If B is the midpoint of ac, ab=x+6, and ac =5x-6, then what is bc?

user100 [1]

Answer:945

Step-by-step explanation:

4 0

2 years ago

Determine whether the equation is exact. If it is, then solve it. e Superscript t Baseline (7 y minus 3 t )dt plus (2 plus 7 e

umka21 [38]

Answer:

$F(t,y)=(2+7e^t)y+3(1-t)e^t +C$

Step-by-step explanation:

You have the following differential equation:

$e^t(7y-3t)dt+(2+7e^t)dy=0$

This equation can be written as:

$Mdt+Ndy=0$

where

$M=e^t(7y-3t)\\\\N=(2+7e^t)$

If the differential equation is exact, it is necessary the following:

$\frac{\partial M}{\partial y}=\frac{\partial N}{\partial t}$

Then, you evaluate the partial derivatives:

$\frac{\partial M}{\partial y}=\frac{\partial}{\partial t}e^t(7y-3t)\\\\\frac{\partial M}{\partial t}=7e^t\\\\\frac{\partial N}{\partial t}=\frac{\partial}{\partial t}(2+7e^t)\\\\\frac{\partial N}{\partial t}=7e^t\\\\\frac{\partial M}{\partial t} = \frac{\partial N}{\partial t}$

The partial derivatives are equal, then, the differential equation is exact.

In order to obtain the solution of the equation you first integrate M or N:

$F(t,y)=\int N \partial y = (2 +7e^t)y+g(t)$ (1)

Next, you derive the last equation respect to t:

$\frac{\partial F(t,y)}{\partial t}=7ye^t+g'(t)$

however, the last derivative must be equal to M. From there you can calculate g(t):

$\frac{\partial F(t,y)}{\partial t}=M=(7y-3t)e^t=7ye^t+g'(t)\\\\g'(t)=-3te^t\\\\g(t)=-3\int te^tdt=-3[te^t-\int e^tdt]=-3[te^t-e^t]$

Hence, by replacing g(t) in the expression (1) for F(t,y) you obtain:

$F(t,y)=(2+7e^t)y+3(1-t)e^t +C$

where C is the constant of integration

8 0

3 years ago

An angle measures 82 degrees more than the measure of its supplementary angle. What is the measure of each angle

dolphi86 [110]

Smaller Angle: 49 degrees

Bigger Angle: 131 degrees

Note that supplementary angles add up to be 180 degrees. Knowing this and the information provided in the question, we can use the following system of equations:

x + y = 180 (showing they both add up to 180)

x + 82 = y (to show one angle is 82 more than the other)

We can use the substitution method to solve. Since the second equation ends in "= y" we can substitute the value of it into y for the first equation.

x + y = 180; x + 82 = y ==> x + (x + 82) = 180

And now, solve for x:

x + (x + 82) = 180

x + x + 82 = 180 > combine like terms

2x + 82 = 180

2x = 98

x = 49

So now we have the value for one of the angles! Remembering that the other angle is 82 degrees bigger, dd 49 + 82, which equals 131.

So, our two angle values are 131 and 49! This is correct since both angle measures add up to be 180, which also makes them supplementary!

6 0

3 years ago

Factorize :3y²-54y+343

arlik [135]

1 In general, given

a

x

2

+

b

x

+

c

ax

2

+bx+c, the factored form is:

a

(

x

−

b

+

b

2

−

4

a

c

2

a

)

(

x

−

b

−

b

2

−

4

a

c

2

a

)

a(x−

2a

−b+

b

2

−4ac

)(x−

2a

−b−

b

2

−4ac

)

2 In this case,

a

=

3

a=3,

b

=

−

54

b=−54 and

c

=

343

c=343.

3

(

y

−

54

+

(

−

54

)

2

−

4

×

3

×

343

2

×

3

)

(

y

−

54

−

(

−

54

)

2

−

4

×

3

×

343

2

×

3

)

3(y−

2×3

54+

(−54)

2

−4×3×343

)(y−

2×3

54−

(−54)

2

−4×3×343

)

3 Simplify.

3

(

y

−

54

+

20

3

ı

6

)

(

y

−

54

−

20

3

ı

6

)

3(y−

6

54+20

3



)(y−

6

54−20

3



)

4 Factor out the common term

2

2.

3

(

y

−

2

(

27

+

10

3

ı

)

6

)

(

y

−

54

−

20

3

ı

6

)

3(y−

6

2(27+10

3

)

)(y−

6

54−20

3



)

5 Simplify

2

(

27

+

10

3

ı

)

6

2(27+10

3

)

to

27

+

10

3

ı

3

27+10

3



.

3

(

y

−

27

+

10

3

ı

3

)

(

y

−

54

−

20

3

ı

6

)

3(y−

3

27+10

3



)(y−

6

54−20

3



)

6 Factor out the common term

2

2.

3

(

y

−

27

+

10

3

ı

3

)

(

y

−

2

(

27

−

10

3

ı

)

6

)

3(y−

3

27+10

3



)(y−

6

2(27−10

3

)

)

7 Simplify

2

(

27

−

10

3

ı

)

6

2(27−10

3

)

to

27

−

10

3

ı

3

27−10

3



.

3

(

y

−

27

+

10

3

ı

3

)

(

y

−

27

−

10

3

ı

3

)

3(y−

3

27+10

3



)(y−

3

27−10

3

I hope this help you

6 0

2 years ago

A savings account pays 4 1/2% interest. How much interest

Ghella [55]

Answer:

Interest = $60.75

Amount = $510.75

Step-by-step explanation:

The formula for finding interest is;

Interest = Principal * Rate * Time

And here;

Principal = $450

Rate = 41/2% or 4.5%

Time = 3 years

Interest = $\frac{450 * 45 * 3}{1000}$

Divided by 100 because of the percentage of the rate but here I made it 1000 because I moved the decimal point in the 4.5 forward once which means I have to add 0 to the denominator.

= $\frac{45*45*3}{100}$

= $\frac{6075}{100}$

= $60.75

Now the amount is simply the Principal + Interest which will be;

= $450 + $60.75

= $510.75

6 0

2 years ago