All categories

2 years ago

The curve produced by the water coming from a fountain is sketched on the graph.

Mathematics

2 answers:

Bas_tet [7]2 years ago

3 0

Answer: B. -(x-2)^2 + 3

The vertex of the parabola is (2,3) so we can plug in those values into the equation for vertex form. And the parabola is facing down, so we know the function is multiplied by -1.

Therefore the equation is -(x-2)^2 + 3

Look at the attached image to see what vertex form is

Inessa05 [86]2 years ago

3 0

Answer:B

Step-by-step explanation:

You might be interested in

The harmonic motion of a particle is given by f(t) = 2 cos(3t) + 3 sin(2t), 0 ≤ t ≤ 8. (a) When is the position function decreas

iren [92.7K]

For the last part, you have to find where $f'(t)$ attains its maximum over $0\le t\le8$ . We have

$f'(t)=-6\sin3t+6\cos2t$

so that

$f''(t)=-18\cos3t-12\sin2t$

with critical points at $t$ such that

$-18\cos3t-12\sin2t=0$

$3\cos3t+2\sin2t=0$

$3(\cos^3t-3\cos t\sin^2t)+4\sin t\cos t=0$

$\cos t(3\cos^2t-9\sin^2t+4\sin t)=0$

$\cos t(12\sin^2t-4\sin t-3)=0$

So either

$\cos t=0\implies t=\dfrac{(2n+1)\pi}2$

$12\sin^2t-4\sin t-3=0\implies\sin t=\dfrac{1\pm\sqrt{10}}6\implies t=\sin^{-1}\dfrac{1\pm\sqrt{10}}6+2n\pi$

where $n$ is any integer. We get 8 solutions over the given interval with $n=0,1,2$ from the first set of solutions, $n=0,1$ from the set of solutions where $\sin t=\dfrac{1+\sqrt{10}}6$ , and $n=1$ from the set of solutions where $\sin t=\dfrac{1-\sqrt{10}}6$ . They are approximately

$\dfrac\pi2\approx2$

$\dfrac{3\pi}2\approx5$

$\dfrac{5\pi}2\approx8$

$\sin^{-1}\dfrac{1+\sqrt{10}}6\approx1$

$2\pi+\sin^{-1}\dfrac{1+\sqrt{10}}6\approx7$

$2\pi+\sin^{-1}\dfrac{1-\sqrt{10}}6\approx6$

4 0

2 years ago

Marlene rides her bike at a rate of 16 miles per hour. The time in hours that she rides is represented by the variable t, and th

White raven [17]

Let

t--------> the time in hours

d-------> the distance in miles

we know that

$d=16t$

this is a linear equation that represent the scenario

in this equation the independent variable is the time t and the dependent variable is the distance d

The distance's equation in function notation is equal to

$f(t)=16t$

Using a graph tool

see the attached figure

The domain of the function is the interval----------> [0,∞)

$t\geq0$

The range of the function is the interval-------> [0,∞)

$f(t)\geq0$

Statements

a) The independent variable, the input, is the variable d, representing distance

The statement is false

Because the independent variable is the variable t

b) The distance traveled depends on the amount of time Marlene rides her bike

The statement is true

Because the distance's equation in function notation is equal to

$f(t)=16t$

c) The initial value of the scenario is 16 miles per hour

The statement is false

Because $16$ represent the rate or the slope of the linear equation

d) The equation t = d + 16 represents the scenario

The statement is false

Because, the scenario is represented by the function $f(t)=16t$

e) The function f(t) = 16t represents the scenario

The statement is true

8 0

2 years ago

Read 2 more answers

A rock is thrown in the air from the edge of a seaside cliff. Its height in feet is represented by f(x) = –16(x^2 – 8x – 9), whe

algol13

Since x is the number of seconds it took the rock to hit the water, x is the value that we are looking for. When the rock hits the water, it's height is 0, therefore, f(x) = 0. So, we can set the expression on the right equal to 0, and solve for 0. Let's do just that:
$0 = -16(x^2-8x-9)$

We can divide by -16, nothing will happen because 0 divided by anything is 0:
$0 = x^2-8x-9$

To factor any trinomial in standard form (given below), we must find two numbers that add to "b" and multiply to "c":
$0 = ax^2 + bx + c$

So, for this specific question, let's find two numbers that add to -8 and multiply to 9. These are clearly 9 and -1. We can write it in this way now:
$0 = (x-9)(x+1)$

Both answers would be valid, but there can't be negative time, so your answer is "It takes 9 seconds for the rock to reach the water."

4 0

2 years ago

Read 2 more answers

a triangle has sides of 4 and 6 units. The measurement of the longest side is missing.Ted says that one possibility for the unkn

tester [92]

This is called the pythagorean theorem: a^2 + b^2 = c^2.
Basically, the sum of one side squared + the side of another side squared = the length of the longest side (or hypotenuse).

We have to do the following math:
4 * 4 = 16
6 * 6 = 36
16 + 36 = 52.

We know that 52 = c^2
So we have to $\sqrt{c}$ to get 7.21

You do not agree with Ted.

7 0

2 years ago

Prove that a line that divides two sides of a triangle proportionally is parallel to the third side. Be sure to create and name

sattari [20]

Answer:

Given: A triangle ABC and a line DE parallel to BC.

To prove: A line parallel to one side of a triangle divides the other two sides proportionally.

Proof: Consider ΔABC and DE be the line parallel to Bc, then from ΔABC and ΔADE, we have

∠A=∠A (Common)

∠ADE=∠ABC (Corresponding angles)

Thus, by AA similarity, ΔABC is similar to ΔADE, therefore

AB/AD= AC/AE

⇒AD+DB/AD = AE+EC/AE

⇒1+DB/AD = 1+ EC/AE

⇒DB/AD = EC/AE

Therefore, a line parallel to one side of a triangle divides the other two sides proportionally.

⇒Therefore Proved

Hope this helps!!!

3 0

2 years ago