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MissTica
3 years ago
5

The numbers $1,$ $2,$ $\dots,$ $10$ are to be entered into the 10 boxes shown below, so that each number is used exactly once: \

[P = (\square + \square + \square + \square + \square)(\square + \square + \square + \square + \square).\]What is the maximum value of $P$? What is the minimum value of $P$?
Mathematics
1 answer:
Agata [3.3K]3 years ago
8 0

Answer:

Maximum =  756

Minimum =  600

Step-by-step explanation:

A square is a shape that has the large areas of a defined perimeter out of available rectangles. It implies they want the two parentheses to be as similar in value. as a result, to establish the maximum value of P.

And to establish the minimum value, to have the greatest difference for them. 1 + 2 + 3 ... +10=55, which wasn't even but which can be split as similarly as possible into 27 and 28 which have a product of 756. In this question it can be done in a variety of ways, one of which is:

(1 + 3 + 5 + 8 + 10) ×  (2 + 4 + 6 + 7 + 9) = 756

At the very least, the biggest difference can be created if one term is made of the smallest numbers, while the other full of the highest, or:

(1 + 2 + 3 + 4 + 5) × (6 + 7 + 8 + 9 + 10)=600

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The graph is of y = f(x) is shown below. What are all of the real solutions of f(x) = 0?
Reika [66]

The real solutions of f(x) = 0 is; x = -8, 0 and 4

<h3>How to find the roots of a polynomial graph?</h3>

When talking about real solutions of a polynomial, we are simply referring to the values of x that make the polynomial f(x) = 0.

Now, in a polynomial graph as attached, the real solutions are the roots and they are the values of x where the curve crosses the x-axis.

From the given graph, the real solutions are at x = -8, 0 and 4

Thus, we conclude that the real solutions of f(x) = 0 is; x = -8, 0 and 4

Read more about Polynomial roots graph at; brainly.com/question/14625910

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8 0
1 year ago
Factor this trinomial completely.
zmey [24]
First you want to write 7x as a sum or difference: 15x-8x
Now, the expression would look like this: 10x^2+15x-8x-12
Next, factor out the 5x and -4 from the expression: 5x(2x+3)-4(2x+3)
Now, factor out the 2x+3 from the expression and you have your answer:
(2x+3)(5x-4)
4 0
3 years ago
As a result of a transfer from one school to another, a boy has to walk one
Softa [21]

Answer:

Let the distance of school and house is x k m

Then time taken at speed 2.5 km\hr=

2.5

x

hr

And time taken at speed 4 km\hr=

4

x

hr

∴

2.5

x

−

4

x

=

60

12

⇒

10

4x−2.5x

=

5

1

⇒x=3 km

Then the distance of school and house is 3 k m

may this help you

6 0
3 years ago
Will all slices created by a slicing plane that passes through a sphere be the same size
Snowcat [4.5K]

Answer:

The suggestion proposed considering special cases, so that’s what we’ll do.

One special case we could consider is when x=0. If h=r, then we have a hemisphere. You may have learnt that the surface area of a sphere is 4πr2, so the answer in this case is 2πr2. Likewise, we can consider the most extreme cases: when h=2r, we get an area of 4πr2 (the entire sphere), and when h=0, we get zero area.

So if we do manage to get a general formula, we will be able to check it in these special cases.

Another possible idea when x=0 is to consider what happens when h is very small. In this case, the surface area looks a lot like a circle, but the radius of the circle does not seem particularly easy to work out, so maybe we’ll leave this one for a moment. (There are things we can do to approximate the radius using more advanced techniques, but they are currently beyond us.)

Another thing we could consider is the situation where h is very small. Then the part of the sphere between the planes looks very much like the frustum of a cone, and we know how to find the (surface) area of such a shape – see Cones.

If we recall our answer from that problem, we find the formulae for the surface area

π(R+r)s=π(R+r)hcosθ=π(R2−r2)sinθ.

Here, R is the radius of the base of the frustum, r is the radius of the top, h is the perpendicular height, s is the slant length and θ is the angle the slant makes with the vertical.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Someone please help me! Studying for finals and don’t understand how to complete problems like this! Thank you!
Drupady [299]

Answer:

(d). \frac{152}{377}

Step-by-step explanation:

sin² β + cos² β = 1

cos (α + β) = cos α cos β - sin α sin β

cos α = √(1 - \frac{400}{841} ) = 21 / 29

cos β = 12 / 13

sin β = √(1 - \frac{144}{169} ) = 5 / 13

sin α = 20 / 29

cos (α + β) = \frac{21}{29} × \frac{12}{13} - \frac{20}{29} × \frac{5}{13} = \frac{152}{377}

6 0
3 years ago
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