Solve for x, please show work!

Answer:

dy/dx = 6x(x²-3)cos2x - 2(x²-3)³sin2x

Step-by-step explanation:

We use the Product Rule:

y= (x²-3)³cos2x

dy/dx =   (x²-3)³ d(cos2x)/dx + cos2x * d ((x²-3)³)/dx

=   (x²-3)³ * -2sin2x + cos2x * 3(x²-3)*2x

= -2sin2x*(x²-3)³ + 6xcos2x*(x²-3)

=  6x(x²-3)cos2x - 2(x²-3)³sin2x

Answer: {x | x is a season}

Step-by-step explanation:

Spring, summer, autumn, and winter are all seasons.

Answer:

[tex]17\sqrt{7z}[/tex]

Step-by-step explanation:

[tex]7\sqrt{28z}+\sqrt{63z}\\ = 14\sqrt{7z}+3\sqrt{7z} \\= 17\sqrt{7z}[/tex]

Answer:

sorry I haven't learned this yet

Step-by-step explanation:

Answer:

2≤7

Step-by-step explanation:

-7+9≤-2+9

2≤7

Answer:

Step-by-step explanation:

3 1/3 is 10/3. 1 1/5 is 6/5. KCF, Keep Change Flip.

10/3 divided by 6/5 becomes 10/3 multiplied by 5/6, or 50/18.

50/18 becomes 25/9, or 2 7/9.

Answer:

2.33 x  10^24  kilograms

Step-by-step explanation:

hope this helps!!

=2.33 × [tex]10{^{21}[/tex]

scientific notation

= 2.33e21

scientific e notation

= 2.33 × [tex]10{^{21}[/tex]

engineering notation

= 2.33 × [tex]10{^{21}[/tex]

21

Order of Magnitude

for scientific and standard forms

two setillion three hundred thirty quintillion

Answer:

  160,000 tins

Step-by-step explanation:

To find the number of tins, divide the fill rate by the volume per tin.

__

  (2·(1000 L)/min)×(60 min)/(1 h)/(0.75 L/tin) = 160,000 tin/h

160,000 tins of paint can be filled in 1 hour.

_____

Additional comment

That's one tin every 22.5 milliseconds. It would be a feat of engineering to move that volume without splashing.

There are 60 minutes per hour. There are 1000 liters per cubic meter.

Answer:

C. 21 1/9

Step-by-step explanation:

6 1/3 cups / 0.3 cups in a serving = 21.11111... or 21 1/9

Answer:

X=42

Step-by-step explanation: x-23=17 you would do the inverse of subtracting which would be addition which would be 23+17 which equals  42

Answer: B

Step-by-step explanation:

Pedro's total distance moved is 7.5 kilometers

The given parameters are:

The total distance is the sum of the above distances i.e.

Total = 1.2 km + 1.5 km + 2 km + 2.8 km

Evaluate

Total = 7.5 km

Hence, Pedro's total distance moved is 7.5 kilometers

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Answer:

55

Step-by-step explanation:

Since whole numbers do not include fractions and decimal values, 55 is the answer

Answer:

SEE BELOW IN BOLD.

Step-by-step explanation:

a.

h = -16t^2 + 50t

h = 20 t

When the height is the same:

-16t^2 + 50t = 20t

-16t^2  + 30t = 0

t(-16t + 30) = 0

t = 0 or  -16t + 30 = 0, so:

t = 0 or -30/-16 = 1.875

So the answer is 1.88 seconds to the nearest hundredth.

b.

For the ball

h = -16t^2 + 50t

Finding the derivative and equating to zero:

dh/dt = -32t + 50 = 0

t = -50/-32 = 1.563

Maximum height after 1.56 seconds to nearest hundredth

c.

When the ball hits the ground h = 0 so

-16t^2 + 50t = 0

-16t(t - 50/16)= 0

T = 3.13 SECONDS TO THE NEAREST HUNDERDTH

[tex]\huge{\color{red}{\fbox{\textsf{\textbf{Answer}}}}} [/tex]

4 hours 12 minutes

Step-by-step explanation:

We need to convert time in hours by diving 15 by 60

[tex] \sf 2 \frac{15}{60} \\ \\ \sf 2 \frac{1}{4} [/tex]

as it is mixed fraction we will convert into improper

[tex] \sf \frac{(2 \times 4) + 1}{4} \\ \\ \sf time = \frac{9}{4} hours[/tex]

Now we need to find distance

[tex] \sf \green {distance = speed \times time}[/tex]

Here speed is 50km/h

[tex] \sf \implies distance = 50 \times \frac{9}{4}km \\ \\ \sf \implies distance = \frac{25 \times 9}{2}km \\ \\ \sf \implies distance = \frac{225}{2} km \\ \\ \sf \implies \red {distance = 112.5km}[/tex]

Now we have to have time at new speed at 27km/h

and distance is same

[tex] \sf \pink{ time = \frac{distance}{speed} }[/tex]

Now substituting the value of speed and distance

[tex] \sf \implies time = \frac{112.5}{27} [/tex]

Now we will remove point(.) from the distance by multiplying 10 with 27

[tex] \sf \implies time = \frac{1125}{27 \times 10} \\ \\ \sf \implies time = \frac{41.6}{10} [/tex]

now we will convert it into mixed fraction

[tex] \sf \implies time = 4 \frac{1}{5} hours [/tex]

Now we will convert fraction hours into minutes by multiply with 60

[tex] \sf \implies time = 4 \: hours \: \frac{1}{5} \times 60 \: minutes \\ \\ \sf \implies \orange{ time = 4 \: hours \: 12 \: minutes}[/tex]

Answer:

x = 4

Step-by-step explanation:

<C = <A

25° = 8x - 7

32 = 8x

x = 4

Answer:

yes

Step-by-step explanation:

1/2 is half of 1.

300 is 300 times greater than 1, so 300 is 600 times greater than 1/2.

Answer:

Yes, 300 is greater than 1/2

Answer: 2,3

Step-by-step explanation: I think this is the right answer. Have a good day!! :)

Answer:

C) f(x) = (x - 1)(x - 1)(x-6)

Explanation:

Multiplicity means number of times a factor appears in a particular equation.

For example, a root of 3 has multiplicity of 3 then = (x - 3)(x - 3)(x - 3)

Breakdown for this question:

If a polynomial where root of 1 has multiplicity of 2, then it means (x - 1)²

Where polynomial of root of 6 has multiplicity of 1, then it means (x - 6)

Joining them together:

(x - 1)²(x - 6) = (x -1)(x - 1)(x - 6) Hence option C is correct.

Answer:

a = 10

a = 2

a = 8

Step-by-step explanation:

  The inequality:

11 ≥ a

   We will go through all the options:

-> In short, all values less than or equal to 11 will be solutions.

a = 10

11 ≥ a

11 ≥ 10 ✓

-

a = 2

11 ≥ a

11 ≥ 2 ✓

-

a = 8

11 ≥ a

11 ≥ 8 ✓

-

2 = 3

N/A, no 'a' variable given.

Answer:

The answer is 3 cm.

Step-by-step explanation:

To find the width of the cereal box, we must first take the volume and divide it by the length and then divide that by the height.

For this equation, we would do the following:

3456 ÷ 36 = 96 cm²

Now that we have divided volume by length, let's divide by height next:

96 ÷ 32 = 3 cm

Now we know the height of the box. To check if this is correct, lets multiply the length, height, and width and see if we get the volume that we started with.

3 × 32 × 36 = 3456 cm³

Since we got the original volume that we started with, we know that the width is 3 cm which is your answer.

The concavity of the function in this problem is classified as follows:

Hence the intervals are given as follows:

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Answer:

0.5 feet

Step-by-step explanation:

Volume = Length × Width × Depth

Here :

Solving :

Answer: (10x + 9) (x - 3)

Step-by-step explanation:

Factor by grouping

The “Volume” in finance means total shares traded during a certain time frame option (B) is correct.

To make a profit, share traders buy and sell the stock of companies listed on the stock exchange.

The number of shares traded in a certain stock, index, or other investment during a given period of time is known as volume.

Thus, the “Volume” in finance means total shares traded during a certain time frame.

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Hey there!

[tex] \displaystyle{ \red{ \boxed{ \green{ \bold{m = - 1}}}}}[/tex]

[tex] \\ [/tex]

To find the slope of a line using two points [tex] \displaystyle{(x_1 , y_1)} [/tex] and [tex] \displaystyle{(x_2 , y_2)} [/tex] , we can use the slope formula.

This formula corresponds to the quotient of the change in y [tex] \: [/tex] over [tex] \: [/tex] the change in x :

[tex] \displaystyle{m = \frac{ \blue{y_2} - \orange{y_1}}{ \green{x_2} - \red{x_1} }}[/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow [/tex] We are given the points (-2 , 3) and (-5 , 6) where:

[tex] \\ [/tex]

[tex]\displaystyle{ \hookrightarrow m = \frac{\blue{6} - \orange{3}}{\green{-5} - \red{(-2)}}} \\ \\ \displaystyle{\implies m=\frac{3}{-3}} \\ \\ \displaystyle{\purple{\implies} \boxed{\bold{m=-1}}}[/tex]

Therefore, the slope of the line is -1.

[tex] \\ [/tex]

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Answer:

(a) The number of accidents was reduced by 0.67 per month for every additional 100 drivers in the program.

Step-by-step explanation:

We are given the options,

(a) The number of accidents was reduced by 0.67 per month for every additional 100 drivers in the program.

(b) The number of accidents was reduced by 0.67 per month every month.

(c) The number of accidents increased by 0.67 per month for every additional 100 drivers in the program.

(d) There were 0.67 accidents per month.

We can eliminate option 'c' because the accidents are obviously not increasing, but rather, decreasing. We can also eliminate option 'd' (which to a certain extent is rather vague) because there is a trend in the data. If there were only 0.67 accidents per month (which is impossible anyway), then the graph would be that of [tex]y=0.67[/tex] which is indeed a straight line. Finally, we can eliminate option 'b' because the x-axis isn't in terms of months, but drivers in the program. This leaves 'a' as the only logical answer, which we can see is true because the graph trends downward (hence the negative slope) by about 0.67 per 100 drivers. With a bit of understanding about the problem, we can eliminate the illogical answers to find the correct one!

Note: you may be wondering why the slope isn't just -0.67, but that is because then it would go down by 0.67 for each driver in the program. Therefore, the slope was divided by 100 to yield us a slope of -0.0067 which makes it go down 0.67 per 100 drivers instead of only 1 driver.

The car that travels for 7 hours and 50 minutes at an average speed of 130 km/h covered a distance of 1017.9 km.

The car travels for 7 hours and 50minutes at an average speed  of 130 km/h.

Therefore,

speed = distance / time

speed = 130 km/h

time = 7 hours 50minutes = 7 + 0.833333 = 7.83 hours

Therefore,

130 = distance / 7.83

cross multiply

distance = 7.83 × 130

distance = 1017.9 km

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