the radius(which is always half the size of the diameter which in this case is 3 in). You will then need to do this formula: 2 x 3.14 x 3 which equals to 18.85.

Answer:

The circumference of a circle is about 18.85 inches.

Step-by-step explanation:

The radius is always half of the diameter, and the diameter is 6 inches.

6 divided by 2 is 3, so the radius of this circle is 3 inches.

The formula for circumference of a circle is :

C = 2πr = 2 · π · 3 ≈ 18.84956

The circumference of a circle is about 18.85 inches.

Answer:

C

Step-by-step explanation:

the probability of the outcome being greater than 63 is x≥63

Answer:

Kindly check explanation

Step-by-step explanation:

When certain variables are examined, there seems to be a sort of spurious relatuoshipnornassocuation between the two variables, this is evident in the relationship between churches and the number of homicide, when a strong positive correlation is observed between number of churches and number of homicides, this relationship is most likely to be due to the effect of a lurking or third variable which creeped into our analysis, a factor which has a posithe correlation on both number of churches and homicide level, Number of homicide and number of churches could have been correlated by the lncreasing population which may lead to overcrowding and competition Hence increasing rate of homicide, similarly, with high rise in population, the growth of church to accommodate the populees will also creep in.

Answer:

-3/9x

Step-by-step explanation:

You rearrange for 'y' so divide both sides by it's coefficient which is 9.

Answer:

The slope is -1/3

Answer:

3 /4

Step-by-step explanation:

The probability that selected person is a female Given she is married :

This is a conditional probability in the form ; A given B

P(A|B) = P(AnB) / P(B)

Let, Female = F ; Married = M

P(F|M) = P(FnM) / P(M) = 150 / 200 = 3 / 4

Answer:

[tex]S(y)=36000*(1+0.03)^{y}[/tex]

Step-by-step explanation:

Answer:

y=36,000×1.03^x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Soooo, angle 1 is 157 degrees

That means:

Angle 2 is 23 degrees                                   Supplementary Angles

Angle 3 is 157 degrees                                  Vertical Angle to Angle 1

Angle 4 is 23 degrees                                   Vertical angle to Angle 2

Answers:

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

Explanation:

Angles 1 and 2 are supplementary as they form a straight line. So the angles add to 180

(angle1)+(angle2) = 180

angle2 = 180-(angle1)

angle2 = 180-157

angle2 = 23 degrees

Angle 4 is congruent to this because angles 2 and 4 are vertical angles. Vertical angles are always congruent. Note how angles 1 and 4 are supplementary.  

Since angles 1 and 3 are the other pair of vertical angles, this must mean angle 3 is 157 degrees.

Answer:

=$21075

Step-by-step explanation:

Given data

Earnings =$415 per hour

Commission =5%

Sales =$89500

Time =40 hours

Let us find the commission

5/100*89500

0.05*89500

=4475

Let us find the amount earned in 40 hours

40*415

=16600

Total

=16600+4475

=21075

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

Explanation:

Focus on the upper semicircle. It's composed of the arc pieces that are 30 degrees, x degrees, and y degrees. The y is the missing unmarked portion of the upper semicircle.

Subtract the 30 and y degree angles, divide by 2, and set that result equal to 10. This will help us solve for y

(30-y)/2 = 10

30-y = 10*2

30-y = 20

-y = 20-30

-y = -10

y = 10

Because the 30, x and y arcs form a semicircle, this must mean the three arcs add to 180 degrees

30+x+y = 180

30+x+10 = 180

x+40 = 180

x = 180-40

x = 140

Answer:

[tex]x= \frac{2046}{74}\\\\y = \frac{366234}{74}[/tex]

Step-by-step explanation:

[tex]y = 179x\ ----- ( 1 ) \\\\y= 105x + 2046 \ ----- (2)\\\\[/tex]

[tex](1) => y - 179x = 0 \ ----- ( 3)\\\\(2) => y - 105x = 2046 \ ------ ( 4)[/tex]

[tex]( 3 ) - ( 4) =>\\\\(-179x +105x ) = 0 - 2046\\\\-74x = -2046\\\\x = \frac{2046}{74}[/tex]

[tex]Substitute \ x \ in ( 1 )\\\\y = 179x \\\\y = 179 \times \frac{2046}{74} = \frac{366234}{74}[/tex]

Answer:

6 3/8 units

Step-by-step explanation:

1 1/2* 4 1/4= 6 3/8

Answer:

Hope you find it helpful

Answer:

Z-value is what we called the number of standard deviations from the mean.  62% is 8% one standard deviation to the left, or a Z-value of -1.  94 is 24% to the right of the mean, or 3 standard deviations for a z-value of three.  You can look on a Z-table to find the area between -1 and 3, which is .840 or 84%

Step-by-step explanation:

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Answer:

1/4

Step-by-step explanation:

4 divide in half so should be 1/4

The answer is attached. I hope this helps answer your question!

Answer:

y = 1 and y = 5

Step-by-step explanation:

[tex]( 3 y -9)^2 + 7 = 43\\\\((3y)^2 + (-9)^2 + 2(3y)(-9)) = 43 - 7\\\\(9y^2 + 81 -54y) = 36\\\\9y^2 -54y + 81 -36 = 0\\\\9y^2 -54y + 45 = 0\\\\9(y^2 -6y + 5) = 0\\\\y^2 - 6y + 5 = 0\\\\y^2 - 5y - y + 5 = 0\\\\y(y - 5) -1(y - 5 ) = 0 \\\\( y - 1 )( y - 5) = 0\\\\y = 1 \ , \ y = 5[/tex]

The values of y in the equation (3y-9)^2+7 = 43 are 1 and 5

The equation is given as:

(3y-9)^2+7 = 43

Subtract 7 from both sides of the equation

(3y - 9)^2 = 36

Take the square root of both sides

3y - 9 = ±6

Add 9 to both sides

3y = 9 ± 6

Divide through by 3

y = 3 ± 2

Expand

y = (3 - 2 or 3 + 2)

Evaluate

y = 1 or 5

Hence, the values of y are 1 and 5

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Answer:

Step-by-step explanation:

5x + 150 = 180

5x = 30

x = 6

Hope this help!!!

Have a nice day!!!

Answer:

[tex]\begin{array}{ccc}{Industry} & {Frequency} & {RF}& {Bank} & {26} & {13\%}& {Cable} & {44} &{22\%} & {Car} & {42} & {21\%} &{Cell} & {60} & {30\%} & {Collection} & {28} & {14\%} &{Total} & {200} & {100\%}\ \end{array}[/tex]

Step-by-step explanation:

Given

[tex]n =200[/tex]

[tex]Bank = 26; Cable = 44; Car = 42; Cell = 60; Collection = 28[/tex]

Required

The frequency relative frequency table

The frequency table is as follows:

[tex]\begin{array}{cc}{Industry} & {Frequency} & {Bank} & {26} & {Cable} & {44} & {Car} & {42} & {Cell} & {60} & {Collection} & {28} & {Total} & {200} \ \end{array}[/tex]

Relative frequency (RF) is calculated using:'

[tex]RF = \frac{Frequency}{Total} * 100\%[/tex]

So, we have:

[tex]Bank = \frac{26}{200} * 100\% = 13\%[/tex]

[tex]Cable = \frac{44}{200} * 100\% = 22\%[/tex]

[tex]Car = \frac{42}{200} * 100\% = 21\%[/tex]

[tex]Cell = \frac{60}{200} * 100\% = 30\%[/tex]

[tex]Collection = \frac{28}{200} * 100\% = 14\%[/tex]

So, we have:

[tex]\begin{array}{ccc}{Industry} & {Frequency} & {RF}& {Bank} & {26} & {13\%}& {Cable} & {44} &{22\%} & {Car} & {42} & {21\%} &{Cell} & {60} & {30\%} & {Collection} & {28} & {14\%} &{Total} & {200} & {100\%}\ \end{array}[/tex]