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3 years ago

5. Find the Slope given the points: (-4,-1) and (2, 2) Your answer

Mathematics

2 answers:

AleksAgata [21]3 years ago

8 0

Answer:

1/2

Step-by-step explanation:

(-4,-1) and (2, 2)

slope = difference of y/difference of x

m = (2 - -1)/(2 - -4) =3 / 6 = 1/2

tensa zangetsu [6.8K]3 years ago

6 0

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4. Simplify - 4b +(-9k) – 6 – 3b + 12.

diamong [38]

Answer:

−7b−9k+6

Step-by-step explanation:

−4b+(−3b)=−7b

+(−9k)=−9k

12−6=6

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3 years ago

Area of the figure??

8_murik_8 [283]

Answer:

28.5 sq. meters

Step-by-step explanation:

6x3=18 + 6 x 2 divided by 2=6 + 3x3 divided by 2=4.5

=28.5

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3 years ago

Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview

svetlana [45]

Answer: The required solution is

$y=(-2+t)e^{-5t}.$

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

$y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)$

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

$m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.$

So, the general solution of the given equation is

$y(t)=(A+Bt)e^{-5t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.$

According to the given conditions, we have

$y(0)=-2\\\\\Rightarrow A=-2$

and

$y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.$

Thus, the required solution is

$y(t)=(-2+1\times t)e^{-5t}\\\\\Rightarrow y(t)=(-2+t)e^{-5t}.$

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3 years ago

Write the equation for an exponential function that triples ever year, x, when the original amount is 4.

Citrus2011 [14]

Answer:

y = 4(3)^x

Step-by-step explanation:

Here, we want to write the exponential equation

From the question, we have the equation tripling in x value every year and the original amount is 4

The exponential equation is of the form;

y = a(b)^n

In this case;

a = 4 , b = 3 and n = x

So we have the equation as;

y = 4(3)^x

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2 years ago

When writing an equation, your “y-intercept” is whatever the value of y is when x =

ki77a [65]

the value of Y is when X crosses the X axis.

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3 years ago