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iVinArrow [24]
3 years ago
10

If [x] denotes the least integer greater than or equal to x and [x/2] = 0, which of the following could be the value of x?A. -2B

. -3/2C. 1/2D. 1E. 2
Mathematics
1 answer:
podryga [215]3 years ago
3 0

Answer:

B) -3/2

Step-by-step explanation:

If [x/2]=0 then x/2 is a number such that the least integer greater than or equal to x/2 is 0. We can rewrite this as the inequality x/2≤0. Then, the value of x in C, D and E is wrong because they are positive numbers, then x/2 would be a positive number which contradicts this inequality.

Now, 0 is the least integer that satisfies this inequality, therefore we cannot have that x/2≤-1 since -1 is an integer and -1<0. Then x/2>-1. This discards A as wrong, because for x=-2, x/2=-1, contrary to x/2>-1.

Thus B is the right answer. To verify, if x=-3/2, then x/2=-3/4 and we have that -1<-3/4≤0 as required.

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What will happen to the ratios as you increase the number of sides of the regular polygon?
earnstyle [38]

Answer: increase

Step-by-step explanation:

Number of sides of the polygon, The number of sides of a regular polygon and the measure of the exterior angle are inversely proportional. <em><u>As one quantity increases, the other decreases and vice versa.</u></em>

4 0
3 years ago
The following table shows the first segment of a five-year amortization schedule.
ELEN [110]

After one year of payments, the amount need to be paid to interest is $1100.42 if the first segment of a five-year amortization schedule is a 5-year amortization schedule option (a) is correct.

<h3>What is a loan amortization schedule?</h3>

It is defined as the systematic way of representation of loan payments according to the time in which the principal amount and interest mentioned in a list manner.

We have a table given that showing a first segment of a five-year amortization schedule that has a 5-year amortization schedule and the amount of interest paid for months 1 through 12.

As the loan amount is not mentioned in the question, we are assuming the loan amount is $1184.6

Therefore, loan amount = $1184.6

The outstanding amount at the end of one year, which is 12 months, is shown in the table as $84.18

After one year of payments, the amount need to be paid to interest:

= Loan amount - Outstanding amount after 12 months

= 1184.6 - 84.18

= $1100.425

Thus, after one year of payments, the amount need to be paid to interest is $1100.42 if the first segment of a five-year amortization schedule is a 5-year amortization schedule option (a) is correct.

Learn more about the amortization schedule here:

brainly.com/question/15357884

4 0
2 years ago
Bank account balance:$357 check written for:$486 what was the new balance?
Bezzdna [24]
All u have to do is substract wich equals -129
5 0
3 years ago
Read 2 more answers
Find the solution of the differential equation dy/dt = ky, k a constant, that satisfies the given conditions. y(0) = 50, y(5) =
irga5000 [103]

Answer:  The required solution is y=50e^{0.1386t}.

Step-by-step explanation:

We are given to solve the following differential equation :

\dfrac{dy}{dt}=ky~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.

From equation (i), we have

\dfrac{dy}{y}=kdt.

Integrating both sides, we get

\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}]

Also, the conditions are

y(0)=50\\\\\Rightarrow ae^0=50\\\\\Rightarrow a=50

and

y(5)=100\\\\\Rightarrow 50e^{5k}=100\\\\\Rightarrow e^{5k}=2\\\\\Rightarrow 5k=\log_e2\\\\\Rightarrow 5k=0.6931\\\\\Rightarrow k=0.1386.

Thus, the required solution is y=50e^{0.1386t}.

8 0
3 years ago
Read 2 more answers
Solve the triangle.
vova2212 [387]

9514 1404 393

Answer:

  b = 71 m

  A = 83°

  C = 29°

Step-by-step explanation:

Many calculators can solve triangles. Apps are available for phone and tablet, or on the internet, like the one used here. In general, it takes less time to use one of these than to type your question into Brainly.

Given two sides and the angle between them, the Law of Cosines is the appropriate relation to use for finding the third side.

  b = √(a² +c² -2ac·cos(B))

  b = √(76² +37² -2·76·37·cos(67.75°)) ≈ √5015.48

  b ≈ 70.82005 ≈ 71 . . . meters

__

One a side and its opposite angle are known, the remaining angles are found using the Law of Sines.

  sin(A)/a = sin(B)/b

  A = arcsin(a·sin(B)/b) = arcsin(76·sin(67.75°)/70.82005) ≈ 83.33°

  A ≈ 83°

  C = arcsin(37·sin(67.75°)/70.82005) ≈ 28.92°

  C ≈ 29°

Or, you can find the remaining angle from 180° -68° -83°  = 29°.

3 0
3 years ago
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