find the length of the curve described by the parametric
equations: x=3t^2, y=2t^3, 0 a. 3V3 -1
b. 2(√3-1)
c. 14
d. no correct choices

Answer:

268

Step-by-step explanation:

2(2×6+2×2+2×6) + 2(4×5+4×10+10×5) - 2(2×2)

= 56+220-8

= 268 cm²

Answer:

272cm

Step-by-step explanation:

So the green block has 6 sides

the height of the prism is 4cm

the length is 10cm

and the width is 5cm

to find the top and bottom sides we must find the width and length

5x10=50cm so The bottom and top are double that so 100cm is covered so far

to find the longer sides, we times 4 by 10 = 40x2 = 80cm which covers 2 sides

and the last 2 sides of the green block are the smaller ones so 4x5 = 20 but that covers one side so we times by 2 andd that gives us both sides so 40cm

all 6 sides are covered so we can add up the numbers

top and bottom = 100cm

front back = 80cm

left and right = 40

add them all up and we get 220

now we see the purple block, this is the Same process as before

top = 2x2 = 4

bottom = 2x2 = 4

front = 6x2 = 12

back = 6x2 = 12

left = 6x2 = 12

right = 6x2 = 12

add them together and we get 56cm

the surface area of both of them Is 220+56 = 276cm

however the bottom of the purple prism is on top of the top of the green prism. Because we know the surface area of the bottom of the purple  (4) and the top Surface of the green (50).

this allows us to subtract the prism above because of the bottom shapes surface so the actual answer is  272cm hope this helped

Answer:

5%

Step-by-step explanation:

10/200 × 100 = 5

hope this helps...

-21 - (-14) = -7; Absolute value measures the distance from zero on the number line; "Random" refers to lack of pattern or predictability; A calculator is used for mathematical calculations; The value of "m" depends on the context or equation; Absolute value in math is the numerical value without considering the sign.

-21 - (-14) simplifies to -21 + 14 = -7.

The absolute value of a number is its distance from zero on the number line, regardless of its sign. It is denoted by two vertical bars surrounding the number. For example, the absolute value of -5 is written as |-5| and is equal to 5. Similarly, the absolute value of 5 is also 5, so |5| = 5.

"Random" refers to something that lacks a pattern or predictability. In the context of the question, it seems to be used as a term rather than a specific question.

A calculator is an electronic device or software used to perform mathematical calculations. It can be used for various operations such as addition, subtraction, multiplication, division, exponentiation, and more.

The value of "m" cannot be determined without additional information. It depends on the specific context or equation in which "m" is being used.

Absolute value in math refers to the numerical value of a real number without considering its sign. It represents the magnitude or distance of the number from zero on the number line. The absolute value of a number is always positive or zero.

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Answer:

y2 = m(x2-x1)+y1

Step-by-step explanation:

Given the formula for finding the slope of a linear equation to be;

m = y2-y1/x2-x1 where x and y are from the ordered pairs (x1,y1) and (x2,y2)

To get the equivalent equation for y2, we will make y2 the subject of tbw formula from the equation as shown:

m = y2-y1/x2-x1

Cross multiplying

m(x2-x1) = y2-y1

mx2-mx1 = y2-y1

Adding y1 to both sides of the equation we have;

mx2-mx1 + y1= y2-y1+y1

y2 = mx2-mx1 + y1

y2 = m(x2-x1)+y1

This gives the resulting equation to solve for y2

Answer:

c

Step-by-step explanation:

edg

Answer:

two

Step-by-step explanation:

Answer:

\(\frac{16}{35}\)

Step-by-step explanation:

\(\frac{\frac{2}{5} }{\frac{7}{8} }\)

There is a couple of ways that you can do this.  I am going to divide the top and bottom fractions by \(\frac{8}{7}\)

\(\frac{\frac{2}{5} }{\frac{7}{8} }\) x \(\frac{\frac{8}{7} }{\frac{8}{7} }\) = \(\frac{\frac{16}{35} }{\frac{56}{56} }\) = \(\frac{\frac{16}{35} }{1}\) = \(\frac{16}{35}\)

Answer:

22

Step-by-step explanation:

we have the sequence

6 10 14 18

well we can see that from 6 to 10 we add 4

and from 10 to 14 we continue to add 4

and that pattern applies to the next

so we can conclude that to 18 we need to add 4 to get the next one

18 + 4 = 22

so the next number is 22

Answer:

Number of students tickets sold= 184

Number of adults tickets sold= 192

Step-by-step explanation:

I assume we need to calculate the number of student and adult tickets sold.

First, we establish the system of equations:

x= number of students tickets sold

y= number of adults tickets sold

4*x + 7*y= 2,080

x + y= 376

Now, we isolate x in one formula and substitute it in the other:

x= 376 - y

4*(376 - y) + 7y = 2,080

1,504 - 4y + 7y = 2,080

3y = 576

y= 192

x= 376 - 192

x= 184

Number of students tickets sold= 184

Number of adults tickets sold= 192

Answer:

5 movies and 1 video game

Step-by-step explanation:

4 x 5 = 20 + 6 = 26

We are asked to determine the volume of the cylinder. To do that we will use the following formula:

Where "r" is the radius and "h" is the height. Replacing the values:

Solving the operations:

Therefore, the volume is 502.4 cubic centimeters.

The interest earned on Account B is $264.73 more than Account A.

Given data:

Principal = $5865.28

Account A earns an annual simple interest rate of 5.738%

Account B earns an annual interest rate of 5.738% compounded weekly

Time (n) = 7 years

Part 1: Calculation of simple interest in Account A

We have; Simple Interest (I) = P × r × t

where P is the principal,

r is the rate of interest per annum,

and t is the time in years.

So, Putting the values we get,

I = P × r × tI = 5865.28 × 5.738% × 7I = $2366.18

Hence, the amount in Account A after 7 years = Principal + Simple Interest = $5865.28 + $2366.18 = $8231.46

Part 2: Calculation of compound interest in Account B

We have; Compound Interest (A) = P(1 + r/n)^(n × t)

where P is the principal,

r is the rate of interest per annum,

t is the time in years,

and n is the number of compounding periods.

So, here the interest is compounded weekly so, n = 52.

Putting the values we get, A = P(1 + r/n)^(n × t)A = 5865.28(1 + 5.738%/52)^(52 × 7)A = $8496.19

Hence, the amount in Account B after 7 years = $8496.19

Therefore, the amount in Account A is $8231.46 and the amount in Account B is $8496.19.

Part 3: Calculation of difference in interest earned in both accounts

We have, I(A) = $2366.18 and I(B) = $8496.19 - $5865.28 = $2630.91

The difference between the interest earned on Account B and Account A is $2630.91 - $2366.18 = $264.73

Therefore, the interest earned on Account B is $264.73 more than Account A.

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Answer:

20.5

Step-by-step explanation:

25-9=16

16+4.5=20.5

Answer:

47 pupils

Step-by-step explanation:

Since there are 15 pupils who play both sports, we can subtract 15 from both of the totals. (25 - 15 = 10 and 32 - 15 = 17)

From this we can see that there are 10 pupils who play volleyball, 17 who play basketball, 15 who play both, and 5 who don't participate.

Adding these numbers up:

10 + 17 + 15 + 5 = 47 pupils

Once the dimensions of the triangular pyramid are provided, we can perform these calculations to find the volume of the remaining piece in cubic inches.

To determine the volume of the remaining piece, we need to find the volume of the triangular pyramid that was cut off and then subtract it from the original volume of the rectangular prism.

Here are the steps:
Step 1: Determine the volume of the rectangular prism.

The student question already provides this information: 12 cubic inches.
Step 2: Determine the volume of the triangular pyramid.

In order to do this, we need the base area and the height of the pyramid.

However, the diagram is not provided in the question. Please provide the dimensions of the base and height of the triangular pyramid.
Step 3: Calculate the volume of the triangular pyramid using the formula:
Volume = (1/3) × Base area × Height
Step 4: Subtract the volume of the triangular pyramid from the volume of the rectangular prism to find the volume of the remaining piece:
Remaining Volume = Volume of Rectangular Prism - Volume of Triangular Pyramid.

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Answer: 50

Step-by-step explanation: Common factor of 150 and 350 = 1, 2, 5, 5. Highest common factor of 150 and 350 = 2 × 5 × 5 = 50.

Answer:

slope = (y₂ - y₁) / (x₂ - x₁)

18-9/-10-10

=9/0

The slope is undefined and it is a vertical line.

Step-by-step explanation:

OR

since x₂ , x₁ are the same value -10 the slope is undefined.

a) logn(14) = logn(2) + logn(7) = B + AWe can use the properties of logarithms to express logn(14) in terms of A and B.

According to the product rule of logarithms, logn(a * b) = logn(a) + logn(b). In this case, we can rewrite 14 as the product of 2 and 7, so logn(14) can be expressed as logn(2) + logn(7), which is B + A.

b) logn(49) = 2 * logn(7) = 2A

Using the power rule of logarithms, logn(a^b) = b * logn(a), we can express logn(49) in terms of A. Since 49 is equal to 7 raised to the power of 2, we have logn(49) = 2 * logn(7), which simplifies to 2A.

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16 is a perfect square

16 = 2 × 2 × 2 × 2

16 = (2 × 2) × (2 × 2)

16 = 4 × 4

Perfect squares numbers whose squares are whole numbers. Square root of 16 gives 4.

Hence, 16 is a perfect square

Answer:

p = 4

Step-by-step explanation:

2p + 7 = 15 ( subtract 7 from both sides )

2p = 8 ( divide both sides by 2 )

p = 4

Answer:

P = 4

Step-by-step explanation:

2P + 7 =15

2P = 15 - 7

2P = 8

P = 8/2

P = 4

The inequality that can be used with the squeeze theorem to calculate the limit of f(x) is \(-x^{2} \leq x^{2} cos\frac{1}{x^{2} } \leq x^{2} or -x^{2} \leq f(x)\leq x^{2}\)

Squeeze Theorem,

If f(x)g(x)h(x) for all numbers and at some point x=k we get f(k)=h(k), then g(k) must also be equal to them, according to the squeeze (or sandwich) theorem. Theorem: By "squeezing" sin(x)/x between two better functions and using them to discover the limit at x=0, we can utilize them to obtain tricky limits like sin(x)/x at x=0.

The given function is \(f(x) = x^{2} cos(\frac{1}{x} )\)

The range of the cos function is from -1 and 1.

We have,

\(-1\leq cos\frac{1}{x^{2} } \leq 1\\\)

Multiplying the above inequality by x^2, we get :

\(-x^{2} \leq x^{2} cos\frac{1}{x^{2} } \leq x^{2}\)

The above equation can be rewritten as,

\(-x^{2} \leq f(x)\leq x^{2}\)

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Answer:

B) 26%

Step-by-step explanation:

The yellow part of the graph represents Rock, which is 15%, and the red part of the graph represents Classical. So, you simply add them together.

Answer:

B) 26%.

Step-by-step explanation:

Find the Rock percentage in the chart. (15%)

Find the Classical percentage in the chart. (11%)

Add the Rock and Classical percentages together. (26%)

The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

The two most important parts of a vehicle in preventing traction loss are the tires and the traction control system.

Tires: Tires are the primary point of contact between the vehicle and the road surface. The quality and condition of the tires greatly influence traction. Tires with good tread depth and appropriate tread pattern are essential for maintaining grip on the road. Tread depth helps to channel water, snow, or debris away from the tire, preventing hydroplaning or loss of traction. Additionally, tire pressure should be properly maintained to ensure even contact with the road. Choosing tires suitable for the specific driving conditions, such as all-season, winter, or performance tires, is crucial for optimal traction and handling.

Traction Control System: The traction control system is a vehicle safety feature that helps prevent the wheels from slipping or spinning on low-traction surfaces. It uses various sensors to monitor the speed and rotation of the wheels. If the system detects a loss of traction, it will automatically reduce engine power and apply braking force to the wheels that are slipping. By modulating power delivery and braking, the traction control system helps maintain traction and prevent wheel spin, especially in challenging conditions like slippery roads or during quick acceleration.

The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

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a)

Given,

3/x+2 = 1/7-x

Now further simplifying,

3(7-x) = x+2

21 - 3x = x + 2

19 = 4x

x = 19/4

Hence for the given expression the value of x is 19/4

b)

Given,

3-x/x-5 - 2x²/x² - 3x 10 = 2/x+2

Factorize the quadratic equation,

x² - 3x -10 = 0

(x+2)(x-5) = 0

3-x/x-5 - 2x²/ (x+2)(x-5) = 2/x+2

Taking LCM,

(3-x)(x-2) - 2x²/(x-5)(x+2) = 2/x+2

Further simplifying,

(3-x)(x-2) - 2x²= 2(x-5)

x² - 3x - 4 = 0

x² -4x +x - 4 = 0

x(x-4) + 1(x-4) = 0

(x+1)(x-4) = 0

x = -1 , 4 .

Hence for the given expression the value of x is -1, 4 .

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The correct answer is d) To avoid a large number of classes with very small frequencies.

Unequal class intervals are sometimes used in a frequency distribution to avoid a large number of classes with very small frequencies. This can occur when the data range is very large or when there is a lot of variability in the data.

For example, if we have a dataset with values ranging from 0 to 1000, using equal class intervals of size 100 would result in 10 classes. However, if the data is skewed and most of the values fall in the lower range, many of the classes may have very small frequencies. Using unequal class intervals can help group the data in a way that results in more meaningful class frequencies.

Additionally, unequal class intervals can be used to better represent the distribution of the data. For example, if there is a cluster of values around a certain range, using a smaller class interval around that range can provide more detail and information about the data distribution.

Therefore, the correct answer is d) To avoid a large number of classes with very small frequencies.

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(1) (4.17 x 10⁻³) (4 x 10⁻²), the simplified expression is 1.67 x 10⁻⁴

(2) \(\frac{2 \times 10^{-6} }{8.38 \times 10^{-2}}\) , the simplified expression is 2.39 x 10⁻⁵.

(3) \(\frac{7.72 \times 10^{2} }{4.39 \times 10^{3}}\), the simplified expression is 0.176.

(4) \(\frac{4 \times 10^{3} }{2 \times 10^{4}}\),  the simplified expression is 0.2.

(5) \(\frac{8.96 \times 10^{-5} }{4.6 \times 10^{-4}}\), the simplified expression is 0.195.

(7) (7.4 x 10⁻³)⁻², the simplified expression is 1.826 x 10⁴.

(8) (5 x 10²) (3.5 x 10³), the simplified expression is 1.75 x 10⁶.

(9) (3.2 x 10²)³, the simplified expression is 3.28 x 10⁷.

(10) (7 x 10⁻⁴) (6.29 x 10⁻⁴), the simplified expression is 4.403 x 10⁻⁷.

(11) (4.95 x 10² ) ( 7.29 x 10⁴), the simplified expression is 3.609 x 10⁷.

The simplification of the expressions is calculated by applying the following method.

(1) (4.17 x 10⁻³) (4 x 10⁻²)

The expression is simplified as follows;

= (4.17 x 4 ) x 10⁻³ ⁻ ²

= 16.7 x 10⁻⁵

= 1.67 x 10⁻⁴

(2) \(\frac{2 \times 10^{-6} }{8.38 \times 10^{-2}}\)

The expression is simplified as follows;

= (2/8.38) x 10⁻⁶ ⁺ ²

= 0.239 x 10⁻⁴

= 2.39 x 10⁻⁵

(3) \(\frac{7.72 \times 10^{2} }{4.39 \times 10^{3}}\)

The expression is simplified as follows;

= 0.176

(4) \(\frac{4 \times 10^{3} }{2 \times 10^{4}}\)

The expression is simplified as follows;

= (4/2) x 10⁻¹

= 2 x 10⁻¹

= 0.2

(5) \(\frac{8.96 \times 10^{-5} }{4.6 \times 10^{-4}}\)

The expression is simplified as follows;

= 0.195

(7) (7.4 x 10⁻³)⁻²

The expression is simplified as follows;

= (1000/7.4)²

= 1.826 x 10⁴

(8) (5 x 10²) (3.5 x 10³)

The expression is simplified as follows;

= (5 x 3.5) x 10²⁺³

= 17.5 x 10⁵

= 1.75 x 10⁶

(9) (3.2 x 10²)³

The expression is simplified as follows;

= 3.28 x 10⁷

(10) (7 x 10⁻⁴) (6.29 x 10⁻⁴)

The expression is simplified as follows;

= (7 x 6.29) x 10⁻⁴⁻⁴

= 44.03 x 10⁻⁸

= 4.403 x 10⁻⁷

(11) (4.95 x 10² ) ( 7.29 x 10⁴)

The expression is simplified as follows;

= ( 4.95 x 7.29) x 10²⁺⁴

= 36.09 x 10⁶

= 3.609 x 10⁷

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Answer: all points are a solution except for (4, 2) (and (2, 0) i think)

Step-by-step explanation:

Greetings from Brasil...

Note the graph of the function eˣ (or e⁻ˣ). We conclude that for any value of X, the result will be between 0 and +∞.\

So there is no value for X that the result of m.eˣ (or m.e⁻ˣ) is negative.

So you can answer:

For the equation of the statement of the question, with any value of X, we will always obtain a number greater than zero

(OBS: we'll never get zero. We can get very close, but never zero)

Answer:

1 2/21 liters

Step-by-step explanation:

Damon drank 2/3 liter of water Monday before going jogging. He drank 3/7 liter of water after his jog. How much water did Damon drink altogether?

Volume of water Damon drank before jogging = 2/3 liters

Volume of water Damon drank after jogging = 3/7 liters

Total volume of water Damon drank altogether = 2/3 liters + 3/7 liters

= 2/3 + 3/7

= 14+9/21

= 23/21

= 1 2/21

Total volume of water Damon drank altogether = 1 2/21 liters