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3 years ago

If the smallest angle of rotation for a regular polygon is 18°, how many sides does polygon have?

Mathematics

1 answer:

lora16 [44]3 years ago

4 0

Answer:

20 sides.

Step-by-step explanation:

The external angles of a polygon sum to 360 degrees.

So it's 360/18 = 20.

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A line has a slope of 8 and includes the points (1, z) and (2,8). What is the value of z?

NISA [10]

The value of z is zero

Step-by-step explanation:

The slope is the steepness of the line.

The formula for slope is given by:

$m=\frac{y_2-y_1}{x_2-x_1}\\Here\\(x_1,y_1)\ are\ the\ coordinates\ of\ first\ point\ on\ line\\(x_2,y_2)\ are\ the\ coordinates\ of\ second\ point\ on\ line$

Here

(x1,y1) = (1,z)

(x2,y2) = (2,8)

So,

$m=\frac{y_2-y_1}{x_2-x_1}\\8 = \frac{8-z}{2-1}\\8=\frac{8-z}{1}\\8-8 = -z\\z = 0$

The value of z is zero

Keywords: slope, Line

Learn more about slope at:

#LearnwithBrainly

6 0

3 years ago

What is the real interest rate if the nominal interest rate is 1 when the rate of inflation is 2

vovikov84 [41]

Answer:

Real interest rate = -1%

Step-by-step explanation:

Real interest rate=Nominal interest rate - inflation rate

From the above,

Nominal interest rate=1%

Inflation rate=2%

Real interest rate=Nominal interest rate - inflation rate

=1% - 2%

= -1%

Real interest rate = -1%

Real interest rate shows you what it really costs borrowers to pay back their loans.

if the real interest rate is greater than zero, the amount you pay back is worth more in real terms than the money you borrowed.

if the real interest rate is below zero as in the above case, the amount you will pay back is less worth in real terms than the money you borrowed.

7 0

4 years ago

Write the following in slope intercept form:

BabaBlast [244]

To change it into slope intercept (y=mx+b) you just replace the inequality with an equality and isolate y

x<=2:
x=2=y-> y=2 or y=2+0x

2x-3y>=4:
2x-3y=4
2x-4=3y
(2/3)x-(4/3))=y
y=(2/3)x-(4/3)

x+y>0:
x+y=0
y=-x or y=-x+0

7 0

3 years ago

Y=x.arctan(x)^1/2. find dy/dx. pls show steps

Whitepunk [10]

$y=x(\arctan x)^{1/2}$

Use the product rule first:

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dx}{\mathrm dx}(\arctan x)^{1/2}+x\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}$

$\dfrac{\mathrm dy}{\mathrm dx}=(\arctan x)^{1/2}+x\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}$

Use the chain rule to compute the derivative of $(\arctan x)^{1/2}$ . Let $z=(\arctan x)^{1/2}$ and take $u=\arctan x$ , so that by the chain rule

$\dfrac{\mathrm dz}{\mathrm dx}=\dfrac{\mathrm dz}{\mathrm du}\dfrac{\mathrm du}{\mathrm dx}$

$\dfrac{\mathrm dz}{\mathrm du}=\dfrac{\mathrm du^{1/2}}{\mathrm du}=\dfrac12u^{-1/2}$

$\dfrac{\mathrm du}{\mathrm dx}=\dfrac{\mathrm d\arctan x}{\mathrm dx}=\dfrac1{1+x^2}$

$\implies\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}=\dfrac1{2(\arctan x)^{1/2}(1+x^2)}$

So we have

$\dfrac{\mathrm dy}{\mathrm dx}=(\arctan x)^{1/2}+\dfrac x{2(\arctan x)^{1/2}(1+x^2)}$

You can rewrite this a bit by factoring $(\arctan x)^{-1/2}$ , just to make it look neater:

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac1{2(\arctan x)^{1/2}}\left(2\arctan x+\dfrac x{1+x^2}\right)$

3 0

3 years ago

D-8/-2= 12<br> Solve<br> d=<br> please help

kenny6666 [7]

8 is the right awnser

8 0

3 years ago

Read 2 more answers