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stepan [7]
3 years ago
7

Identify the function shown in this graph

Mathematics
1 answer:
alexandr402 [8]3 years ago
4 0
It’s c since the line goes down 5 and the y intercept is 3 so it would be y=-5x+3
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What is the equation of the following graph in vertex form?
Elza [17]
\bf \boxed{y=(x-{{ h}})^2+{{ k}}}\\\\
x=(y-{{ k}})^2+{{ h}}\qquad\qquad  vertex\ ({{ h}},{{ k}})\\\\
-----------------------------\\\\
\textit{vertex is at 4,-4}\implies 
\begin{cases}
h=4\\
k=-4
\end{cases}\implies y=(x-4)^2+(-4)
\\\\\\
\boxed{y=(x-4)^2-4}
6 0
3 years ago
Read 2 more answers
Solve 5y'' + 3y' – 2y = 0, y(0) = 0, y'(0) = 2.8 y(t) = 0 Preview
mario62 [17]

Answer:  The required solution is

y(t)=-\dfrac{7}{3}e^{-t}+\dfrac{7}{3}e^{\frac{1}{5}t}.

Step-by-step explanation:   We are given to solve the following differential equation :

5y^{\prime\prime}+3y^\prime-2y=0,~~~~~~~y(0)=0,~~y^\prime(0)=2.8~~~~~~~~~~~~~~~~~~~~~~~~(i)

Let us consider that

y=e^{mt} be an auxiliary solution of equation (i).

Then, we have

y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.

Substituting these values in equation (i), we get

5m^2e^{mt}+3me^{mt}-2e^{mt}=0\\\\\Rightarrow (5m^2+3y-2)e^{mt}=0\\\\\Rightarrow 5m^2+3m-2=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow 5m^2+5m-2m-2=0\\\\\Rightarrow 5m(m+1)-2(m+1)=0\\\\\Rightarrow (m+1)(5m-1)=0\\\\\Rightarrow m+1=0,~~~~~5m-1=0\\\\\Rightarrow m=-1,~\dfrac{1}{5}.

So, the general solution of the given equation is

y(t)=Ae^{-t}+Be^{\frac{1}{5}t}.

Differentiating with respect to t, we get

y^\prime(t)=-Ae^{-t}+\dfrac{B}{5}e^{\frac{1}{5}t}.

According to the given conditions, we have

y(0)=0\\\\\Rightarrow A+B=0\\\\\Rightarrow B=-A~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

and

y^\prime(0)=2.8\\\\\Rightarrow -A+\dfrac{B}{5}=2.8\\\\\Rightarrow -5A+B=14\\\\\Rightarrow -5A-A=14~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Uisng equation (ii)}]\\\\\Rightarrow -6A=14\\\\\Rightarrow A=-\dfrac{14}{6}\\\\\Rightarrow A=-\dfrac{7}{3}.

From equation (ii), we get

B=\dfrac{7}{3}.

Thus, the required solution is

y(t)=-\dfrac{7}{3}e^{-t}+\dfrac{7}{3}e^{\frac{1}{5}t}.

7 0
3 years ago
Need help again please...
Greeley [361]
40 - 4 = 36

average = 36/9 = 4

answer
average number of members who joined the math club is 4 per month

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Martin drew a triangle. Its sides are 3 cm, 4 cm, and 5 cm. What type of triangle is Martin drawing?
kolbaska11 [484]

Answer:

A scalene triangle .......

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Three friends owe $18 to another friend for gas. If they plan to split the cost evenly, which of the following expressions could
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The first one.. 18/3 is the answer
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