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3 years ago

50 POINTS

Mathematics

2 answers:

ikadub [295]3 years ago

8 0

You would have to do 6x2= 12 so it’s 12 outcomes

Stolb23 [73]3 years ago

8 0

Answer:

since dice had 6 faces

coin has 2 sides

in total,

6×2= 12 ways

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Volume of a cube measuring 4 yd on each edge

sattari [20]

Volume is L×W×H so when you plug in your variables you get 4×4×4 or 60

4 0

3 years ago

Read 2 more answers

what is the equation of the line that passes through (-2,-3) and is perpendicular to 2x-3y=6? ...?

sergij07 [2.7K]

The equation given in the question is

2x - 3y = 6
Dividing both sides of the equation by 3, we get
2/3 x - y = 2
y = 2/3 x - 2
Then, from the above equation we can tell that the slope of the line in the graph is 2/3. The slope of a line perpendicular to this slope will be - 3/2. The line also contains the points (-2,-3).
Then, the equation of the perpendicular line will be
y = mx + b
- 3 = (- 3/2)(- 2) + b
- 3 = 3 + b
b = - 6
Then
y = (-3/2)x - 6
y + 6 = (- 3/2)x
2y + 12 = - 3x
3x + 2y = - 12

4 0

2 years ago

Find general solutions of the differential equation. Primes denote derivatives with respect toÂ x.

zepelin [54]

Answer:

$\mathbf{3x^2y^3+2xy^4=C}$

Step-by-step explanation:

From the differential equation given:

$6xy^3 +2y ^4 +(9x^2y^2+8xy^3) y' = 0$

The equation above can be re-written as:

$6xy^3 +2y^4 +(9x^2y^2+8xy^3)\dfrac{dy}{dx}=0$

$(6xy^3 +2y^4)dx +(9x^2y^2+8xy^3)dy=0$

Let assume that if function M(x,y) and N(x,y) are continuous and have continuous first-order partial derivatives.

Then;

M(x,y) dx + N (x,y)dy = 0; this is exact in R if and only if:

$\dfrac{{\partial M }}{{\partial y }}= \dfrac{\partial N}{\partial x}}} \ \ \text{at each point of R}$

relating with equation M(x,y)dx + N(x,y) dy = 0

Then;

$M(x,y) = 6xy^3 +2y^4\ and \ N(x,y) = 9x^2 y^2 +8xy^3$

So;

$\dfrac{\partial M}{\partial y }= 18xy^3 +8y^3$

$\dfrac{\partial N}{\partial y }$

Let's Integrate $\dfrac{\partial F}{\partial x}= M(x,y)$ with respect to x

Then;

$F(x,y) = \int (6xy^3 +2y^4) \ dx$

$F(x,y) = 3x^2 y^3 +2xy^4 +g(y)$

Now, we will have to differentiate the above equation with respect to y and set $\dfrac{\partial F}{\partial x}= N(x,y)$ ; we have:

$\dfrac{\partial F}{\partial y} = \dfrac{\partial}{\partial y } (3x^2y^3+2xy^4+g(y)) \\ \\ = 9x^2y^2 +8xy^3 +g'(y) \\ \\ 9x^2y^2 +8xy^3 +g'(y) =9x^2y^2 +8xy^3 \\ \\ g'(y) = 0 \\ \\ g(y) = C_1$

Hence, $F(x,y) = 3x^2y^3 +2xy^4 +g(y) \\ \\ F(x,y) = 3x^2y^3 + 2xy^4 +C_1$

Finally; the general solution to the equation is:

$\mathbf{3x^2y^3+2xy^4=C}$

5 0

2 years ago

the formula an=1.5 (an-1) with an initial value of 40 describes a sequence. Use the explicit formula to determine the 5th term o

nika2105 [10]

$\text{If } a_n=1.5(a_n-1) \text{ this is a geometric sequence with a ratio of 1.5. The first term is 40. }a_n=40(1.5)^{n-1},\ a_5=40(1.5)^4=202.5$

3 0

3 years ago

The difference between the measures of two supplementary angles is 92 degrees°. determine the measures of the two angles.

zalisa [80]

Supplementary angles add up to 180 degrees

x + y = 180
x - y = 92
---------------add
2x = 272
x = 272/2
x = 136 <=== this is one angle

x + y = 180
136 + y = 180
y = 180 - 136
y = 44 <=== this is ur other angle

5 0

3 years ago