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3 years ago

10

a game is played with a circular spinner that contains 7 different colors. the design of the spinner is the order in which the c

olors are arranged. how many ways can this spinner be designed

1 answer:

dmitriy555 [2]3 years ago

8 0

Answer:

This spinner can be designed in 5040 ways.

Step-by-step explanation:

Number of possible arrangements:

The number of possible arrangements of n elements is given by:

$A_{n} = n!$

In this question:

7 colors, so:

$A_{7} = 7! = 5040$

This spinner can be designed in 5040 ways.

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Amy says that the 9 in the number 900.876 is 1/1,000 the size of the 9 in 6.91. Is she correct? How do you know?

Oksi-84 [34.3K]

Answer:

No

Step-by-step explanation:

The 9 in 900.876 is 900 and the 9 in 6.91 is .9 and if you look at the place value, you'll see that 900 is larger than .9

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2 years ago

Read 2 more answers

Graph g(x)=-5|x+2|+2

Llana [10]

This is the graph for the equation, it crosses through points (0,-8) (-2,4) (-1.6,0) and its vertex is (-2,2)

Hope this helps !!

7 0

3 years ago

What equation represents y=2x^2+24x+85 in vertex form

Andrej [43]

Y=a(x-h)^2+k

vertex form is basically completing the square

what you do is
for
y=ax^2+bx+c
1. isolate x terms
y=(ax^2+bx)+c
undistribute a
y=a(x^2+(b/a)x)+c
complete the square by take 1/2 of b/a and squaring it then adding negative and postive inside
y=a(x^2+(b/a)x+(b^2)/(4a^2)-(b^2)/(4a^2))+c
complete square
too messy \
anyway

y=2x^2+24x+85
isolate
y=(2x^2+24x)+85
undistribute
y=2(x^2+12x)+85
1/2 of 12 is 6, 6^2=36
add neagtive and postivie isnde
y=2(x^2+12x+36-36)+85
complete perfect square
y=2((x+6)^2-36)+85
distribute
y=2(x+6)^2-72+85
y=2(x+6)^2+13

vertex form is
y=2(x+6)^2+13

8 0

3 years ago

The indicated function y1(x is a solution of the given differential equation. use reduction of order or formula (5 in section 4.

Taya2010 [7]

Given a solution $y_1(x)=\ln x$ , we can attempt to find a solution of the form $y_2(x)=v(x)y_1(x)$ . We have derivatives

$y_2=v\ln x$
${y_2}'=v'\ln x+\dfrac vx$
${y_2}''=v''\ln x+\dfrac{v'}x+\dfrac{v'x-v}{x^2}=v''\ln x+\dfrac{2v'}x-\dfrac v{x^2}$

Substituting into the ODE, we get

$v''x\ln x+2v'-\dfrac vx+v'\ln x+\dfrac vx=0$
$v''x\ln x+(2+\ln x)v'=0$

Setting $w=v'$ , we end up with the linear ODE

$w'x\ln x+(2+\ln x)w=0$

Multiplying both sides by $\ln x$ , we have

$w' x(\ln x)^2+(2\ln x+(\ln x)^2)w=0$

and noting that

$\dfrac{\mathrm d}{\mathrm dx}\left[x(\ln x)^2\right]=(\ln x)^2+\dfrac{2x\ln x}x=(\ln x)^2+2\ln x$

we can write the ODE as

$\dfrac{\mathrm d}{\mathrm dx}\left[wx(\ln x)^2\right]=0$

Integrating both sides with respect to $x$ , we get

$wx(\ln x)^2=C_1$
$w=\dfrac{C_1}{x(\ln x)^2}$

Now solve for $v$ :

$v'=\dfrac{C_1}{x(\ln x)^2}$
$v=-\dfrac{C_1}{\ln x}+C_2$

So you have

$y_2=v\ln x=-C_1+C_2\ln x$

and given that $y_1=\ln x$ , the second term in $y_2$ is already taken into account in the solution set, which means that $y_2=1$ , i.e. any constant solution is in the solution set.

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2 years ago

Gabe built a toy tower that measured 1 m 78 cm. After building some more, he measured it, and it was 82 cm taller. How tall is h

Leto [7]

Answer:

78 + 82 = 160cm = 1m 60 cm. + 1 m. = 2m 60cm

Step-by-step explanation:

8 0

2 years ago