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gulaghasi [49]
4 years ago
14

Find all the natural numbers, which when divided by 7, leave the same number for the quotient and the remainder.

Mathematics
1 answer:
Anna11 [10]4 years ago
5 0

Answer:

8,16,24,32,48

Step-by-step explanation:

When dividing a number by 7, only 7 different remainders are possible.

The remainders when dividing by 7 can not exceed 6, so the numbers in which we are interested can be represented as 7k+k or just 8k, where k=1, 2, ... , 6.

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The range of y = - 32x ^ 2 + 90x + 3
mariarad [96]

Given:

The given function is:

y=-32x^2+90x+3

To find:

The range of the given function.

Solution:

We have,

y=-32x^2+90x+3

It is a quadratic function because the highest power of the variable x is 2.

Here, the leading coefficient is -32 which is negative. So, the graph of the given function is a downward parabola.

If a quadratic function is f(x)=ax^2+bx+c, then the vertex of the quadratic function is:

Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)

In the given function, a=-32,b=90,c=3.

\dfrac{-b}{2a}=\dfrac{-90}{2(-32)}

\dfrac{-b}{2a}=\dfrac{-90}{-64}

\dfrac{-b}{2a}=\dfrac{45}{32}

The value of the given function at x=\dfrac{45}{32} is:

y=-32(\dfrac{45}{32})^2+90(\dfrac{45}{32})+3

y=\dfrac{2121}{32}

The vertex of the given downward parabola is \left(\dfrac{45}{32},\dfrac{2121}{32}\right). It means the maximum value of the function is y=\dfrac{2121}{32}. So,

Range=\left\{y|y\leq \dfrac{2121}{32}\right\}

Range=\left(-\infty, \dfrac{2121}{32}\right ]

Therefore, the range of the given function is \left (-\infty, \dfrac{2121}{32}\right ].

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Answer:

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Step-by-step explanation:

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Below is a list of numbers. Use them to answer question 3.
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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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What is the relationship between rate of change and slope?
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Answer:

The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run.

The slope formula is often shortened to the phrase “rise over run.”

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