Find the lowest common multiple of 28 and 210

Based on the information given, it should be noted that the slant height will be 2✓3 meters.

Therefore, the calculation of the slant height goes thus:

Tan 60° = x/2

x = 2 × tan 60°

x = 2 × ✓3

x = 2✓3

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Final answer:

In calculus, summation involves adding discrete values, while integration is akin to adding an infinite number of infinitesimally small products to find areas, volumes, etc. Integral calculus extends these concepts to continuous functions and is used, for example, to find position from acceleration by integrating twice.

Explanation:

The transition from summation to integral in calculus is an important concept that bridges the discrete world with the continuous. When we summate, we're adding together values to find a total amount. In a similar vein, an integral can be thought of as a continuous sum, where we're adding up infinitely small products to calculate an area, volume, or other quantities.

When performing an integral, the dimensions of what we're integrating must be consistent. For example, if we're integrating velocity (v) with respect to time (t), we obtain a dimension that is the product of the two, such as distance. This principle is rooted in the requirement of dimensional consistency, analogously understood in the phrase "You can't add apples and oranges."

Understanding the relationship between discrete sums and continuous integrals is crucial for applications in various fields, such as physics where integrals can represent cumulative effects over time or space. For example, integrating an acceleration function gives us velocity, and further integration yields position. This process allows us to work backward from acceleration to position, utilizing the power of integral calculus.

Answer:

T series

Step-by-step explanation:

Answer:

Option B) 3

Step-by-step explanation:

we have the number

4162 0012 3456 789a

Find the value of a (check number)

step 1

Multiply every even-position digit (when counted from the right) in the number by two. If the result is a two digit number, then add these digits together to make a single digit

4162 0012 3456 789a

9(2)+7(2)+5(2)+3(2)+1(2)+0(2)+6(2)+4(2)

(18)+(14)+(10)+(6)+(2)+(0)+(12)+(8)

Remember that If the result is a two digit number, then add these digits together to make a single digit

so

(1+8)+(1+4)+(1+0)+(6)+(2)+(0)+(1+2)+(8)

(9)+(5)+(1)+(6)+(2)+(0)+(3)+(8)=34

step 2

add every odd-position digit

4162 00123456 789a

so

8+6+4+2+0+2+1=23

step 3

Adds  the result in step 1 and the result in step 2

34+23=57

The check-digit is what number needs to be added to this total to make the next multiple of 10

In our case, we’d need to add 3 to make 60

therefore

The check number is 3

The easiest method to use to solve this equation is substitution. This is because we already have our second equation set equal to the variable y, so we can substitute the x values in for the variable y in the first equation, as follows:

y = x + 2

y = -3x

-3x = x + 2

To simplify, we should subtract x from both sides of the equation so that we can have all of the x terms isolated on the left side of the equation.

-3x - x = x - x + 2

-4x = 2

Finally, we must divide both sides of the equation by -4 to get the variable x alone.

x = -2/4

Because both the numerator and denominator of this fraction are divisible by 2, we can use this knowledge to simplify the fraction by dividing by the GCF of 2.

x = -1/2

Now that we know the value of x, we can substitute this value into either of our original equations to find out the value of y.

y = -3x

y = -3(-1/2)

y = 3/2

Therefore, your answer is x = -1/2 and y = 3/2, or written as an ordered pair (-1/2, 3/2).

Hope this helps!

The correct cash price is d) $27,228.33.

To determine the cash price of the car, we need to calculate the present value of all payments made by Esther, including her down payment.

Calculate the total number of monthly payments:
Total number of payments: 5 * 12 = 60

Determine the monthly interest rate:
Monthly interest rate: 0.071 / 12 = 0.0059167 (approximately)

Calculate the present value of the monthly payments using the formula for the present value of an annuity:

P = PMT × [tex]\frac{[1 - (1 + r)^{-n]} }{ r}[/tex]

P = 467 × [tex]\frac{ [1 - (1 + 0.0059167)^{-60}]}{ 0.0059167}[/tex] = $23,528.33

Add the down payment to the present value of the monthly payments to get the total cash price of the car:

Total cash price = $23,528.33 + $3,700 = $27,228.33

Therefore, the correct answer is (d) $27,228.33.

The complete question is

Esther pays $467 per month for 5 years for a car. she made a down payment of $3,700. if the loan costs 7.1% per year compounded monthly, what was the cash price of the car?

a) $23,528.33

b) $19,828.33

c) $29,820.57

d) $27,228.33

e) $37,220.57

Answer:

Option A

Step-by-step explanation:

From the graph attached, we will write the transformation as followed.

a. Trapezoid k is dilated by a scale factor of [tex]\frac{3}{2}[/tex]

   [ Since scale factor = [tex]\frac{\text{Largest side of k'}}{\text{Largest side of k}}[/tex]

                                   =  [tex]\frac{12units}{8units}[/tex]

                                   = [tex]\frac{3}{2}[/tex] ]

2. scaled trapezoid then rotated by 180°.

3. Then rotated trapezoid is shifted 1 unit down.

  By these transformations Bella's sequence was correct.

Therefore, Option A is the answer.

Answer:

43 degrees

Step-by-step explanation:

You can see that the triangle is congruent, so x is equal to 43. dont forget to include degrees!

Answer:

109.14

Step-by-step explanation:

to Start off do 60 x .70, then add the answer to 60, then multiply by .07 then add that to 102, for the answer of 109.14

Let the number of rabbits in the pet store is x

And the number of hamsters in the pet store is y.

Now, we have been given that pet store has 26 rabbits and hamsters. Thus, we have the linear equation

[tex]x+y=26...........(1)[/tex]

Now, number of rabbits is 2 more than double the number of hamsters. Hence, we have

[tex]x=2+2y[/tex]

Substituting this value of x in equation 1, we get

[tex]2+2y+y=26\\ 3y=24\\ y=8[/tex]

Thus, there are 8 hamsters in the pet store.

Answer:12   2/4

Step-by-step explanation:

First of all that eqation is improper. So lets make that proper. To do that you just count by five till you get close to the number. 5,10,15,20 im  close so lets stay there. So then it would be 4 1/5. Then you have to multiple that by 12.

And your awnser would be 50/4

then you need to make it propper.

12  2/4

To sketch the solution curves passing through (0, 2) and (1, 0), we can use the slope field provided. The tangent line to y = f(x) at x = 1 can be found by taking the derivative of f(x) and substituting x = 1. We can find the particular solution to the differential equation by integrating it with the given initial condition f(1) = 0.

To sketch the solution curves, we can use the slope field provided. For the point (0, 2), the slope is 1/3(0)(2-2)^2 = 0. Thus, at (0, 2) the solution curve is horizontal. For the point (1, 0), the slope is 1/3(1)(0-2)^2 = 8/3. Thus, at (1, 0) the solution curve is directed upwards with a slope of 8/3.

Since f(1) = 0, we already know that the point (1, 0) lies on the graph of y = f(x). The equation of the tangent line to y = f(x) at x = 1 can be found by finding the derivative of f(x) and substituting x = 1. In this case, the derivative is dy/dx = 1/3x(y-2)^2, so at x = 1, we have dy/dx = 1/3(1)(0-2)^2 = -8/3. Therefore, the equation of the tangent line is y - 0 = (-8/3)(x - 1), which simplifies to y = -8/3(x-1). To approximate f(0.7), we can substitute x = 0.7 into the equation of the tangent line to get y = -8/3(0.7 - 1) = -8/3(0.3) = -8/10 = -0.8.

To find the particular solution, we can integrate the differential equation with the given initial condition. Starting with dy/dx = 1/3x(y-2)^2, we can rewrite it as (y-2)^(-2)dy = 1/3xdx. Integrating both sides will give us the equation of the particular solution.

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Answer:

b. X and Z

Step-by-step explanation:

Since, the effective rate is,

[tex]r=(1+\frac{i}{n})^i-1[/tex]

Where, i is the nominal rate,

n is the number of compounding periods,

For loan X,

i = 7.815 % = 0.07815,

n = 2, ( 1 year = 2 semiannual )

Thus, the effective rate would be,

[tex]r=(1+\frac{0.07815}{2})^2-1[/tex]

[tex]=0.079676855625[/tex]

[tex]=7.9676855625\%\approx 7.968\%[/tex]

Since, 7.968 % < 8.000 %,

⇒ Loan X meets Mike's criteria,

For loan Y,

i = 7.724 % = 0.07724,

n = 12 ( 1 year = 12 months ),

Thus, the effective rate would be,

[tex]r = ( 1+\frac{0.07724}{12})^{12}-1[/tex]

[tex]=0.0800339518197[/tex]

[tex]=8.00339518197\% \approx 8.003\%[/tex]

Since, 8.003 % > 8.000 %,

⇒ Loan Y does not meet his criteria,

For loan Z,

i = 7.698 % = 0.07698,

n = 52 ( 1 year = 52 weeks ),

Thus, the effective rate would be,

[tex]r = (1+\frac{0.07698}{52})^{52}-1[/tex]

[tex]=0.0799589986135[/tex]

[tex]=7.99589986135\%[/tex]

[tex]\approx 7.996\%[/tex]

Since, 7.996 % < 8.000 %,

⇒ Loan Z meets his criteria.

Therefore, Option 'b' is correct.

To find the number of rows needed for 528 students to each have a seat in a school auditorium with 33 seats in each row, divide the total number of students by the number of seats in each row. The answer is 16 rows.

To find the number of rows needed for 528 students to each have a seat in a school auditorium with 33 seats in each row, we need to divide the total number of students by the number of seats in each row.

So, the number of rows needed would be:

Rows needed = Total number of students ÷ Number of seats in each row

Substituting the given values:

Rows needed = 528 ÷ 33 = 16

Therefore, 16 rows are needed for 528 students to each have a seat in the auditorium.

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Answer:

3.14 2^2

Step-by-step explanation:

The expressions shows the area, in square inches, of the circle will be 3.14 × 2² square units. Then the correct option is C.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The image below is a triangle drawn inside a circle with center O:

A triangle is shown inscribed inside a circle.

The leg of the triangle labeled 4 inches passes through the center of the circle, O.

The other two legs are labeled as 2 inches and 3 inches.

The expressions shows the area, in square inches, of the circle will be

Area of circle = (π/4) d²

The diameter of the circle is passing through center. Then the length of the diameter is 4.

Then the area of circle will be,

Area = (π/4) 4²

A = 3.14 × 4

A = 3.14 × 2² square units

The expressions shows the area, in square inches, of the circle will be 3.14 × 2² square units.

Then the correct option is C.

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Answer:

6.74

Step-by-step explanation:

add all numbers and divide how many numbers there are.