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solmaris [256]
4 years ago
11

Is y=7x-3 have a proportional relationship

Mathematics
1 answer:
Black_prince [1.1K]4 years ago
8 0

Answer:

my name is mmmmmmm

Step-by-step explanation:

hehehehe

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Find the area of a circle with a radius of 5 feet. Round your answer to the nearest tenth.
klio [65]

Answer:

78.6

Step-by-step explanation:

Area of  circle = Pi*r^2

r=5

for pi use calculator or pi=3.142

area =Pi*r2=(3.142)*5^2=(3.142)*25=78.55 = 78.6 (1 decimal place which is same with tenth)

7 0
3 years ago
Determine the exact formula for the following discrete models:
marshall27 [118]

I'm partial to solving with generating functions. Let

T(x)=\displaystyle\sum_{n\ge0}t_nx^n

Multiply both sides of the recurrence by x^{n+2} and sum over all n\ge0.

\displaystyle\sum_{n\ge0}2t_{n+2}x^{n+2}=\sum_{n\ge0}3t_{n+1}x^{n+2}+\sum_{n\ge0}2t_nx^{n+2}

Shift the indices and factor out powers of x as needed so that each series starts at the same index and power of x.

\displaystyle2\sum_{n\ge2}2t_nx^n=3x\sum_{n\ge1}t_nx^n+2x^2\sum_{n\ge0}t_nx^n

Now we can write each series in terms of the generating function T(x). Pull out the first few terms so that each series starts at the same index n=0.

2(T(x)-t_0-t_1x)=3x(T(x)-t_0)+2x^2T(x)

Solve for T(x):

T(x)=\dfrac{2-3x}{2-3x-2x^2}=\dfrac{2-3x}{(2+x)(1-2x)}

Splitting into partial fractions gives

T(x)=\dfrac85\dfrac1{2+x}+\dfrac15\dfrac1{1-2x}

which we can write as geometric series,

T(x)=\displaystyle\frac8{10}\sum_{n\ge0}\left(-\frac x2\right)^n+\frac15\sum_{n\ge0}(2x)^n

T(x)=\displaystyle\sum_{n\ge0}\left(\frac45\left(-\frac12\right)^n+\frac{2^n}5\right)x^n

which tells us

\boxed{t_n=\dfrac45\left(-\dfrac12\right)^n+\dfrac{2^n}5}

# # #

Just to illustrate another method you could consider, you can write the second recurrence in matrix form as

49y_{n+2}=-16y_n\implies y_{n+2}=-\dfrac{16}{49}y_n\implies\begin{bmatrix}y_{n+2}\\y_{n+1}\end{bmatrix}=\begin{bmatrix}0&-\frac{16}{49}\\1&0\end{bmatrix}\begin{bmatrix}y_{n+1}\\y_n\end{bmatrix}

By substitution, you can show that

\begin{bmatrix}y_{n+2}\\y_{n+1}\end{bmatrix}=\begin{bmatrix}0&-\frac{16}{49}\\1&0\end{bmatrix}^{n+1}\begin{bmatrix}y_1\\y_0\end{bmatrix}

or

\begin{bmatrix}y_n\\y_{n-1}\end{bmatrix}=\begin{bmatrix}0&-\frac{16}{49}\\1&0\end{bmatrix}^{n-1}\begin{bmatrix}y_1\\y_0\end{bmatrix}

Then solving the recurrence is a matter of diagonalizing the coefficient matrix, raising to the power of n-1, then multiplying by the column vector containing the initial values. The solution itself would be the entry in the first row of the resulting matrix.

5 0
3 years ago
How to multiply Decimals by power of 10?
Ilia_Sergeevich [38]

Answer:

maybe this well help

Step-by-step explanation:

When you multiply a decimal by a power of 10, simply move the decimal place to the right as many places as there are 0s in the power of 10. When you divide a decimal by a power of 10, simply move the decimal place to the left as many places as there are 0s in the power of 10.

5 0
3 years ago
Read 3 more answers
Marco needs to buy some cat food At the nearest store, 3 bags of cat food cost $16.50. How muc
madreJ [45]
He would spend $27.50, because each bag costs $5.50. Multiply that by 5 and you have your answer :)
6 0
3 years ago
WILL GIVE BRAINLIEST IF CORRECT
Ivahew [28]

Answer:

The second answer.

Step-by-step explanation:

Tim is correct. Absolute value is just the distance away from 0. In this case, both P and Q are 3/8 away from zero, even though they have opposite signs. In fact, opposites signs of the same number will always have the same absolute value because they are the same distance from 0.

So, it is the second one.

Hope this helps!

8 0
3 years ago
Read 2 more answers
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