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goldfiish [28.3K]
3 years ago
11

True or false the pre-image and image of a dilation are always similar.

Mathematics
1 answer:
Dmitry [639]3 years ago
7 0
False: although the size increases to its ratio, it is not considered similar
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Consider the initial value problem:
Inessa [10]

Answer:

\left \{ {{u'=v} \atop {v'=5v-6u-5\sin(2t)}} \right. \\u(0)=-5;u'(0)=2

Step-by-step explanation:

The given initial value problem is;

y''-5y'+6y=-5\sin(2t)---(1)\\y(0)=-5,y'(0)=2

Let

u(t)=y(t)----(2)\\v(t)=y'(t)----(3)

Differentiating both sides of equation (1) with respect to t, we obtain:

u'(t)=y'(t)---(4)\\ \\\implies u'(t)=v(t)---(5)

Differentiating both sides of equation (2) with respect to t gives:

v'(t)=y''(t)----(6)

From equation (1),

y''=5y'-6y-5\sin(2t)\\y''=5v(t)-6u(t)-5\sin(2t)\\\implies v'(t)=5v(t)-6u(t)-5\sin(2t)----(7)

Putting t=0 into equation (2) yields

u(0)=y(0)\\\implies u(0)=-5

Also putting t=0 into equation (3)

u'(0)=y'(0)\\u'(0)=2

The system of first order equations is:

\left \{ {{u'=v} \atop {v'=5v-6u-5\sin(2t)}} \right. \\u(0)=-5;u'(0)=2

3 0
3 years ago
To ensure that the horizontal segments are parallel, x must equal
andrezito [222]

Answer:

53

Step-by-step explanation:

Because its 53.

6 0
3 years ago
i sell a jacket i bought for 200 dollars at a 20% increase. how much money will i make off of selling it
Ann [662]

Answer:

$40

Step-by-step explanation:

4 0
3 years ago
If your cell phone bill was 67 Point $82 and there is a 7.5% late fee how much will your bill be with the late fee included
Ivenika [448]

\frac{7.5}{100}  =  \frac{x}{82}  \\ x =  \frac{82 \times 7.5}{100}  =  \frac{615}{100 }  = 6.15
82 + 6.15 = 88.15
the answer is $88.15
7 0
3 years ago
Find the value of tan theta if sin theta = 12/13 and theta is in quadrant 2
8090 [49]

Answer:

tanΘ = - \frac{12}{5}

Step-by-step explanation:

Using the trigonometric identities

• sin²x + cos²x = 1, hence

cosx = ± √(1 - sin²x )

• tanx = \frac{sinx}{cosx}

given sinΘ = \frac{12}{13}, then

cosΘ = ±  \sqrt{1-(12/13)^2}

Since Θ is in the second quadrant where cosΘ < 0, then

cosΘ = - \sqrt{1-\frac{144}{169} }

         = - \sqrt{\frac{25}{169} } = - \frac{5}{13}

tanΘ = \frac{\frac{12}{13} }{\frac{-5}{13} }

        = \frac{12}{13} × - \frac{13}{5} = - \frac{12}{5}



5 0
3 years ago
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