How much is the interest on my loan?
I borrowed $400 to buy an MP3 player. I got a two-year loan,
and the lender is charging 8% Simple annual interest. How
much money will I have to pay back?
Time
Interest Principal
$ ?
$400
Rate
0.08
2
/= Prt
1 = 400 x 0.08 x 2
Interest
I
1.00

Answer:

y=1/4x-5

Step-by-step explanation:

y=mx+b is slope intercept form

m is slope

b is y intercept

we know m is 1/4 so we fill it in

y=1/4x+b

fill is the coordinates to find b

-3=1/4(8)+b

-3=2+b

-2. -2

-5=b

place b in

y=1/4x-5

hopes this helps

Answer:y=1/4x-5

Step-by-step explanation:

Your point was (8,-3) and your rise is 1 and your run is 4 so if you want to get from 0 to 8 and count by 4 you need to move twice, and if you established that you will move twice then you need a number that you add 2 to that will give you -3. And that number is -5 so your y-intercept is

To calculate the duration of the shift, you need to subtract the clock-in time from the clock-out time.

In this case, the shift worker clocked in at 1730 hours (5:30 PM) and clocked out at 0330 hours (3:30 AM). However, since the clock is based on a 24-hour format, it's necessary to consider that the clock-out time of 0330 hours actually refers to the next day.

To calculate the duration of the shift, you can perform the following steps:

1. Calculate the duration until midnight (0000 hours) on the same day:

  - The time between 1730 hours and 0000 hours is 6 hours and 30 minutes (1730 - 0000 = 6:30 PM to 12:00 AM).

2. Calculate the duration from midnight (0000 hours) to the clock-out time:

  - The time between 0000 hours and 0330 hours is 3 hours and 30 minutes (12:00 AM to 3:30 AM).

3. Add the durations from step 1 and step 2 to find the total duration of the shift:

  - 6 hours and 30 minutes + 3 hours and 30 minutes = 10 hours.

Therefore, the duration of the shift was 10 hours.

The rate of change of the angle of elevation is -2π/3 radians/second.

We can use the tangent ratio to solve this problem. Since the rope is attached to the boat, we can draw a right triangle with the rope as the hypotenuse. The angle of elevation is the angle formed by the rope and the horizon.

The pulley is 5 feet above the water level, so the length of the opposite side (the side adjacent to the angle) is 5 feet. The length of the hypotenuse is 12 feet, since the boat is 12 feet from the dock.

Using the tangent ratio, we can calculate the angle of elevation:

tan(θ) = opp/hyp = 5/12

θ = arctan(5/12) = 0.927 rad

Now, since the rope is being pulled in at 3 ft/sec, the length of the hypotenuse is decreasing at a rate of 3 ft/sec. Therefore, the rate of change of the angle of elevation is:

rate of change of θ = -(3 ft/sec) / (12 ft) = -2π/3 radians/second

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5515828288777776677

12

Step-by-step explanation:

since theta is opposite divided by hypotenuse.

so sine 31=3÷AD

Therefore AD=3÷sine 31

thus AD=5.8248

in nearest hundredth, it will be 5.82 units

The length of AD to the nearest hundredth is 5.82 units.

Trigonometric ratios are particular measurements of a right triangle, which is a triangle having a 90° angle. The legs are the two sides that make up the right angle in a right triangle, while the hypotenuse is the third side that is across from the right angle.

Types of trigonometric ratios:

The six trigonometric ratios are

Calculation for the side AD:

In triangle ACD,

Angle CAB = 34 degrees

Angle ADC = 31 degrees

Side AB = 3 units

Now, consider triangle ABD.

Sin (31) = AB/AD

AD = AB/sin 31

AD  = 3/sin 31

AD = 5.82

Therefore, the length of the side AD is 5.82 units.

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Answer: yesterdays price was $700

Step-by-step explanation:

$497 = 71% of the RP (100 - 29)

RP*0.71 = 497

RP = 497/0.71

RP = $700

The best linear approximation to the function f(x) = e^x near x = 0 is L(x) = x + 1.

The given function is f(x) = e^x near x = 0.

To find the best linear approximation, L(x), we use the formula:

L(x) = f(a) + f'(a)(x-a),

where a is the point near which we are approximating.

Let a = 0, so that a is near the point x = 0.

f(a) = f(0) = e^0 = 1

f'(x) = d/dx (e^x) = e^x;

so f'(a) = f'(0) = e^0 = 1

Substituting these values into the formula: L(x) = 1 + 1(x-0) = x + 1

Therefore, the best linear approximation to f(x) = e^x near x = 0 is L(x) = x + 1.

For instance, linear approximation is used to approximate the change in a physical quantity due to a small change in another quantity that affects it.

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Answer:

Line A

Step-by-step explanation:

Any line facing towards the left side of the coordinate plane will have a negative slope.

Line C is facing towards the right

Line D and B doesn't have a slope

A is the only right answer

The amount of drugs remaining into the body:

After t minutes is A0 × e^(-k(t)) mg

After 2t minutes amount of drugs remaining will be A0 × e^(-k(2t)) mg

After 3t minutes it will be A0 × e^(-k(3t)) mg. (A0 is the initial amount of medication, k is the elimination rate constant, and t is the time elapsed)

Assuming that the medication follows first-order kinetics and that the rate of elimination is proportional to the amount of medication present in the body, we can use the following formula to calculate the amount of medication remaining after a certain time:

A = A0 × e^(-kt)

( Here A0 is the initial amount of medication, k is the elimination rate constant, and t is the time elapsed )

After t minutes,

The amount of medication remaining after t minutes can be calculated using the above formula, where t is the time elapsed since the medication was administered.

A = A0 × e^(-kt)

Since d mg of medication were administered every t minutes, the initial amount of medication can be expressed as:

A0 = d * (6*60)/t

(6×60 is the number of minutes in 6 hours)

The elimination rate constant, k, can be calculated from the half-life of the medication, which is given by:

t1/2 = ln(2)/k

If the half-life of the medication is known, we can use this equation to calculate k.

Once we have calculated k, we can use the above formula to calculate the amount of medication remaining after t minutes i.e. A = A0 × e^(-kt)

After 2t minutes,

To calculate the amount of medication remaining after 2t minutes, we can use the same formula as before, but with t replaced by 2t,  A = A0 * e^(-k(2t))

After 3t minutes:

Similarly, to calculate the amount of medication remaining after 3t minutes, we can use the same formula, but with t replaced by 3t,  A = A0 * e^(-k(3t))

Therefore, from the above calculations it can be inferred that the amount of dosage remaining after t minutes is A0 × e^(-k(t)) mg, the amount of dosage remaining after 2t minutes is A0 × e^(-k(2t)) mg and the amount of dosage remaining after 3t minutes is A0 × e^(-k(3t)) mg.

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Answer:

1/9

Step-by-step explanation:

slope = rise/run

slope = (-3--4)/(7--2)=1/9

Dugan's average velocity for the entire race is 0 m/s

To determine Dugan's average speed for the entire race, we can use the formula:

Average speed = Total distance / Total time

In this case, the total distance is 50 meters (25 meters for the first leg and 25 meters for the return leg), and the total time is the sum of the times for both legs, which is:

Total time = 10.02 seconds + 10.16 seconds

a. Average speed for the entire race:

Average speed = 50 meters / (10.02 seconds + 10.16 seconds)

Average speed ≈ 50 meters / 20.18 seconds ≈ 2.47 m/s

Therefore, Dugan's average speed for the entire race is approximately 2.47 m/s.

To determine Dugan's average speed for the first 25.00 m leg of the race, we divide the distance by the time taken for that leg:

b. Average speed for the first 25.00 m leg:

Average speed = 25 meters / 10.02 seconds ≈ 2.50 m/s

Therefore, Dugan's average speed for the first 25.00 m leg of the race is approximately 2.50 m/s.

To determine Dugan's average velocity for the entire race, we need to consider the direction. Since the race is along a straight line, and Dugan returns to the starting point, the average velocity will be zero because the displacement is zero (final position - initial position = 0).

c. Average velocity for the entire race:

Average velocity = 0 m/s

Therefore, Dugan's average velocity for the entire race is 0 m/s
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Answer:

Step-by-step explanation:

The volume of a cylinder is 3 times bigger than a cone with equal radius and height

To know this we have to compare the volumes of both solids first.

Let us assume the height and radius of the cone and radius are

6 and 2 mm respectively

so that the volume of a cone is given as

Volume of cone= 1/3 πr^2h

and the volume of cylinder is given as

Volume of cylinder= πr^2h  

1. Volume of cone= 1/3 πr^2h

Volume of cone= 1/3 *3.142*(2)^2(6)

Volume of cone= 75.408/3

2.  Volume of cylinder= πr^2h

Volume of cone= 3.142*(2)^2(6)

Volume of cone= 75.408

From the analysis the volume of a cylinder is three times bigger the volume of a cone with similar radius and height

The tangent vector  → \(r(t)=〈4cos(2t),4sin(2t),5t〉\), normal vector at t=0 is given by →N(0) = 〈-1,0,0〉, and binormal vector at t=0 is given by →\(B(0) = 〈0, -0.441, -0.898〉\)

The tangent vector, normal vector, and binormal vector of the given curve are as follows:

Given curve:

→ \(r(t)=〈4cos(2t),4sin(2t),5t〉\) at the point t=0

To find: Tangent vector, the Normal vector, and the Binormal vector (→T, →N and →B) at the point t=0

Tangent vector: To find the tangent vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\) at the point t=0,

we need to differentiate the equation of the curve with respect to t.t = 0, we have:

→\(r(t) = 〈4cos(2t),4sin(2t),5t〉→r(0) = 〈4cos(0),4sin(0),5(0)〉= 〈4,0,0〉\)

Differentiating w.r.t t:→\(r(t) = 〈4cos(2t),4sin(2t),5t〉 → r'(t) = 〈-8sin(2t),8cos(2t),5〉t = 0\),

we have:

→\(r'(0) = 〈-8sin(0),8cos(0),5〉= 〈0,8,5〉\)

Therefore, the tangent vector at t = 0 is given by

→\(T(0) = r'(0) / |r'(0)|= 〈0,8,5〉 / sqrt(89)≈〈0.000,0.898,0.441〉\)

Normal vector:To find the normal vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0, we need to differentiate the equation of the tangent vector with respect to t.t = 0, we have:

→\(T(0) = 〈0.000,0.898,0.441〉\)

Differentiating w.r.t t:

→\(T'(t) = 〈-16cos(2t),-16sin(2t),0〉t = 0\),

we have:

→\(T'(0) = 〈-16cos(0),-16sin(0),0〉= 〈-16,0,0〉\)

Therefore, the normal vector at t = 0 is given by

→\(N(0) = T'(0) / |T'(0)|= 〈-16,0,0〉 / 16= 〈-1,0,0〉\)

Binormal vector: To find the binormal vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0, we need to cross-product the equation of the tangent vector and normal vector of the curve.t = 0, we have:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉\)

The cross product of two vectors:

→\(B(0) = →T(0) × →N(0)= 〈0.000,0.898,0.441〉 × 〈-1,0,0〉= 〈0, -0.441, -0.898〉\)

Therefore, the binormal vector at t = 0 is given by→B(0) = 〈0, -0.441, -0.898〉

Hence, the tangent vector, normal vector, and binormal vector of the given curve at t=0 are as follows:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉→B(0) = 〈0, -0.441, -0.898〉\)

The given curve is

→\(r(t)=〈4cos(2t),4sin(2t),5t〉 at the point t=0.\)

We are asked to find the tangent vector, the normal vector, and the binormal vector of the given curve at t=0.

the tangent vector at t=0. To find the tangent vector, we need to differentiate the equation of the curve with respect to t. Then, we can substitute t=0 to find the tangent vector at that point. the equation of the curve Is:

→\(r(t) = 〈4cos(2t),4sin(2t),5t〉\)

At t = 0, we have:

→\(r(0) = 〈4cos(0),4sin(0),5(0)〉= 〈4,0,0〉\)

We can differentiate this equation with respect to t to get the tangent vector as:

→\(r'(t) = 〈-8sin(2t),8cos(2t),5〉\)

At t=0, the tangent vector is:

→\(T(0) = r'(0) / |r'(0)|= 〈0,8,5〉 / sqrt(89)≈〈0.000,0.898,0.441〉\)

Next, we find the normal vector. To find the normal vector, we need to differentiate the equation of the tangent vector with respect to t. Then, we can substitute t=0 to find the normal vector at that point.

At t=0, the tangent vector is:

→\(T(0) = 〈0.000,0.898,0.441〉\)

Differentiating this equation with respect to t, we get the normal vector as:

→\(T'(t) = 〈-16cos(2t),-16sin(2t),0〉\)

At t=0, the normal vector is:

→\(N(0) = T'(0) / |T'(0)|= 〈-16,0,0〉 / 16= 〈-1,0,0〉\)

Finally, we find the binormal vector. To find the binormal vector, we need to cross-product the equation of the tangent vector and the normal vector of the curve.

At t=0, we can cross product →T(0) and →N(0) to find the binormal vector.

At t=0, the tangent vector is:

→\(T(0) = 〈0.000,0.898,0.441〉\)

The normal vector is:

→N(0) = 〈-1,0,0〉Cross product of two vectors →T(0) and →N(0) is given as:

→\(B(0) = →T(0) × →N(0)= 〈0.000,0.898,0.441〉 × 〈-1,0,0〉= 〈0, -0.441, -0.898〉\)

Therefore, the tangent vector, normal vector, and binormal vector of the given curve at t=0 are:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉→B(0) = 〈0, -0.441, -0.898〉\)

The tangent vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0 is given by →\(T(0) = 〈0.000,0.898,0.441〉.\)

The normal vector at t=0 is given by →N(0) = 〈-1,0,0〉.

The binormal vector at t=0 is given by →B(0) = 〈0, -0.441, -0.898〉.

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The equation that shows the operations that Jeremy performs to get y is given as follows:

y = 4x - 3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

When x increases by 2, y increases by 8, hence the slope m is given as follows:

m = 8/2

m = 4.

Hence:

y = 4x + b

When x = 2, y = 5, hence the intercept b is obtained as follows:

5 = 4(2) + b

b = 5 - 8

b = -3.

Thus the equation is:

y = 4x - 3.

The problem is given by the image presented at the end of the answer.

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\( \huge \boxed{\mathfrak{Question} \downarrow}\)

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

__________________

\( {x}^{2} + 4x + 4\)

Factor the expression by grouping. First, the expression needs to be rewritten as x²+ax+bx+4. To find a and b, set up a system to be solved.

\(a+b=4 \\ ab=1\times 4=4 \)

As ab is positive, a and b have the same sign. As a+b is positive, a and b are both positive. List all such integer pairs that give product 4.

\(1,4 \\ 2,2 \)

Calculate the sum for each pair.

\(1+4=5 \\ 2+2=4 \)

The solution is the pair that gives sum 4.

\(a=2 \\ b=2 \)

Rewrite x² + 4x + 4 as (x² + 2x) + (2x + 4)

\(\left(x^{2}+2x\right)+\left(2x+4\right) \)

Take out the common factors.

\(x\left(x+2\right)+2\left(x+2\right) \)

Factor out common term x+2 by using distributive property.

\(\left(x+2\right)\left(x+2\right) \)

Rewrite as a binomial square.

\( b. \: \: \boxed{ \boxed{{(x + 2)}^{2} }}\)

__________________

\(x ^ { 2 } - 8 x + 16\)

Factor the expression by grouping. First, the expression needs to be rewritten as x²+ax+bx+16. To find a and b, set up a system to be solved.

\(a+b=-8 \\ ab=1\times 16=16 \)

As ab is positive, a and b have the same sign. As a+b is negative, a and b are both negative. List all such integer pairs that give product 16.

\(-1,-16 \\ -2,-8 \\ -4,-4 \)

Calculate the sum for each pair.

\(-1-16=-17 \\ -2-8=-10 \\ -4-4=-8 \)

The solution is the pair that gives sum -8.

\(a=-4 \\ b=-4 \)

Rewrite x²-8x+16 as \(\left(x^{2}-4x\right)+\left(-4x+16\right)\).

\(\left(x^{2}-4x\right)+\left(-4x+16\right) \)

Take out the common factors.

\(x\left(x-4\right)-4\left(x-4\right) \)

Factor out common term x-4 by using distributive property.

\(\left(x-4\right)\left(x-4\right) \)

Rewrite as a binomial square.

\( d. \: \: \boxed{\boxed{\left(x-4\right)^{2} }}\)

__________________

\(4 x ^ { 2 } + 12 x y + 9 y ^ { 2 }\)

Use the perfect square formula, \(a^{2}+2ab+b^{2}=\left(a+b\right)^{2}\), where a=2x and b=3y.

\( e. \: \: \boxed{ \boxed{\left(2x+3y\right)^{2} }}\)

__________________

\(x ^ { 4 } - 2 x ^ { 2 } + 1\)

To factor the expression, solve the equation where it equals to 0.

\(x^{4}-2x^{2}+1=0 \)

By Rational Root Theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term 1 and q divides the leading coefficient 1. List all candidates p/q.

\(± \: 1 \)

Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.

\(x=1 \)

By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x⁴-2x²+1 by x-1 to get x³+x²-x-1. To factor the result, solve the equation where it equals to 0.

\(x^{3}+x^{2}-x-1=0 \)

By Rational Root Theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term -1 and q divides the leading coefficient 1. List all candidates p/q.

\(± \: \: 1 \)

Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.

\(x=1 \)

By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x³+x²-x-1 by x-1 to get x²+2x+1. To factor the result, solve the equation where it equals to 0.

\(x^{2}+2x+1=0 \)

All equations of the form ax²+bx+c=0 can be solved using the quadratic formula: \(\frac{-b±\sqrt{b^{2}-4ac}}{2a}\). Substitute 1 for a, 2 for b and 1 for c in the quadratic formula.

\(x=\frac{-2±\sqrt{2^{2}-4\times 1\times 1}}{2} \\ \)

Do the calculations.

\(x=\frac{-2±0}{2} \\ \)

Solutions are the same.

\(x=-1 \)

Rewrite the factored expression using the obtained roots.

\(\left(x-1\right)^{2}\left(x+1\right)^{2} \\ = a. \: \: \boxed{ \boxed{\left(x^{2}-1\right)^{2}}}\)

__________________

The speed of the water wave is 2.0 meters per second.

The speed of a wave is calculated by dividing the distance traveled by the time it takes to travel that distance. In this case, the distance traveled by the water wave is 10.0 meters, and the time taken is 5.0 seconds.

To determine the speed, we use the formula:

Speed = Distance / Time

Substituting the given values, we have:

Speed = 10.0 meters / 5.0 seconds = 2.0 meters per second

Therefore, from the given information, we can determine that the speed of the water wave is 2.0 meters per second.

This information about the speed of the water wave is useful for various purposes. It allows us to understand how quickly the wave is propagating through the medium. It also helps in analyzing wave behavior, such as interference, reflection, or refraction, and studying the characteristics of the medium through which the wave is traveling. Additionally, the speed of the wave can be used in calculations involving wave frequencies, wavelengths, and periods.

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Answer:

x is 3.\(\overline{72}\)

Step-by-step explanation:

The given points on the line are;

R(-5, -6), S(1, 5) and T(x, 10)

The number of points required to find the equation of the line = 2 points

The slope, m, of the line using points R(-5, -6) and S(1, 5) is given as follows;

m = (5 - (-6))/(1 - (-5)) = 11/6

The equation of the line in slope and point form, using point S(1, 5) is therefore;

y - 5 = (11/6)·(x - 1) = 11·x/6 - 11/6

y - 5 = 11·x/6 - 11/6, given that the x-value is required, we have;

x = (y - 5 + 11/6) × 6/11 = 6·y/11 - 19/11

x = 6·y/11 - 19/11

At point T(x, 10), y = 10, therefore, we have;

x = 6×10/11 - 19/11 = 41/11 = 3.\(\overline{72}\)

x = 3.\(\overline{72}\).

0.3814 is the probability that the sample contains two white balls and two red ones .

What is probability in math?

Total number of balls = 8 + 12 = 20

Total number of elementary cases

           = ( 20 4 )

Total number of favourable cases

           = ( 8 2 ) * ( 12 2 )

Required probability

   = ( 8 2 )  *  ( 12 2 )/( 20  4 )

 = 0.3814

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Answer:  See the image below.

Therefore , the solution of the given problem of expression comes out to be -2,4 and 1.

It is important to multiply, divide, add, or delete in mathematics. The following is how an expression is put together: Number, expression, and mathematical operator The components of a mathematical statement, such as additions, subtraction, multiplication, or division, etc., include numbers, variables, and functions. It is possible to contrast expressions and phrases.

Here,

Given  :x = -8.x = 16, and x = 4.

The expression is:

=> X/4

For x =-8

=> -8/4 =-2

For x =16

=> 16/4 =4

For x=4

=>4/4 =1

Therefore , the solution of the given problem of expression comes out to be -2,4 and 1.

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The second derivative is negative, the point (x, y) = (3, 7) corresponds to a local maximum on the curve.

To find the leftmost point on the curve defined by the parametric equations x = t² + 2t and y = t² - 2t + 3, we need to find the value of t that corresponds to this point. We can do this by analyzing the derivative of the curve with respect to t.

The leftmost point on the curve corresponds to the point where the slope of the curve is zero or undefined. This occurs when the derivative of y with respect to x is zero or undefined.

We can express y as a function of x by eliminating t from the given parametric equations. Solving for t in terms of x, we get:

t = -1 ± √(x + 1)

Substituting this value of t in the equation for y, we get:

y = (x + 1) ± 4√(x + 1) + 3

y = ±4√(x + 1) + x + 4

To find the leftmost point on the curve, we need to find the value of x that corresponds to this point. We can do this by finding the minimum value of x for which y is defined.

Differentiating y with respect to x, we get:

dy/dx = 1 + 2/√(x + 1)

Setting dy/dx = 0, we get:

1 + 2/√(x + 1) = 0

2/√(x + 1) = -1

Solving for x, we get:

x = 3

Note that this value of x is within the given range of -2 ≤ t ≤ 3. Therefore, the leftmost point on the curve is the point corresponding to t = 1.

To justify that we have found the requested point, we can analyze the second derivative of y with respect to x. The second derivative will tell us whether the point corresponds to a local minimum, local maximum, or inflection point.

Differentiating dy/dx with respect to x, we get:

d²y/dx² = -2/\((x + 1)^{(3/2)}\)

Substituting x = 3, we get:

d²y/dx² = -2/64

Since the second derivative is negative, the point (x, y) = (3, 7) corresponds to a local maximum on the curve. Therefore, we have found the leftmost point on the curve as requested.

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The question is -

Identify the requested point and justify that you have found the requested point by analyzing an appropriate derivative. x = t² + 2t, y = t² - 2t + 3, - 2 ≤ t ≤ 3 Leftmost point

Answer:

Its first option. bcz its doubled... right..

They’re the same.

Give them common denominators by looking at their least common multiples. 6 and 21 are the denominators and they have to be the same to compare. Their least common multiple is 42.

So 1 4/6 will turn into 1 28/42. I know this because their least common multiple is 42. So I multiplied the 6 by 7 to get 42 as the denominator and you must also multiply the numerator by 6.

1 14/21 will need to be multiplied by 2 to get a denominator of 42. It will turn into 1 28/42. Both simplify down to 1 2/3.

Answer:

The are the same.

Step-by-step explanation:

Because both begin with a 1, ignore that for now.

You have 4/6 and 14/21. Do your best to reduce each. Think about a number that can go into each.

Start with 4/6. They are both even numbers, so 2. 4/2 =  2 and 6/2 = 3

so 4/6 can be reduced to 2/3.

14/21 is trickier, one is odd and the other is even, so no even number will work. 3 can't go in to 14, or 5, but 7 can, and cool! 7 can go in to 21 as well!

14/7 = 2   21/7 = 3    so 14/21 can be reduced to 2/3!

You can also use a common denominator, but you need a calculator for this problem. To solve that way you would take 4/6 and multiply by 21/21 and you would multiply 14/21 by 6/6, this way you'll end up with 126 on the bottom, and you'll see you get 84 on the top.

\(\frac{4}{6} * \frac{21}{21} = \frac{84}{124}\)

\(\frac{14}{21} * \frac{6}{6} = \frac{84}{124}\)

This is much harder without a calculator. Always try and reduce first, because if you end up having to find a common denominator, it will be smaller and more manageable.

If the scale of drawing is 1 inches : 250 inche and the real horse height is 15 inche, then the height of the horse in drawing is 0.06 inches.

The ratio that describes the relationship between the true figure itself and model is called the scale. It serves as a representation of the real statistics in smaller units on maps. A scale of 1:5, for instance, indicates that 1 on the map is approximately the size of 5 in the actual world.

The scale of drawing the horse = 1 inch :

Therefore in scale

Horse height in drawing equals one inch

The  height of the horse = 250 inche

The original height of the horse = 15 inche

The height in the picture = x inches

To find the height the horse in the picture, we have to use proportion

1 inch : 250 inche = x inches : 15 inche

1 / 250 = x / 15

1 × 15= 250x

250x = 15

x = 15/250

x = 0.06 inches

Therefore, the height of the horse in drawing is 0.06 inches

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The empty set {} is a subset of A, and therefore a member of P(A). Therefore, option C is true.Option D. ϕ is a subset of the power set P(A).The empty set {} is a member of P(A), but ϕ (the set containing no elements) is not a subset of P(A). Therefore, option D is false.

Suppose A

= {a, b, c} Indicate which statements below are TRUE are:Option A. {b, c} is an element of the power set P(A).The power set of A (denoted by P(A)) is the set of all subsets of A, including the empty set {} and the set A itself. Therefore, {b, c} is a subset of A but not an element of P(A). Therefore, option A is false.Option B. {a} is a subset of the power set P(A).As a set with a single element, {a} is a subset of A, and therefore a member of P(A) (i.e. a set that contains the single element {a}). Therefore, option B is true.Option C. {} is an element of the power set P(A).The empty set {} is a subset of A, and therefore a member of P(A). Therefore, option C is true.Option D. ϕ is a subset of the power set P(A).The empty set {} is a member of P(A), but ϕ (the set containing no elements) is not a subset of P(A). Therefore, option D is false.

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