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2 years ago

3 plus the quotient of a number and 2 is 7. What is the number?

Mathematics

2 answers:

Sidana [21]2 years ago

8 0

3 + x/2 = 7
x = (7-3)*2 = 8 = the number

TEA [102]2 years ago

3 0

Answer:

The required number is 8.

Step-by-step explanation:

Let the required number be x.

Now, it is given that, 3 plus quotient of a number and 2 is 7, then

$3 + \frac{x}{2}=7$

Subtracting '3' from both sides of the above equation, we get

$3 + \frac{x}{2}-3=7-3$

$\implies\frac{x}{2} =4$

Now, multiplying both sides by '2' in the above obtained equation, we get

$\frac{x}{2}\times2 = 4\times2$

$\implies x = 8$

So, the required number is 8.

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Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of f :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of g :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where n is any integer. We get 4 critical points in the interval [0, 2π) at

$t=0\implies f(10,0)=155$

$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So f has a minimum of -7 and a maximum of 299.

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3 years ago

Mark’s brother is five years older than Mark. Their combined ages add up to 23. How old is Mark? Write an equation to help you s

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2 years ago

How to Simplify (x-2)(3x2 + 3x + 2) to a polynomial in standard form:

swat32

Answer: 3x^3 - 3x^2 - 4x - 4

Explanation:

(x - 2)(3x^2 + 3x + 2)

= x(3x^2 + 3x + 2) - 2(3x^2 + 3x + 2)

= 3x^3 + 3x^2 + 2x - 6x^2 - 6x - 4

= 3x^3 - 3x^2 - 4x - 4

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2 years ago

Presley is organizing the school book sale. Each stall will have 40 books on the shelf and 2 boxes of books with b books inside.

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40s+2bs+200=number of books needed

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b=12
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7 0

3 years ago

Read 2 more answers

The first 4 terms of a geometric sequence are 2, 6, 18, 54. Part A: Find the common ratio. Remember the common ratio is the numb

ra1l [238]

Answer:

Common ratio is 3

The three terms are 162, 486, 1458

Step-by-step explanation:

Given: The first 4 terms of a sequence are $2,6,18,54$

To find:

A. the common ratio

B. the next 3 values in the geometric sequence

Solution:

Geometric sequence is a sequence in which each of the terms is obtained by multiplying the previous term by a fixed number.

$\frac{6}{2}=3\\\\\frac{18}{6}=3\\\\\frac{54}{18}=3$

So, the common ratio is $3$

The next three values are as follows:

$54(3)=162\\162(3)=486\\486(3)=1458$

8 0

2 years ago

3 plus the quotient of a number and 2 is 7. What is the number?​

3 plus the quotient of a number and 2 is 7. What is the number?