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Semmy [17]
3 years ago
5

The slope of the tangent to the curve y^3x + y^2x^2 = 6 at (2,1)

Mathematics
1 answer:
arlik [135]3 years ago
7 0
Y^3x + y^2x^2 = 6 

<span>Using implicit differentiation </span>
<span>
3 y^2.y'.x+y^3+2 y.y'.x^2+2 y^2.x=0
 </span>
<span>y'(3 y^2.x+2 y. x^2) = -y^3-2 y^2.x </span>
<span>
y' = -[y^2(y+2 x)]/[x y(3 y+2 x)] </span>
<span>
   = -[y(y+2 x)]/[x(3 y+2 x)] </span>
<span>
Substituting x =2 and y = 1:
 </span>
<span>y' = -(1)(1+4)/[2(3+4)] </span>
<span>   = -5/14 </span>

<span>The slope of the tangent of the curve at (2,1) will be:
 m = -5/14</span>
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A random sample of 12 men age 60-65 has a mean blood pressure of 142. 3 mmHg and a standard deviation of 20.8 mmHg. Construct a
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Answer:

The 99% confidence interval = (126.93,157.67)

Step-by-step explanation:

The formula for Confidence Interval =

Mean ± z × Standard deviation /√n

Mean = 142. 3 mmHg

Standard deviation = 20.8 mmHg.

n = 12

Z score for 99% confidence interval = 2.56

Confidence Interval =

142.3 ± 2.56 × 20.8/√12

142.3 ± 2.56 × 6.0044427996

142.3 ± 15.371373567

Confidence Interval

= 142.3 - 15.371373567

= 126.92862643

≈ 126.93

142.3 + 15.371373567

= 157.67137357

≈ 157.67

Therefore, the 99% confidence interval = (126.93,157.67)

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Aunt Maggie’s car broke down on iterestate 10. Sams towing charges a $57 hoop up fee and $2.00 per mile towed. Reginas towing ch
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Answer:

Both situations can be modeled using linear functions

The rate of change of the function that models Regina's towing charge is 2.5

The y-intercept of the functions that model both situations represents the hook up fee

Step-by-step explanation:

Let

x -----> the number of miles towed

y ----> the total charge in dollars

we know that

The linear equation in slope intercept form is equal to

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value (value of y when the value of x is equal to zero)

we have

Sam’s Towing

In this case the slope of the linear equation is equal to the unit rate

The unit rate is $2.00 per mile towed

so

The y-intercept is equal to the charge per fee

so

therefore

the linear equation is

Regina’s Towing

In this case the slope of the linear equation is equal to the unit rate

The unit rate is $2.50 per mile towed

so

The y-intercept is equal to the charge per fee

so

therefore

the linear equation is

Verify each statement

case 1) Both situations can be modeled using linear functions

The statement is true

See the explanation

case 2) The y-intercept of the function that models Sam's Towing charges is 2

The statement is False

The y-intercept of the function that models Sam's Towing charges is $57

case 3) The rate of change of the function that models Regina's towing charge is 2.5

The statement is true

See the explanation

case 4) The y-intercept of the functions that model both situations represents the hook up fee

The statement is true

See the explanation

case 5) The rate of change of the functions that model both situations represent the miles traveled per hour

The statement is False

The rate of change of the functions that model both situations represent dollars by mile towed

8 0
3 years ago
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