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2 years ago

11

21. Given the pattern below, which recursive formula represents the number of triangles in this sequence?

1 answer:

Tamiku [17]2 years ago

6 0

Answer:

its 4

Step-by-step explanation:

a 1 = 3 , a n = a n - 1 + 2

because if you aply this to the shapes that you see at problem 21 you will see that it meaches them

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Circle 1: center (8, 5) and radius 6

PolarNik [594]

We have that
<span>Circle 1: center (8, 5) and radius 6
</span><span>Circle 2: center (−2, 1) and radius 2

we know that
the equation of a circle is
(x-h)</span>²+(y-k)²=r²
for the circle 1---------> (x-8)²+(y-5)²=36
for the circle 2---------> (x+2)²+(y-1)²=4

using a graph tool
see the attached figure

Part A)<span>What transformations can be applied to Circle 1 to prove that the circles are similar?

we know that
r1/r2---------> 6/2------> 3
</span><span>
to prove that the circle 1 and circle 2 are similar, the radius of circle 1 </span>must be divided by 3 and translate the center of the circle 1 (10) units to the left and (4) units down
<span>
the answer part A) is
</span>the radius of circle 1 must be divided by 3 and translate the center of the circle 1 (10) units to the left and (4) units down

Part B) <span>What scale factor does the dilation from Circle 1 to Circle 2 have?

the answer Part B) is
the scale factor is (3/1)</span>

6 0

3 years ago

Find gradient <br><br>xe^y + 4 ln y = x² at (1, 1)

cricket20 [7]

$xe^y+4\ln y=x^2$

Differentiate both sides with respect to <em>x</em>, assuming <em>y</em> = <em>y</em>(<em>x</em>).

$\dfrac{\mathrm d(xe^y+4\ln y)}{\mathrm dx}=\dfrac{\mathrm d(x^2)}{\mathrm dx}$

$\dfrac{\mathrm d(xe^y)}{\mathrm dx}+\dfrac{\mathrm d(4\ln y)}{\mathrm dx}=2x$

$\dfrac{\mathrm d(x)}{\mathrm dx}e^y+x\dfrac{\mathrm d(e^y)}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x$

$e^y+xe^y\dfrac{\mathrm dy}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x$

Solve for d<em>y</em>/d<em>x</em> :

$e^y+\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x$

$\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x-e^y$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x-e^y}{xe^y+\frac4y}$

If <em>y</em> ≠ 0, we can write

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2xy-ye^y}{xye^y+4}$

At the point (1, 1), the derivative is

$\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=1,y=1}=\boxed{\dfrac{2-e}{e+4}}$

4 0

3 years ago

The axis of symmetry for the function f(x)=-2x^2+4x+1 is the line x=1 where it's the vertex of the function located

vodomira [7]

Vertex has the coordinate (1;3)

8 0

3 years ago

Read 2 more answers

A map has a scale of 1 in. 4 mi. You measure 3 inches between your house and the movie theatre. How many miles is it from your h

suter [353]

Hi!

1in:4m
3in:xm

3/1 = 3
4 x 3 = 12

1in:4m
3in:12m

The answer is 12

Hope this helps! :)

5 0

3 years ago

Paul plans to buy a movie that has a regular price of $19.99. It is on sale for 25% off, but Paul will have to pay 6% sales tax.

d1i1m1o1n [39]

Answer:

16.00

Step-by-step explanation:

19.99 - 25% + 6% = 15.89 =16.00

8 0

2 years ago