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4 years ago

Two consecutive integers have a sum of 513. find the smaller of these two number

Mathematics

2 answers:

nexus9112 [7]4 years ago

5 0

513/2=256.5
which means 256 and 257 are the answers

Alona [7]4 years ago

4 0

Answer:

The smaller of these two number is 256.

Step-by-step explanation:

Suppose, the two consecutive integers are $n$ and $n+1$

Here, the smaller integer is $n$ and the larger integer is $n+1$

The sum of two integers is given as $513$ . So, the equation will be....

$n+(n+1)= 513\\ \\ n+n+1= 513\\ \\ 2n+1=513\\ \\ 2n= 513-1\\ \\ 2n= 512\\ \\ n= \frac{512}{2}=256$

So, the smaller integer is $256$ .

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3 years ago

Read 2 more answers

A plane flying horizontally at an altitude of 3 miles and a speed of 500 mi/h passes directly over a radar station. Find the rat

konstantin123 [22]

Answer:

The rate at which the distance from the plane to the station is increasing is 331 miles per hour.

Step-by-step explanation:

We can find the rate at which the distance from the plane to the station is increasing by imaging the formation of a right triangle with the following dimensions:

a: is one side of the triangle = altitude of the plane = 3 miles

b: is the other side of the triangle = the distance traveled by the plane when it is 4 miles away from the station and an altitude of 3 miles

h: is the hypotenuse of the triangle = distance between the plane and the station = 4 miles

First, we need to find b:

$a^{2} + b^{2} = h^{2}$ (1)

$b = \sqrt{h^{2} - a^{2}} = \sqrt{(4 mi)^{2} - (3 mi)^{2}} = \sqrt{7} miles$

Now, to find the rate we need to find the derivative of equation (1) with respect to time:

$\frac{d}{dt}(a^{2}) + \frac{d}{dt}(b^{2}) = \frac{d}{dt}(h^{2})$

$2a\frac{da}{dt} + 2b\frac{db}{dt} = 2h\frac{dh}{dt}$

Since "da/dt" is constant (the altitude of the plane does not change with time), we have:

$0 + 2b\frac{db}{dt} = 2h\frac{dh}{dt}$

And knowing that the plane is moving at a speed of 500 mi/h (db/dt):

$\sqrt{7} mi*500 mi/h = 4 mi*\frac{dh}{dt}$

$\frac{dh}{dt} = \frac{\sqrt{7} mi*500 mi/h}{4 mi} = 331 mi/h$

Therefore, the rate at which the distance from the plane to the station is increasing is 331 miles per hour.

I hope it helps you!

4 0

3 years ago

A rectangular rug is 1.8m long 0.7 wide, all measurement are given to 1 decimal place

Nikolay [14]

Answer:

Explanation:

A. The minimum possible length of the rug is 1.

B. The maximum area of the rug is 2m^2

3 0

3 years ago

Ella invested $2,700 in an account paying an interest rate of 5.4% compounded

Dmitry [639]

Answer:

The account will take 7 years to reach a value of $4,020

Step-by-step explanation:

Compound Interest

When it occurs interest in the next period is then earned on the principal sum plus previously accumulated interest.

The formula is:

$A=P\left(1+{\frac {r}{n}}\right)^{nt}$

Where:

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Ella invested P=$2,700 in an account with an interest rate of r=5.4% (0.054) compounded monthly. Since there are 12 months in a year, n=12.

It will be calculated when will the account have a value of A=$4,020. Substituting all the values in the formula:

$4,020=2,700\left(1+{\frac {0.054}{12}}\right)^{12t}$

Calculating:

$4,020=2,700\left(1.0045)^{12t}$

Dividing by 2,700:

$\frac{4,020}{2,700}=\left(1.0045)^{12t}$

To solve this equation for t, we need to apply logarithms:

$\log\frac{4,020}{2,700}=\log\left(1.0045)^{12t}$

Applying the logarithm power rule:

$\displaystyle \log\frac{4,020}{2,700}=12t\log 1.0045$

Dividing by 12log 1.0045:

$\displaystyle t=\frac{\log\frac{4,020}{2,700}}{12\log 1.0045}$

Calculating:

t= 7.39 years

Rounding to the nearest year, the account will take 7 years to reach a value of $4,020

3 0

3 years ago

Read 2 more answers

the family size bottle holds 12 fluid ounces of sunscreen the regular bottle holds 75% less how many fewer fluid ounces does the

MakcuM [25]

Answer:

9 fluid ounces

Step-by-step explanation:

12 multiplied by .75 = 9

7 0

3 years ago