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REY [17]
3 years ago
6

A graphic designer is drawing a pattern of four concentric circles on the coordinate plane. the center of the circles is located

at (-4, 3). the smallest circle has a radius of 3 units. if the radius of each circle is 4 units greater than the largest circle within it, then the equation of the fourth circle is
Mathematics
1 answer:
Luden [163]3 years ago
3 0

Hi!

The equation of a circle is (x – h)² + (y – k)² = r², with (h, k) being the center, r being the radius, and x + y being left as just x and y.

If the smallest circle has a radius of 3 units, then the next one is 7 units (4 units greater), and then the second largest 11 units, and then the largest 15. That means, for r in our equation, we're going to put in 15.

So we get:

(x – h)² + (y – k)² = 15², or

(x – h)² + (y – k)² = 225

The center of our circle is at (-4, 3). That means h = -4 and k = 3 in our equation. So let's substitute that in.

(x – (-4))² + (y – 3)² = 225

(x + 4)² + (y - 3)² = 225 is our final equation.

Hope this helped!

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Finding an Equation of a tangent Line in Exercise, find an equation of the tangent line to the graph of the function at the give
frutty [35]

Answer:

y=\dfrac{3x}{e}+\dfrac{4}{e}

this is the equation of the tangent at point (-1,1/e)

Step-by-step explanation:

to find the tangent line we need to find the derivative of the function g(x).

g(x) =e^{x^3}

  • we know that \frac{d}{dx}(e^{f(x)})=e^{f(x)}f'(x)

g'(x) =e^{x^{3}}(3 x^{2})

g'(x) =3 x^{2} e^{x^{3}}

this the equation of the slope of the curve at any point x and it also the slope of the tangent at any point x. hence, g'(x) can be denoted as 'm'

to find the slope at (-1,1/e) we'll use the x-coordinate of the point i.e. x = -1

m =3 (-1)^{2} e^{(-1)^{3}}\\m =3e^{-1}\\m=\dfrac{3}{e}

using the equation of line:

(y-y_1)=m(x-x_1)

we'll find the equation of the tangent line.

here (x1,y1) =(-1,1/e), and m = 3/e

(y-\dfrac{1}{e})=\dfrac{3}{e}(x+1)\\y=\dfrac{3x}{e}+\dfrac{3}{e}+\dfrac{1}{e}\\

y=\dfrac{3x}{e}+\dfrac{4}{e}

this is the equation of the tangent at point (-1,1/e)

3 0
3 years ago
Sonya took out a mortgage of $65,000 at 7% for 25 years. What is the cost of the mortgage?
Vika [28.1K]

The cost of the mortgage is $81250

<h3>What are interests?</h3>


Interests are percentages of a principal

Given the following parameters

Principal = $65000

Rate = 7% = 0.07
Time = 5 years

<h3>Calculate the interest</h3>

I = PRT/100
I = 65000*0.07*25
I = 16,250

<h3>Determine the cost of the mortgage</h3>

Cost of mortgage = Principal + Interest

Cost of mortgage = 65000 + 16250
Cost of mortgage = 81,250

Hence the cost of the mortgage is $81250

Learn more on mortgage here: brainly.com/question/22846480

5 0
2 years ago
Read 2 more answers
Square root of 32 = 25/2 true or false ?
USPshnik [31]
False, the estimated square root of 32 is 5.65685424... while 25/2 = 12.5
3 0
3 years ago
Read 2 more answers
A trough of water is 20 meters in length and its ends are in the shape of an isosceles triangle whose width is 7 meters and heig
Vaselesa [24]

Answer:

a) Depth changing rate of change is 0.24m/min, When the water is 6 meters deep

b) The width of the top of the water is changing at a rate of 0.17m/min, When the water is 6 meters deep

Step-by-step explanation:

As we can see in the attachment part II, there are similar triangles, so we have the following relation between them \frac{3.5}{10} =\frac{a}{h}, then a=0.35h.

a) As we have that volume is V=\frac{1}{2} 2ahL=ahL, then V=(0.35h^{2})L, so we can derivate it \frac{dV}{dt}=2(0.35h)L\frac{dh}{dt} due to the chain rule, then we clean this expression for \frac{dh}{dt}=\frac{1}{0.7hL}\frac{dV}{dt} and compute with the knowns \frac{dh}{dt}=\frac{1}{0.7(6m)(20m)}2m^{3}/min=0.24m/min, is the depth changing rate of change when the water is 6 meters deep.

b) As the width of the top is 2a=0.7h, we can derivate it and obtain \frac{da}{dt}=0.7\frac{dh}{dt}  =0.7*0.24m/min=0.17m/min The width of the top of the water is changing, When the water is 6 meters deep at this rate

8 0
3 years ago
Seth invested a certain amount of money and got back an amount of $ 8400. If
kupik [55]

Answer:

$7700

Step-by-step explanation:

amount invested + interest = total

amount invested + 700 = 8400

Subtract 700 from both sides.

amount invested = 7700

Answer: $7700

5 0
2 years ago
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