Ask question

Ask question

All categories

3 years ago

6

In a class 0f 25, 10boys play cricket, 5 boys play football, 4boys play hockey. 3boys play both football and cricket and 2 boys

play both football and hockey. how many boys are there in class who play any game?

1 answer:

V125BC [204]3 years ago

4 0

1

as you can possibly realize i am just trying to get to the charachter count

You might be interested in

A ball is thrown in the air from a platform that is 96 feet above ground level with an initial vertical velocity of 32 feet per

pishuonlain [190]

Answer:

y = -16 (x - 1)^2 + 112

The object lands on the ground in approximately 3.6s

Explanation:

The equation given is that of a parabola.

Now the maximum (local) point of a parabola is the vertex. Therefore, if we want to rewrite our function in the form that would be used to find the maximum height, then that form must be the vertex form of a parabola.

The vertex form of a parabola is

$y=a(t-h)^2+k$

where (h, k) is the vertex.

The only question is, what is the vertex for our function h(t)?

Remember that if we have an equation of the form

$y=ax^2+bx+c$

then the x-coordinate of the vertex is

$h=-\frac{b}{2a}$

Now in our case b = 32 and a = -16; therefore,

$h=\frac{-32}{2(16)}=1$

We've found the value of the x-coordinate of the vertex. What about the y-coordinate? To get the y-coordinate, we put x = 1 into h(t) and get

$k=-16(1)+32(1)+96=112$

Hence, the y-coordindate is k = 112.

Therefore, the vertex of the parabola is (1, 112).

With the coordinates of the vertex in hand, we now write the equation of the parabola in vertex form.

$h(t)=a(t-1)^2+112$

The only problem is that we don't know what the value of a is. How do we find a?

Note that the point (0, 96) lies on the parabola. In other words,

$h(0)=-16(0)^2+32(0)+96=96$

Therefore, the vertex form of the parabola must also contain the point (0, 96).

Putting in t = 0, h = 96 into the vertex form gives

$96=a(0-1)^2+112$ $96=a+112$

subtracting 112 from both sides gives

$a=-16$

With the value of a in hand, we can finally write the equation of the parabola on vertex form.

$\boxed{h\mleft(t\mright)=-16\left(t-1\right)^2+112.}$

Now when does the object hit the ground? In other words, for what value of t is h(t) = 0? To find out we just have to solve the following for t.

$h(t)=0.$

We could either use h(t) = -16t^2 + 32t + 96 or the h(t) = -16(t - 1)^2 + 112 for the above equation. But it turns out, the vertex form is more convenient.

Thus we solve,

$-16\left(t-1\right)^2+112=0$

Now subtracting 112 from both sides gives

$-16(t-1)^2=-112$

Dividing both sides by -16 gives

$(t-1)^2=\frac{-112}{-16}$ $(t-1)^2=7$

taking the square root of both sides gives

$t-1=\pm\sqrt{7}$

adding 1 to both sides gives

$t=\pm\sqrt{7}+1$

Hence, the two solutions we get are

$t=\sqrt{7}+1=3.6$ $t=-\sqrt{7}+1=-1.6$

Now since time cannot take a negative value, we discard the second solution and say that t = 3.6 is our valid solution.

Therefore, it takes about 3.6 seconds for the object to hit the ground.

3 0

1 year ago

Second street bank charges an overdraft fee of $35.00 for insuficient funds transactiond. Malcom's check register showed up bala

Leya [2.2K]

He will have enough money in his bank to avoid an insufficient fund charge because when you add 250+36.21+94.30 it equals 380.51. He had 386.49 in his account before he withdrawal that money, so he still had money in his account when he got money out.

4 0

3 years ago

Christopher Columbus set sail from Spain in 1492. In what year did the Civil War end?

xxTIMURxx [149]

Answer:

May 9, 1865

Step-by-step explanation:

7 0

3 years ago

Can a pentagon be a cross section of a triangular prism?

nikitadnepr [17]

Answer:

<em>No</em>, a pentagon can NOT be a cross-section of a triangular prism.

Step-by-step explanation:

Prisms have a uniform cross-section and are named after their cross-section. Hence, the cross section of a triangular prism is a triangle. The only prism with a pentagon cross-section is a pentagonal prism.

3 0

3 years ago

Х<br> If<br> 5.3<br> =<br> 12, what is the value of x?<br> 8<br> 0 ООО<br> 18<br> o 24

gladu [14]

Answer:18

Step-by-step explanation:

8 0

3 years ago