MATHEMATICS HIGH SCHOOL

Part 1: Find the tangent line approximation to cos x at x=π/4.Part 2: To one decimal place, estimate the maximum value of the error on the interval 0≤x≤π/2.

Answers

Answer 1

Answer:

Equation of the tangent line is ${2}(y+x)= (\pi)/(4)+1$ and maximum value of the error is 1.3

Part 1: Equation of the tangent line is $y-y_(1) =m(x-x_(1) )$

Let y=cos(x) then

$y((\pi)/(4)) =cos((\pi)/(4)) \ny=(1)/(√(2) )$

Now, find a slope

$y=cos(x)\ny'=-sin(x)\ny'((\pi)/(4) ) =-(1)/(√(2) )$

Equation of the tangent line is:

$y-\frac{1}√(2) } =-(1)/(√(2) ) (x-(\pi)/(4) )\n{2}(y+x)= (\pi)/(4)+1$

Part 2: Tangent line to approximate the value at x=pi/2

$y=(-√(2) \pi)/(8)+(1)/(√(2) ) \ny=1.3$

The maximum value of error is 1.3

Learn more:brainly.com/question/15523943

Answer 2

Answer: Part 1: To find the tangent line, we need a point and a slope because we are using point slope form: y-y1=m(x-x1)
To get the y-value for our point, plug pi/4 into the original as x
y=cos(x)
y=cos(pi/4)
y=√2/2
Then to find a slope, we need to get the derivative:
y=cos(x)
y'=-sin(x) (and plug in pi/4 as x to find the slope at this point)
=-sin(pi/4)
=-√2/2

So the tangent line is y-√2/2=-√2/2(x-pi/4)

Part 2: I'm not positive on this but I think you're supposed to use this tangent line to approximate the value at x=pi/2 and find the degree of error.
y-√2/2=-√2/2(pi/2-pi/4)
y=-pi√2/8+√2/2
y=1.3 rounded to the nearest tenth

So since we know that cos(pi/2) is actually 0, the maximum value of error would be 1.3 (1.3-0=1.3)

Hope this helps

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Beth does not charge a registration fee for her dog-walking service, but she charges $5 per mile that each dog is walked. Tonya's dog-walking service charges a registration fee of $20, plus $3 per mile that each dog is walked. Write and solve an equation to find the number of miles m for which Tonya and Beth would charge the same amount.

Answers

Answer:

The indifference point is 10 miles.

Step-by-step explanation:

Giving the following information:

Beth:

$5 per mile

Tonya's:

registration fee of $20

$3 per mile

First, we need to structure the income formulas:

Beth= 5x

Tonya= 20 + 3x

x= miles

Now, to determine the indifference point, we equal both formulas and isolate "x":

5x = 20 + 3x

2x= 20

x=10

The indifference point is 10 miles.

Beth= 5*10= $50

Tonya= 20 + 3*10= $50

The zeros of the function f(x)=3x^2-3x-6 are

Answers

$3x^2-3x-6=0\n 3(x^2-x-2)=0\n x^2-x-2=0 x^2+x-2x-2=0\n x(x+1)-2(x+1)=0\n (x-2)(x+1)=0\n x=2 \vee x=-1$

Suree can run 6 miles per hour. One mile is equal to 5280 feet. What is her running speed in feet per minute?A. 14.67 ft per minute
B. 88 ft per minute
C. 5528 ft per minute
D. 860 ft per minute

Answers

It's probably B. 88 ft per minute.
on the calculator, I got 880, but the zero's don't matter sometimes, so I believe it's B.

If c = 18, what is 2 x (74 - c)?

Answers

First you substitute 18 into c and solve what's inside the paranthesis which is 56. Distribute the 2 to 56 and you should be getting 112 as your answer. 2x(74-c)=112 if c=18.

2 x (74 - 18)
74-18=56
2x(56)
112x

Sparkle is 464 mm long and twilight is 46 cm long which of Amelia's cats is longer

Answers

If Sparkle is 464 mm long and twilight is 46 cm long then Sparkle is longer than Twilight by 4 mm.

What is Unit of Measurement?

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

To compare the length of Sparkle and Twilight, we need to convert their lengths to the same unit of measurement.

Sparkle's length is given in millimeters (mm), while Twilight's length is given in centimeters (cm).

To convert Twilight's length to millimeters, we can multiply by 10

1 centimeter = 10 milli meters

Twilight's length in millimeters

= 46x 10

= 460 mm

Now we can compare the lengths:

Sparkle: 464 mm

Twilight: 460 mm

Therefore, Sparkle is longer than Twilight by 4 mm.

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