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The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its position after t seconds is

iren [92.7K]

Answer:

The temperature is increasing at the rate of 6.5 degree celcius per second.

Step-by-step explanation:

We are given the following information:

Temperature of a point is given by T(x,y)

After t seconds a bug reaches a point $x = \sqrt{2 + t}, y = 3 + \frac{1}{2}t$

At t = 2, x = 2, y = 4

The temperature function satisfies:

$T_x(2,4) = 8\\T_y(2,4) = 9$

We have to find:

$\displaystyle\frac{dT}{dt} = T_t(x(t), y(t))\\\\= T_x(x(t),y(t)).x'(t) + T_y(x(t),y(t)).y'(t) \\\\= T_x(x(t),y(t)).\displaystyle\frac{1}{2\sqrt{(t+2)}} + T_y(x(t),y(t)).\displaystyle\frac{1}{2} \\\\\displaystyle\frac{dT(x,y)}{dt}_{at~t=2} = \displaystyle\frac{dT(2,4)}{dt}_{at~t=2} = 8.\displaystyle\frac{1}{4} + 9.\displaystyle\frac{1}{2} = 2 + 4.5 = 6.5$

Hence, the temperature is increasing at the rate of 6.5 degree celcius per second.

3 0

4 years ago

What is the slope of the line that passes through the points (-4,9) and (-8,3)? Group of answer choices 3/2 -2/3 -1/2

nataly862011 [7]

Answer:

3/2

Step-by-step explanation:

3-9/-8-(-4). -6/-4. turn into positive due to the two negatives and becomes 3/2

8 0

3 years ago

Determine whether this pair of lines is parellel, perpendicular, or neither 6+2x=3y 3x+2y=9 Choose the correct answer below. A.

andriy [413]

Answer:

Option A. These two lines are perpendicular

Step-by-step explanation:

we know that

If two lines are parallel, then their slopes are equal

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

step 1

Convert the given equation A in slope intercept form

$y=mx+b$

where

m is the slope

b is the y-intercept

we have

$6+2x=3y$ ----> equation A

Solve for y

That means----> isolate the variable y

Divide by 3 both sides

$y=\frac{2}{3}x+2$

so

$m_A=\frac{2}{3}$

step 2

Convert the given equation B in slope intercept form

$y=mx+b$

where

m is the slope

b is the y-intercept

we have

$3x+2y=9$ ----> equation B

Solve for y

That means----> isolate the variable y

subtract 3x both sides

$2y=-3x+9$

Divide by 2 both sides

$y=-\frac{3}{2}x+4.6$

so

$m_B=-\frac{3}{2}$

step 3

Compare the slopes

$m_A=\frac{2}{3}$

$m_B=-\frac{3}{2}$

The slopes are opposite reciprocal (the product is equal to -1)

therefore

These two lines are perpendicular

3 0

4 years ago

Find x. 28 28 12 12 42 х

sukhopar [10]

Answer:

c 18

Step-by-step explanation:

12+12-(12/2)=18

8 0

3 years ago

The Sweater Shack is offering a 15% discount on sweaters. If the regular price of a sweater is $30.00, what is the discount? Wha

Zarrin [17]

Answer:

The discount is $4.50. The sale price is $25.50.

Step-by-step explanation:

Discount: 30(.15)=4.50

Sale Price: 30.00-4.50=25.50

6 0

3 years ago