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2 years ago

Solve the equation 1/3m+6m-9/3m=3m-3/4m

Mathematics

1 answer:

vekshin12 years ago

3 0

M
=
0

O
r

m
=
23
15

Explanation:
1
3
m
+
6
m
−
9
3
m
=
3
m
−
3
4
m

⇒
1
+
6
m
−
9
3
m
=
3
m
−
3
4
m

⇒
−
8
+
6
m
3
m
=
3
m
−
3
4
m

⇒
(
−
8
+
6
m
)
×
4
m
=
(
3
m
−
3
)
×
3
m

⇒
−
32
m
+
24
m
2
=
9
m
2
−
9
m

⇒
−
32
m
+
24
m
2
−
9
m
2
+
9
m
=
0

⇒
15
m
2
−
23
m
=
0

⇒
m
(
15
m
−
23
)
=
0

m
=
0

Or

15
m
−
23
=
0
⇒
15
m
=
23
⇒
m
=
23
15

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Given: KPST is a trapezoid, KP=ST, MN is a midsegment, MN=20, h=15, PS:KT=3:7 Find: KS and KP

lions [1.4K]

Answer:

Length of KS = 25 units and

Length of KP = 17 units.

Step-by-step explanation:

Given: KPST is a trapezoid, KP =ST, MN is a mid segment, h is the height =15

Also it is given that, MN = 20 , h = 15 and PS:KT = 3:7.

If two sides of the trapezoid are equal then, it is an isosceles trapezoid.

Mid-segment of a trapezoid is a line segment which connects the midpoints of the non-parallel sides.

A trapezoid mid segment connects the midpoints of two congruent sides of the trapezoid and is parallel to the pair of parallel sides.

Length of the mid segment is the sum of two bases divide by 2

Since, the length of Mid-segment MN = 20.

Also, it is given: PS:KT = 3:7

Let PS = 3x and KT = 7x respectively.

then;

$\frac{PS+KT}{2} = 20$

$\frac{3x+7x}{2} = 20$

$\frac{10x}{2} =20$

On Simplify, we get;

5x =20

Divide both sides by 5 we get;

x =4

Then:

Length of base PS = 3x = 3(4) = 12 and Length of base KT = 7x = 7(4) = 28.

Now, In triangle PLK

Using Pythagoras theorem to find KP;

It is given here, PL =h =15 and KL= 8 {you can see in the figure as shown below};

$KP^2= PL^2 + KL^2$

$KP^2 = 15^2+8^2 =225 +64 = 289$

$KP = \sqrt{289}$

Simplify:

KP = 17

therefore, the length KP = 17 units

To, construct a line: Join K and S

Now, in triangle KRS

KR = KL +LR = 8 +12 =20 and SR = h= 15

Using Pythagoras theorem in KRS to find KS;

$KS^2 = SR^2+KR^2$

$KS^2 = 15^2 + 20^2 = 225 + 400 = 625$

$KS = \sqrt{625}$

On simplify:

KS = 25

Therefore, the length of KS is, 25 units.

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2 years ago

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2 years ago

Solve the following differential equation: (2x+5y)dx+(5x−4y)dy=0 *Hint: they are exact<br><br> C=.

Tpy6a [65]

Answer with Step-by-step explanation:

The given differential equation is

$(2x+5y)dx+(5x-4y)dy=0$

Now the above differential equation can be re-written as

$P(x,y)dx+Q(x,y)dy=0$

Checking for exactness we should have

$\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}$

$\frac{\partial P}{\partial y}=\frac{\partial (2x+5y)}{\partial y}=5$

$\frac{\partial Q}{\partial x}=\frac{\partial (5x-4y)}{\partial x}=5$

As we see that the 2 values are equal thus we conclude that the given differential equation is exact

The solution of exact differential equation is given by

$u(x,y)=\int P(x,y)dx+\phi(y)\\\\u(x,y)=\int (2x+5y)dx+\phi (y)\\\\u(x,y)=x^2+5xy+\phi (y)$

The value of $\phi (y)$ can be obtained by differentiating u(x,y) partially with respect to 'y' and equating the result with P(x,y)

$\frac{\partial u}{\partial y}=\frac{\partial (x^2+5xy+\phi (y)))}{\partial y}=Q(x,y))\\\\5y+\phi '(y)=(5x-4y)\\\\\phi '(y)=5x-9y\\\\\int\phi '(y)\partial y=\int (5x-9y)\partial y\\\\\phi (y)=5xy-\frac{9y^2}{2}\\\\\therefore u(x,y)=x^2+10xy-\frac{9y^2}{2}+c$

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2 years ago

An experiment is carried out 400 times.

MissTica

Answer:

You would expect the outcome to be void 240 times

Step-by-step explanation:

1000 x 0.24

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2 years ago

A square has side length of 8 in. If the area is multiplied by 36, what happens to the side length? HELP PLEASE!!

GaryK [48]

Answer:

The side length is multiplied by 6.

Step-by-step explanation:

The area of a square is A = s². Suppose the side is 8 inches. This means the area is A = 8² = 64.

If you were to multiply by 36, then it becomes 64*36 = 2,304. Since squaring gave the area, it's side length would be found using the reverse operation a square root. Take the square root of 2,304.

√2304 = 48

The side length changed from 8 to 48 which is a scale factor of 6. This means 8 * 6 = 48.

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2 years ago