The radius of a circle is increasing. At a certain instant, the rate of increase in the area of the circle is numerically equal to twice the rate of increase in its circumference. What is the radius of the circle at that instant

Answer:

9.434 units

Step-by-step explanation:

Given data

points (5,4) and (-3,-1)

x1= 5

y1= 4

x2= -3

y2= -1

The expression for the distance between two points is

d=√((x_2-x_1)²+(y_2-y_1)²)

substitute

d=√((-3-5)²+(-1-4)²)

d=√((-8)²+(-5)²)

d=√64+25

d=√89

d=9.4339

d= 9.434 units

Hence the distance between the points is 9.434 units

Answer:

scale factor = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, scaled copy to original

scale factor = [tex]\frac{3}{9}[/tex] = [tex]\frac{1}{3}[/tex]

Answer:

4.03cm

Step-by-step explanation:

Note that the diameter of the circumscribed circle to the right triangle is the hypotenuse of the triangle.

To get the diameter, we will use the pythagoras theorem as shown;

d² = 7² + 4²

d² = 49 + 16

d² = 65

d = √65

d = 8.0622577

Since radius = d/2

radius = 8.0622577/2

radius = 4.0311288

Hence the radius of the circumscribed circle to the nearest hundredth is 4.03cm

Answer:

5.8

Step-by-step explanation:

Answer:

[tex]20 = \frac{Far \ arc - Near \ arc}{2}\\\\20 = \frac{160 - (2m +12)}{2}\\\\40 = 160 - (2m + 12)\\2m + 12 = 160 - 40\\2m = 120 -12\\2m = 108\\m = 54[/tex]

Answer:

m = 54

Step-by-step explanation:

The secant- secant angle 20° is half the difference of the intercepted arcs, that is

[tex]\frac{1}{2}[/tex] (160 - 2m - 12) = 20° ( multiply both sides by 2 to clear the fraction )

- 2m + 148 = 40° ( subtract 148 from both sides )

- 2m = - 108 ( divide both sides by - 2 )

m = 54

Answer:

1/4 is the simplified fraction for 12/48.

Answer:

yeah what you need help with

Answer:

x = 16

y = 20

Step-by-step explanation:

the left part of the triangle can be solved first as it already has one angle and 1 side, we use trigonometry for this.

since we have 2 sides and 1 angle, to find the third side length we use the pythagoras theorem. a² + b² = c²

; 9² + 12² = c²

; 225 = c²

;√225 = c

; 15 = c

since we have all the lengths of the triangle, we can find out the angle opposite to the side length '9',

; [tex]\frac{Sin x}{9} = \frac{sin90}{15}[/tex]

; [tex]\frac{Sin 90}{15}[/tex] x 9 = Sinx

36.86 = x

now, we look at the triangle as a whole, the top angle being 90 degrees, we know that we have 36.86.

; 90 - 36.86 = 53.13

[tex]\frac{y}{Sin 90} = \frac{12}{Sin 36.86}[/tex]

; [tex]\frac{12}{sin 36.86}[/tex] x Sin 90 = 20

y = 20

again, since we have 2 sides of a right angled triangle we use a² + b² = c²

we arrange this formula since we have the hypotenuse

; 20² - 12² = 256

; √256 = x

; 16  = x

Answer:

[tex]n = -3[/tex]

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

-5-2n=8n+25

-5-25=8n+2n

-30=10n

-30/10=n

-3=n

Step-by-step explanation:

therefore n=-3

Hope this helps u!!

Given:

[tex]\sin^{-1}\left(\dfrac{5}{8}\right)=A[/tex]

To find:

The correct equivalent equation.

Solution:

We have,

[tex]\sin^{-1}\left(\dfrac{5}{8}\right)=A[/tex]

Taking sin on both sides, we get

[tex]\sin \sin^{-1}\left(\dfrac{5}{8}\right)=\sin A[/tex]

[tex]\dfrac{5}{8}=\sin A[/tex]                      [tex][\because \sin (\sin^{-1}\theta )=\theta][/tex]

Interchanging the sides, we get

[tex]\sin A=\dfrac{5}{8}[/tex]

Therefore, the correct option is 4.

Answer:

See the attached image for the graph of the first system.

Step-by-step explanation:

Here's how to graph the first system.

Start with the inequality [tex]-y \le -2x-3[/tex].  You can make this easier to work with by multiplying through by -1.  Remember to switch the inequality sign when multiplying by a negative number.  OK, you get the inequality

[tex]y \ge 2x+3[/tex].

The graph will be a half-plane -- all the points on one side of a line.  The line that is the boundary of the half-plane has an equation:  [tex]y=2x+3[/tex] -- just use an  =  sign instead of the inequality sign.

Graph the line.

The equation of the line is in slope-intercept form:  y = mx + b, so you can tell the y-intercept is 3 and the slope is 2 (think of it as a fraction 2/1).  Graph the line by going to the point (0, 3) -- the y-intercept -- then use the slope 2/1 interpreted as "rise over run" to go up 2 units and right 1 unit, arriving at the point (1, 5).  Draw the line through those points, (0, 3) and (1, 5).

Now you have to decide which side of the line the inequality [tex]y \ge 2x+3[/tex] is describing. To do this, pick a point which is not on the line, plug its coordinates into the inequality; if the result is true, shade the side of the line the point you picked is on (if false, shade the other side!)

An easy point to pick in this case is the origin, (0, 0).  Put zeros in for x and y in the inequality, and you'll get the statement [tex]0 \ge 2(0)+3 \, \Rightarrow \, 0 \ge 3[/tex].  That's false, so shade the side of the line not containing the origin.  In the image below, the shading is in purple.

All right, now for the other inequality, [tex]x+2\le 0[/tex].  Subtract 2 from both sides and the inequality becomes [tex]x \le -2[/tex].  This, too, graphs as a half-plane whose boundary line has equation [tex]x=-2[/tex].  Graph the line.  A line with an equation that has  x  in it but not  y is a vertical line with all its x-coordinates equal to the number on the right side of the equation.  This line is vertical and goes through points such as (-2, 0).

Pick a point not on the line (the origin works again).  Put the coordinates into the inequality to get [tex]0\le -2[/tex] which is false.  Shade the side of the vertical line which does not contain the origin.  In the image below, the shading is in black.

Finally,  YAY!  \o/ ,  the solutions to the system are all the points in the plane that got shaded twice.  In the image, they are the cross-hatched points above the purple line and to left of the black line.

Note: If you get a system with three inequalities, you'll be graphing three half-planes and looking for points that got shaded three times!

Note: One of your questions has the inequalities [tex]x \ge 0[/tex] and [tex]y \ge 0[/tex] in it.  These two inequalities say that the x and y coordinates are both positive or zero, confining your attention to Quadrant I in the upper-right part of a graph, above the x-axis and to the right of the y-axis.

Answer:

B)

Step-by-step explanation:

to get the converse, interchange the hypothesis and conclusion

in this case the hypothesis is "if it is snowing" and the conclusion is "then it is my birthday"

Converse would then be "If it is my birthday, then it is snowing"

Hi there!  

»»————-　★　————-««

I believe your answer is:  

D) {(1, 2), (2,4), (−1, 2), (0,3)}

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

Option A's answer is incorrect, as the domain value of '5' repeats.

{(5, 0), (0, 1), (5, 2), (4,4)}  

⸻⸻⸻⸻

Option B is not a function due to the repeating '-4' value.

{(0, 1), (−4, 1), (4, 2), (−4,−1)}

⸻⸻⸻⸻

The '3' in option C's given relation repeats.

{(3, 2), (2,1), (−1, 2), (3,3)}

⸻⸻⸻⸻

Option D is the correct answer, as there are no domain values that repeat.  

{(1, 2), (2,4), (−1, 2), (0,3)}

Therefore, option D is a function.

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

B. SF=1/2 (image was reduced)

Step-by-step explanation:

Answer:

Step-by-step explanation:

take 42 degree as reference angle

using sin rule

sin 42=opposite/hypotenuse

0.66=6.4/x

x=6.4/0.66

x=9.69

Answer:

The number is 222

Step-by-step explanation:

The given parameters are;

The method Ashley models the 3 digit number = A mix of six base-ten blocks

The digits of the 3 digit number are equal

Therefore, given that in a 3 digit number, we have, hundreds, 100s, tens, 10s, and units, 1s, we can find the digits as follows;

Let 'x' represent the number of hundreds digits, let 'y' represent the number of tens digits and let 'z' represent the number of units digits, we have;

x = y = z...(1)

x + y + z = 6...(2)

Substituting the value of x = y, and x = z from equation (1), in equation (2), we get;

x + y + z = x + x + x = 6

∴ 3·x = 6

∴ x = 6/3 = 2

x = 2 = y = z

Therefore, the 3-digit numbers xyz = 222

Answer:

1,260 helmets

Step-by-step explanation:

100/225 × 2,835 = 1,260

Answer:

[tex]6[/tex]

[tex]16[/tex]

Step-by-step explanation:

[tex] \frac{x}{12} + \frac{y}{3} = 2[/tex]

[tex] \frac{y}{3 } = 2 - \frac{x}{12} [/tex]

[tex]y = 3( 2 - \frac{x}{12} )[/tex]

[tex]y = 6 - \frac{x}{4} [/tex]

[tex]y = - \frac{x}{4} + 6[/tex]

[tex] {x}^{2} - 8x + c[/tex]

[tex] {x}^{2} + c - 18[/tex]

To find the c value ,

[tex]c = ( \frac{b}{2} {)}^{2} [/tex]

divide the coefficient of x by 2 and square the result.

[tex]( - 1 \times 4 {)}^{2} [/tex]

[tex]( - 4 {)}^{2} [/tex]

[tex]16[/tex]

Answer:

8 + 6 = 14

14 x 4 = 56

56 x 1/2(basically just dividing by 2) = 28 mm2

Formula of area of a trapezoid:

B1(base 1) + B2(base 2) x H(height) x 1/2(basically just dividing by 2)

In this case, 8 is your base your other base is 6 and your height is 4.

Answer:

Value of An if n is 17 = -834

Step-by-step explanation:

Given:

A100 = 245

d = 13

n = 17

Find:

Value of An if n = 17

Computation:

An = a + (n-1)d

A100 = a + (100-1)13

245 = a + (99)17

245 = a + 1,287

a = 245 - 1,287

a = -1,042

So,

Value of An if n = 17

An = a + (n-1)d

A17 = -1,042 + (17-1)(13)

A17 = -1,042 + (16)(13)

A17 = -1,042 + 208

A17 = -834

Value of An if n is 17 = -834

Answer: 18

Step-by-step explanation:

I just found the number in between  

Answer:

8[tex]\sqrt{2}[/tex]

Step-by-step explanation:

The geometric mean of 2 numbers a and b is [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{4(32)}[/tex]

= [tex]\sqrt{128}[/tex]

= [tex]\sqrt{64(2)}[/tex]

= [tex]\sqrt{64}[/tex] × [tex]\sqrt{2}[/tex]

= 8[tex]\sqrt{2}[/tex]

Step-by-step explanation:

the area of :

1) inside surface = (3.14× 1.25²)+(3.14×2.5×1.5)

= 4.90625 + 11.775 = 16.68125 m²

2) upper side surface= (3.14 × (1.35²-1.25²))

= 3.14× (1.8225-1.5625)= 3.14×0.26=0.8164m²

3) lateral surface= 3.14×2.7×1.6=13.5648m²

the total amount of vinyl required for the spa =

16.68125+0.8164+13.5648 = 31.06245 m²

Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

copy the above onto your computer for future reference

sin(g) = 420/427

tan(z) = 77/420

cos(z) = 420/427

sin(m) = 427/427

part (E)   the sin of any right angle will be  1   :)

Answer:

Solution given:

Sin G=opposite/hypotenuse=420/427

TanZ=Opposite/adjacent=77/420

CosZ=adjacent/hypotenuse=420/427

Sin M=opposite/hypotenuse=427/427=1

Answer:

[tex]13194.7\ mm^2[/tex]

Step-by-step explanation:

The total surface area of a cone is given by:

Surface area = [tex]\pi r(r+\sqrt{h^2+r^2} )[/tex]

where r is the radius of the cone, h is the height of the cone, l is the length of the cone = [tex]\sqrt{h^2+r^2}[/tex]

Given that h = 136 mm, r = 60 mm /2 = 30 mm, l = 140 mm. Also the top of the cone is not included in the surface area, hence the surface area becomes:

[tex]Surface \ area=\pi r(\sqrt{h^2+r^2} )=\pi rl\\\\Surface \ area=\pi (30\ mm)(140\ mm)=13194.7\ mm^2[/tex]

Answer:

Step-by-step explanation:

A=bh A=7*8 A=56units^2

Answer:

34

Step-by-step explanation:

i think its 34

Answer:

Less than

Step-by-step explanation:

EX:

1/2 * 1/2 = 1/4

1*1 = 1

2*2 = 4

when you multiply two fractions, you get a fraction of a fraction.