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Tcecarenko [31]

3 years ago

9

Tim has a cylinder that is 6 inches tall with a radius of inches. If he calculates the volume of the cylinder, which unit should

he use?

1 answer:

Svet_ta [14]3 years ago

8 0

Cubic inches
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True or false To increase the size os an drawing we multiply the side lengths by a fraction

Aliun [14]

Answer:

true im not sure

Step-by-step explanation:

5 0

3 years ago

Aflati al 2013 lea termen al unei progresii aritmetice cu termenul al treilea egal cu 12 si diferenta a doi termeni consecutivi,

KATRIN_1 [288]

Răspuns:

8052

Explicație pas cu pas:

Al treilea termen al unei progresii aritmetice:

T (n) = a + (n - 1) d

Unde ;

a = primul termen; d = diferență comună = 4; n = al treilea termen (numărul termenului)

Al treilea (3) termen:

T (3) = a + (3-1) 4

T (3) = 12

12 = a + 2 (4)

12 = a + 8

12 - 8 = a

4 = a

Prin urmare, primul termen = a

Al 2013-lea mandat;

T (2013) = a + (2013-1) d

T (2013) = 4 + (2012) 4

T (2013) = 4 + 8048

= 8052

4 0

2 years ago

a building was decorated with 1240 green bulbs , 1350 red bulbs and 90 yellow bulbs how many bulbs were used in all

MrRa [10]

Answer: 2,680 bulbs were used in all.

I added all of them up so 1240 + 1350 + 90 which equals 2,680.

If you have any questions let me know, have a great day!

5 0

2 years ago

Parallel to y=4x+2,y intercept at 4

seraphim [82]

Answer:

<h2>y = 4x + 4</h2>

Step-by-step explanation:

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

Parallel lines have the same slope.

We have y = 4x + 2 → m = 4.

The slope of parallel line is m = 4 and the y-intercept b = 4.

Therefore we have the equation of a line:

$y=4x+4$

4 0

3 years ago

The height y of a ball (in feet) is given by the function and x is the horizontal distance traveled by the ball.

bazaltina [42]

Given: <em>The height y of a ball (in feet) is given by the function </em><em>y=-1/12x^2+2x+4 </em><em>and x is the horizontal distance traveled by the ball.</em>

Part A:<em> </em><em>How high is the ball when it leaves the child's hand?</em>

Right after the ball leaves the child's hand, it has travelled 0 feet horizontally. Horizontal distance is represented by x, so we could say that x = 0.
Plug in 0 for our equation and solve for y, the height.

$y=-\frac{1}{12}x^2+2x+4\\\\y=\frac{1}{12}\cdot0^2+2\cdot0+4\\\\y=0+0+4\\\\\boxed{y=4}$

Part B & C: <em>How high is the ball at its maximum height?
</em>
What we basically want to do is find the vertex of the function.
There are multiple ways to do this. You could graph it or make a table, but this method is not efficient.
The method I am going to go over right now is putting the equation in vertex form.

$y=-\frac{1}{12}x^2+2x+4$

Move the constant to the left side.

$y-4=-\frac{1}{12}x^2+2x$

Factor out the x² coefficient.

$y-4=-\frac{1}{12}(x^2-24x)$

Find out which number to add to create a perfect square trinomial.
(Half of 24 is 12, 12 squared is 144. We have to add 144/-12 (which is -12) to each side so that we end up with 144 inside the parentheses on the right side)

$y-4-12=-\frac{1}{12}(x^2-24x+144)$

Factor the perfect square trinomial and simplify the right side.

$y-16=-\frac{1}{12}(x-12)^2$

Isolate y on the left side.

$y=-\frac{1}{12}(x+12)^2+16$

And now we are in vertex form.
Vertex form is defined as y = a(x-h)² + k with vertex (h, k).
In this case, our vertex is (12, 16).

You could've also taken the shortcut that for any quadratic f(x) = ax² + bx + c, the vertex (h, k) is (-b/2a, f(h)). That's basically a summation of this method which you can use if your teacher has taught it to you.

Part D & E: <em>What is the horizontal distance travelled by the ball when it hits the ground?</em>
When the ball hits the ground, y is going to be 0, since y is the ball's height.
There are many ways to solve a quadratic...split the middle, complete the square, and the quadratic formula.

$-\frac{1}{12}x^2+2x+4=0$
<u>
</u><u>Solving by splitting the midlde</u>
If your quadratic has fractions, this is not a good option.
<u>
</u><u>Solving by completing the square</u>
Move the constant over the right side.

$y=-\frac{1}{12}x^2+2x=-4$

Divide by the x² coefficient.
(Dividing by -1/12 is the same as multiplying by its reciprocal, -12.)

$x^2-24x=-4\times-12$

Simplify the right side.

$x^2-24x=48$

Halve the x coefficient, square it, and then add it to each side.
(Half of -24 is -12, and -12 squared is 144.)

$x^2-24x+144=192$

Factor the perfect square trinomial.

$(x-12)^2=192$

Take the square root of each side.

$x-12=\pm\sqrt{192}$

192 = 8 × 8 × 3, so we can simplify √192 to 8√3.
Add 12 to each side and we get our answer.

$x=12\pm8\sqrt{3}$

Our function does not apply when x or y is less than 0, of course.
12-8√3 is negative, so this cannot be our answer.
So, the ball had travelled 12+8√3 feet at the time when it hit the ground.

<u>Solving with the quadratic formula</u>
For any equation ax² + bx + c = 0, the solution for x is $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ .

Our equation, y=-1/12x^2+2x+4, has a = -1/12, b=2, and c=4.
Let's plug these values into the quadratic formula.

$\frac{-2\pm\sqrt{2^2-4\cdot\frac{-1}{12}\cdot4}}{2\cdot\frac{-1}{12}}=\frac{-2\pm\sqrt{4-\frac{-4}3}}{\frac{-1}6}=\frac{-2\pm\sqrt{\frac{16}{3}}}{\frac{-1}6}=\frac{-2\pm\frac{4}{\sqrt{3}}}{\frac{-1}6}$

Dividing by a fraction is the same as multiplying by its reciprocal...

$-6(-2\pm\frac{4}{\sqrt{3}})=12\pm\frac{-24}{\sqrt{3}}=12\pm\frac{24}{\sqrt{3}}=12\pm\frac{24\sqrt{3}}3=\boxed{12\pm8\sqrt{3}}$

Of course, we only want the positive value, 12+8√3.

Revisiting Part B & C:
Since parabolae are symmetrical, if you know two values of x for some value of y (like the x-intercepts we just found in part B) then you can find the average between them to find what the x value of the vertex is, then plug that in to find the y value of the vertex (the height we want)

The average between 12+8√3 and 12-8√3 is 12. Plug that in and we get 16!

5 0

2 years ago