What is the value of the digit 4 in the number 524897123

The population of mosquitoes in a certain area as a function of inches of rainfall is modeled in the table. The function is quad

torisob [31]

Answer:

The x-intercept represents that after 10 in. of rain there are mosquitoes.

Or

The x-intercept represents that after 0 in. of rain there are no mosquitoes.

Step-by-step explanation:

We are given a table that represents the population of mosquitoes in a certain area as a function of inches of rainfall :

RAINFALL(in.) POPULATION (millions.)

0 0

1 9

3 21

4 24

5 25

6 24

We will first find the function P(t) which denotes the number of mosquitoes after t inches of rainfall.

As the function is quadratic.

Hence , let:

$P(t)=at^2+bt+c$

At t=0 we have, P(t)=0

$c=0$

at t=1 we have: P(t)=9

i.e.

$a+b=9-----(1)$

Also at t=2 we have: P(t)=21

i.e.

$9a+3b=21-------(2)$

On solving equation (1) and (2) we get:

a= -1 and b=10

Hence,

$P(t)=-t^2+10t$

We know that the x-intercept of a graph is a point where the y-value is zero.

i.e. it is the inches of rainfall when the population of mosquitoes is zero i.e. there are no mosquitoes.

i.e. we have to find t such that:

P(t)=0

i.e.

$-t^2+10t=0\\\\i.e.\\\\t(10-t)=0\\\\i.e.\\\\ t=0\ or\ t=10$

Hence, we have got two x-intercept.

one at t=0 and the other at t=10.

The x-intercept represents that after 10 in. of rain there are no mosquitoes.

Or

The x-intercept represents that after 0 in. of rain there are no mosquitoes.

5 0

4 years ago

Read 2 more answers

Factorise: 4ay-2y can’t seem to do this

qaws [65]

In order to factor, we must pull out factors common to each term. In this case, each term has factors of 2 and y:

4ay = 2 * 2 * a * y
2y = 2 * y

So, we'll pull out the 2y:

$2y(2a-1)$

To check, distribute the 2y back through the terms in parentheses to ensure you end up with the original expression 4ay - 2y.

4 0

4 years ago

Given the figure below, find the measure of

Scilla [17]

Answer:

x = 23.125°

Step-by-step explanation:

∠ACF = ∠GCB (vertically opposite angles)

3x + 5x - 5 = 180° (angles on a straight line are supplementary)

8x = 185°

x = 23.125°

This is a question on angles. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)

6 0

3 years ago

Problem: Report Error Two parallel chords in a circle have lengths 10 and 14, and the distance between them is 6. The chord para

charle [14.2K]

The value of $\sqrt{a} = 2\sqrt{46}$ and a = 184

We let O be the centre, A₁ A A₂ , B₁ B B₂ represent the chords with length 10, 14 respectively.

Connecting the endpoints of the chords with the centre, we have several right triangles. However, we do not know whether the two chords are on the same side or different sides of the centre of the circle.

By the Pythagorean Theorem on Δ OBB₁,

we get x^2 + 7^2 = r^2

⇒ x = $\sqrt{r^{2} - 49 }$ , where x is the length of the other leg. Now the length of the leg of Δ OAA₁ is either 6 + x or 6 - x depending whether or not A₁A₂, B₁B₂ are on the same side of the center of the circle:

$(6$ ± $\sqrt{r^{2} - 49 }$ ) + 5² = r²

12 ± $12 \sqrt{r^{2} - 49}$ = 0

Only the negative works here (thus the two chords are on opposite sides of the center), and solving we get x=1, r = $5\sqrt{2}$ . The leg formed in the right triangle with the third chord is 3 - x = 2, and by the Pythagorean Theorem again,