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3 years ago

How do you know if the greatest common factor of two numbers is two just by looking at it?

1 answer:

3 0

Well, you know just by looking at it because it ends in an even number. Like, the greatest common factor of 4 is 2, 1.) Because no other number can "go into it," and 2.) Because it's even.

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a produce store sells 63 apples if the ratio of red apples to green apples was sold was 7 to 2 what is the combined amount of re

Hitman42 [59]

here is the answer I just took a picture because I already answered this for someone eles

4 0

2 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

the angle of elevation of the top of a building from a point 80 ft away from the building on level ground is 70° determine the b

MA_775_DIABLO [31]

Draw a triangle with shortest side on the ground (horiz.). The length of this side is 80 feet. Two angles touch the ground: a right angle, and the 70 degree angle.

Then the height of the building is the 2nd shortest side.

The tangent function is the appropriate one to use here:
opp h
tan 70 deg = -------- = ----------
adj 80 ft
h
Since tan 70 deg = 2.75, 2.75 = -------
80 ft

so h = building height = (80 ft)(2.75) = 219.8 ft

6 0

3 years ago

Raise g to the 7th power, multiply the result by 4, then subtract f from what you have

WINSTONCH [101]

Answer:

f - 4(g^7)

It's simple algebraic operations!

7 0

2 years ago

The measure of a circumscribed angle is equal to 180° minus the measure of the __________

ss7ja [257]

I believe it is an inscribed angle but I am not positive