if a particle moves along a straight line according to s(t)= t^4 -4t^3 +6t^2 -20, find the maximum and minimum acceleration on 0 less or equal to t less or equal to 3

Answer:

True

Step-by-step explanation:

Each week the amount of radio active material is 100*(1/4)^x which is correct.

So at the end of 4 weeks she will have

amount = 100*(1/4)^x

amount = 100*(1/4)^4

amount = 100 * (1/256)

amount = 0.390625 grams after 4 weeks.

Answer:

Step-by-step explanation:

There is the answer.

Answer:

Step-by-step explanation:

3x + 5 = 19 - 4x     subtract 5 from both sides

3x = 14 - 4x      add 4x to both sides

7x = 14    divide both sides by 7

x = 2

Answer:

x=2

Step-by-step explanation:

3x + 5 = 19 - 4x

Add 4x to each side

3x + 5 +4x= 19 - 4x+4x

7x+5 = 19

Subtract 5 from each side

7x+5-5 =19-5

7x =14

Divide each side by 7

7x/7 = 14/7

x = 2

Put the values of x to the equation y = 2ˣ:

[tex]x=-1\to y=2^{-1}=\dfrac{1}{2}\to\left(-1,\ \dfrac{1}{2}\right)\\\\x=0\to y=2^0=1\to(0,\ 1)\\\\x=1\to y=2^1=2\to(1,\ 2)\\\\x=2\to y=2^2=4\to(2,\ 4)\\\\x=3\to y=2^3=8\to(3,\ 8)\\\\x=4\to y=2^4=16\to (4,\ 16)[/tex]

Answer:

[tex]\left\{\left(-1,\ \dfrac{1}{2}\right);\ (0,\ 1);\ (1,\ 2);\ (2,\ 4);\ (3,\ 8);\ (4,\ 16)\right\}[/tex]

Answer:

SEgment AC is congruent to segment AB

Step-by-step explanation:

given is a triangle ABC with a segment joining A to D on side BC.

To prove that ABD is congruent to ACD

Let us compare these two triangles.

AD = AD (reflexive) Thus one side is equal.

IF AB = AC, then by isosceles triangles property we have angle B = angle C

Thus we get two sides equal.  But this is a necessary condition not sufficient.

Because to prove congruence we need one more condition either CD = BD or Angle CAD = angle DAB

Thus if either AD is angle bisector, or D is mid point besides AC = AB we get

the two triangles are congruent.

PL= sqrt(4^2+12^2)=4sqrt(1+9)=4sqrt(10)

Using similarity gives that AM=4/3.

ML=40/3

[PLMU]=40/3 * 4 = 160/3 (53.33)

Or

PM= sqrt(4^2+16/9)=sqrt(160/9)=4sqrt(10)/3

4sqrt(10)*4sqrt(10)/3=160/3 or approximately 53.33

The earnings for selling the same number of each type of sandwich, considering both Turkey and Ham with Pretzel Roll and Bagel options, amount to $48. This is derived from a simplified expression of $29.10x, factored by 11, indicating a total revenue of $4.30 per sandwich.

Earnings for Selling Sandwiches

1: Identify the Given Information

We have two types of sandwiches: Turkey and Ham.

Each type comes in two types of bread: Pretzel Roll and Bagel.

Prices are provided for each combination:

Turkey Pretzel: $2.25

Turkey Bagel: $2.00

Ham Pretzel: $1.55

Ham Bagel: $1.30

2: Represent the Number of Sandwiches with a Variable

Let x represent the number of each type of sandwich sold (both Turkey and Ham, regardless of bread).

3: Calculate Earnings for Each Type of Sandwich

Turkey Sandwich: $11 (given price) * x (number sold) = $11x

Ham Sandwich: $11 (given price) * x (number sold) = $11x

Step 4: Calculate Earnings for Each Bread Type (excluding overlapping information)

Pretzel Roll: (Earnings from Turkey Pretzel + Earnings from Ham Pretzel) = ($2.25 * x) + ($1.55 * x) = $3.80x

Bagel: (Earnings from Turkey Bagel + Earnings from Ham Bagel) = ($2.00 * x) + ($1.30 * x) = $3.30x

5: Combine Earnings for Total Revenue

Total Earnings = Earnings from Turkey Sandwiches + Earnings from Ham Sandwiches + Earnings from Pretzel Rolls + Earnings from Bagels

Total Earnings = $11x + $11x + $3.80x + $3.30x = $29.10x

6: Simplify the Expression

Total Earnings = $29.10x

Since we are selling the same number of each type of sandwich, 11 is a common factor in all four terms.

We can factor out 11 to obtain:

Total Earnings = 11 * ($2.65 + $1 + $0.35 + $0.30) = 11 * $4.30 = $48

Therefore, the earnings for selling the same number of each type of sandwich are $48.

The average acceleration of the car is 4 m/s²

The given parameters:

initial velocity of the car, u = 2 m/s

final velocity of the car, v = 16 m/s

time of motion of the car, t = 3.5 s

To find:

The average acceleration of the car is calculated as the change in velocity per change in time.

The formula for average acceleration is given below;

[tex]a = \frac{\Delta v}{\Delta t} = \frac{v- u}{t} = \frac{16 - 2}{3.5} = 4 \ m/s^2[/tex]

Thus, the average acceleration of the car is 4 m/s²

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Answer:

DAB must equal 52 because same side interior angles are supplementary. Supplementary describes 2 angles whose measures add up to 180

Answer: May or may not be

Step-by-step explanation:

check the picture and trust me

Final answer:

Since ΔACD is an isosceles right triangle, the two legs AC and CD are equal. Given CD = 6 √ 3, AC is also 6 √ 3 units.

Explanation:

In triangle ΔABC, we are given that m∠ACB = 90°, meaning that ΔACB is a right-angled triangle. We are also given that CD is perpendicular to AB and that m∠ACD = 45°. Since CD is perpendicular to AB at D, triangle ΔACD is also a right-angled triangle with a 45° angle, which makes it an isosceles right triangle. In an isosceles right triangle, the lengths of the legs are equal. Therefore, AC will be equal to CD which is given as 6 √ 3.

The length of AC in triangle ΔACB can be found using Pythagoras' theorem, AC = √(AB² + BC²). But here we need only the length of AC in the right-angled ΔACD where AC equals CD.

Hence, AC = 6 √ 3 units.

Answer:

Each pound of chocolate costs $7.30

Step-by-step explanation:

if 5 pounds of chocolate costs $36.50 then you could simply divide the $36.50 by 5 to calculate the cost of 1 pound of chocolate.

So, 36.50 ÷ 5 = 7.30

Each pound of chocolate costs $7.30

To find the cost of each pound of chocolate, you divide the total cost by the total number of pounds. Given a total cost of $36.50 for 5 pounds of chocolate, the resulting calculation is $36.50 ÷ 5 = $7.30. Thus, each pound costs $7.30.

If you have 5 pounds of chocolate that cost $36.50 in total, and you need to find the cost of each pound of chocolate, you can determine this by dividing the total cost by the number of pounds. This is similar to how in our reference material, to compute the cost of each piece of fruit, you divided the total expense by the quantity of fruit.

In this case, you need to divide the total cost, which is $36.50, by the quantity, which is 5 pounds. So the calculation is $36.50 ÷ 5 = $7.30. Therefore, each pound of chocolate costs $7.30.

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Answer:

Step-by-step explanation:

Please find attachment for step by step explanation.

Answer:

The proportional

Step-by-step explanation:

The complete statement is a division of long form ends with zeroes as remainders

We have the following statement -

A division of _____ ends?

The complete statement is -

A division of long division form ends with zeroes as remainders

Therefore, the complete statement is a division of long form ends with zeroes as remainders.

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Answer: The price per pound is $18

Answer:

Let 5 consecutive no's be x,x+1,x+2,x+3,x+4

90 = x+ x+1+x+2+ x+3+x+4

90 = 5x+10

18 = x+2

x= 16

so smallest is 16

greatest = 16+4 = 20

sum = 16 +20 = 36

Answer:

The domain is all real numbers. The range is {y|y ≤ 16}.

Step-by-step explanation:

The vertex of a parabola is given by

[tex](\frac{-b}{2a}, \frac{4ac-b^2}{4a})[/tex].

As a = -1, b = -2, c= 15 here, then the vertex is at (1,16).

As a is negative, it opens downward, so the range is  {y|y ≤ 16}.

Meanwhile, all parabolic functions have a domain of [tex]\mathbb{R}[/tex].

[ Answer ]

Y = -9

[ Explanation ]

Subtract 15 from both sides:

2/3y + 15 - 15 = 9 - 15

Simplify:

2/3y = -6

Multiply each side by 3:

3 * 2/3y = 3 (-6)

Simplify:

2y = -18

Divide both sides by 2:

2y / 2 = -18/2

y = -9

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Using the simplification, it is proven that the y = -9 from the equation 2/3y + 15 = 9.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given that 2/3y + 15 = 9

Subtract 15 from both sides;

2/3y + 15 - 15 = 9 - 15

Now Simplify,

2/3y = -6

Multiply each side by 3,

3  (2/3y) = 3 (-6)

2y = -18

y = -9

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By using the simple addition operation, the total number of cups of coffee sold in the coffee shop, counting espressos, cappuccinos, and lattes, is 8,594 cups.

To find the total number of cups of coffee sold, we should add up the number of espressos, cappuccinos, and lattes. This principle is known as simple summation or addition operation in mathematics. As per the numbers given:

When we add these together, we get the total cups of coffee sold as:

1627 (Espressos) + 2741 (Cappuccinos) + 4226 (Lattes) = 8594 cups of coffee in total

So, the coffee shop has sold a total of 8594 cups of coffee.

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Answer:

A. The equation has no solution

It's not a rectangle. Look at the picture.

It is a parallelogram.

The area of the red rectangle:

[tex]A_{\boxed{ \ }}=(4+8)(6+3)=(12)(9)=108[/tex]

The areas of the right triangles:

[tex]A_1=\dfrac{1}{2}(3)(4)=6\\\\A_2=\dfrac{1}{2}(6)(8)=24[/tex]

The area of a parallelogram:

[tex]A=A_{\boxed{ \ }}-(2A_1+2A_2)\\\\A=108-(2\cdot6+2\cdot24)=108-(12+48)=108-60=48[/tex]

Answer:

20%

Step-by-step explanation:

Percent increase is difference/original

360-300) / 300

60/300 / 60/60 = 1/5 * 20/20 = 20/100

Percent is out of 100

Answer:

The answer would be 998.4

Step-by-step explanation:

251,589 divided by 252 = 998.36

round it to 998.4

Answer:

an = -6+n

or

an = 1 + 7(n-1)

Step-by-step explanation:

a(1)=1 and a(n+1)=a(n)+7

The explicit formula is

an = a1+ d (n-1)

we know a1 =1

Looking at a(n+1)=a(n)+7

We are adding 7 each time so the common difference is +7

an = 1 + 7(n-1)

We can simplify this

an = 1 + 7n -7

an = -6+n

You can use either formula

Expand to get 35x^3+49x^2-20x-28

Answer:

3x(3x + 2)

Step-by-step explanation:

Answer:

y = 8

Step-by-step explanation:

If y varies directly as x we can write y = kx where k is some constant.

Y = 8 when x = 2 so  8 = k*2

k = 8/2 = 4

so y = 4x

This is the equation of variation.

When x = 6, y = 4*6 = 24  (answer).

Answer:

y =24

Step-by-step explanation:

The equation for direct variation is

y =kx

If we know x and y we can solve for k

y=kx

8 =k*2

Divide each side by 2

8/2 = k2/2

4 =k

y =4x

We want to find y when x=6

y =4*6

y =24

Answer:

2.3 degrees.      

Step-by-step explanation:

Please find the attachment.

We are told that an airplane must clear a 60-foot pole at the end of a runway 500 yards long.

Let us convert 500 yards to feet.

1 yard= 3 feet.

500 yards= 3*500 feet= 1500 feet.

We can see from our attachment pole and runway are in form of a right triangle. The pole is opposite to angle of elevation of plane and length of runway is adjacent.

Since tangent represents the relation between opposite and adjacent of right triangle, So we will use tangent to find angle of elevation that plane must ascend to clear the pole.  

[tex]tan(\theta)=\frac{60}{1500}[/tex]    

[tex]\theta=\tan^{-1}(\frac{60}{1500} )[/tex]

[tex]\theta=\tan^{-1}(0.04)[/tex]

[tex]\theta=2.290610042639[/tex]

Therefore, the airplane must ascend 2.3 degrees to clear the pole.

Answer:

B.) transitive property of equality

Step-by-step explanation:

x = –3 and –3 = z, then x = z.

Symmetric property of equality: if a = b then b = a

Transitive property of equality:  if a = b and b = c, then a = c

Closure property of multiplication:  the set is closed under multiplication

Closure property of addition:  the set is closed under addition