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laiz [17]
3 years ago
6

At a family reunion, a family friend bring 20 lb of ice and 30 cup. Which expression show the greatest common factor , using dis

tribute property of 20 and 30?
Mathematics
1 answer:
Zepler [3.9K]3 years ago
3 0

Answer:

10(2+3)

Step-by-step explanation:

We are given that

Ice=20 lb

Cup=30

We have to find the expression which shows the greatest common factor using distributive property of 20 and 30.

We know that distributive property of integers a,b and c

a\cdot(b+c)=a\cdot b+a\cdot c

20=2\times 10

30=3\times 10

10(2+3)=10\times 2+10\times 3

Hence, the highest common factor of 20 and 30=10

Expression:10(2+3)

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Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of d^2y/dx
nikdorinn [45]

Answer:

Differentiation will give you the gradient for the tangent at any point, and you use the product rule whenever a function can be thought of as two functions multiplied together.

If

f

(

x

)

=

g

(

x

)

×

h

(

x

)

then

f

'

(

x

)

=

g

'

(

x

)

h

(

x

)

+

g

(

x

)

h

'

(

x

)

so if

y

=

x

×

sin

x

then

d

y

d

x

=

1

×

sin

x

+

x

×

cos

x

=

sin

x

+

x

cos

x

We know that

x

=

π

2

, so the gradient is

m

=

sin

(

π

2

)

+

π

2

cos

(

π

2

)

=

1

+

π

2

×

0

=

1

Therefore, we can say that

y

=

m

x

+

c

y

=

(

1

)

x

+

c

y

=

x

+

c

So all we really need to find now is the value for

c

, the

y

intercept. We do this by working out a point

(

x

,

y

)

on the graph. We are already given that

x

=

π

2

, so

y

=

x

sin

x

=

π

2

sin

(

π

2

)

=

π

2

×

1

=

π

2

∴

(

x

,

y

)

=

(

π

2

,

π

2

)

Now we substitute this into the equation we already have for the tangent,

y

=

x

+

c

,

(

x

,

y

)

=

(

π

2

,

π

2

)

π

2

=

π

2

+

c

c

=

π

2

−

π

2

=

0

∴

y

=

x

+

c

=

x

+

(

0

)

=

x

which means the tangent to the curve

y

=

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sin

x

at

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π

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,

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)

is simply

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2 years ago
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