In 12 seconds, Valerie counts 6 vehicles passing by her house. At that rate, how many vehicles would pass by in 4 hours

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

=

π

2

−

π

2

=

0

∴

y

=

x

+

c

=

x

+

(

0

)

=

x

which means the tangent to the curve

y

=

x

sin

x

at

(

π

2

,

π

2

)

is simply

y

=

x

.

3 0

3 years ago

In Rodger's state, unemployment compensation is calculated by finding the total of the quarterly wages of two consecutive quarte

frozen [14]

Rodger's weekly unemployment amount is $ 705.0225

Given,

The total of the quarterly wages of two consecutive quarters and dividing by 26.

The weekly unemployment is 65% of that amount.

Rodger made a total of $13,950.80.

and, he made a total of $14,250.10

We have to follow the some steps for solving question:

Step 1: Find the total of the quarterly wages of two consecutive quarters.

= $ 13,950.80 + $ 14,250.10

= $28,200.90

Step 2 : Divide the total by 26

= $28,200.90 / 26

= 1,084.65

Step 3 : Find the 65%

= 1,084.65 x 65%

= 1,084.65 x 65/100

= 705.0225

Hence, Rodger's weekly unemployment amount is $ 705.0225

Learn more about Wages at:

brainly.com/question/13847060

#SPJ1

4 0

1 year ago

Pls help !! Will give brainliest

blagie [28]

Answer:

the first one (25x + 30y is less than or equal to 100)

Step-by-step explanation:

money for clothing set x amount of sets plus pairs of shoes has to be less than or equal to 100 dollars.

4 0

3 years ago

a spaghetti recipe calls for 72 ounces of ground beef. How many pounds of meat does the recipe call for?

nignag [31]

Answer:

1 ounce =0.0625 pounds

if 72 ounces then you multiply it by 0.0625=45

so the recipe calls for 45 pounds of meat

3 0

3 years ago

Help with both please

Natali5045456 [20]

I hope this helps you

4 0

3 years ago