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3 years ago

Sloane kicked a soccer ball at a speed of 36 feet per second. If the ball never leaves the ground, then it can be represented by

Mathematics

1 answer:

Hoochie [10]3 years ago

6 0

Answer:

t = 2.25 seconds

Step-by-step explanation:

Let

x ----> the time in seconds that the ball traveled

H(t) ---> the height of the ball in feet

we have

$H(t)=-16t^2+36t$

we know that

When the ball hit the ground, the height of the ball is equal to zero

To find out the time the ball traveled, equate the function H(t) to zero

For H(t)=0

$-16t^2+36t=0$

solve for t

Factor -16t

$-16t(t-\frac{9}{4})=0$

The solutions are

$t=0\ sec \\t=9/4=2.25\ sec$

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This Is Graded, Please Help TYSM!

olchik [2.2K]

Answer: For the cirlces since I already answered the triangles

1. Area:660.519855417

Circumference:91.1061869541

2. Area: 572.555261117

Circumference:84.8230016469

3. Area:283.528736986

Circumference:59.6902604182

4. Area:1017.87601976

Circumference:113.097335529

5. Area: 63.6172512352

Circumference: 28.2743338823

6. Area:380.132711084

Circumference:69.115038379

Step-by-step explanation:

The formula for the area of a circle is π*r^2, r being the radius or the half line in the circle, and the formula for the circumference is π*r*2, or π*d, or the diameter which is the line that goes all the way through like number 5. The radius is half the diameter.

4 0

3 years ago

Calculus 2 Master needed, evaluate the indefinite integral of: <img src="https://tex.z-dn.net/?f=%5Cint%5C%28%20%28lnx%29%5E2%7D

viva [34]

Answer:

$\int (\ln(x))^2dx=x(\ln(x)^2-2\ln(x)+2)+C$

Step-by-step explanation:

So we have the indefinite integral:

$\int (\ln(x))^2dx$

This is the same thing as:

$=\int 1\cdot (\ln(x))^2dx$

So, let's do integration by parts.

Let u be (ln(x))². And let dv be (1)dx. Therefore:

$u=(\ln(x))^2\\\text{Find du. Use the chain rule.}\\\frac{du}{dx}=2(\ln(x))\cdot\frac{1}{x}$

Simplify:

$du=\frac{2\ln(x)}{x}dx$

And:

$dv=(1)dx\\v=x$

Therefore:

$\int (\ln(x))^2dx=x\ln(x)^2-\int(x)(\frac{2\ln(x)}{x})dx$

The x cancel:

$=x\ln(x)^2-\int2\ln(x)dx$

Move the 2 to the front:

$=x\ln(x)^2-2\int\ln(x)dx$

(I'm not exactly sure how you got what you got. Perhaps you differentiated incorrectly?)

Now, let's use integrations by parts again for the integral. Similarly, let's put a 1 in front:

$=x\ln(x)^2-2\int 1\cdot\ln(x)dx$

Let u be ln(x) and let dv be (1)dx. Thus:

$u=\ln(x)\\du=\frac{1}{x}dx$

And:

$dv=(1)dx\\v=x$

So:

$=x\ln(x)^2-2(x\ln(x)-\int (x)\frac{1}{x}dx)$

Simplify the integral:

$=x\ln(x)^2-2(x\ln(x)-\int (1)dx)$

Evaluate:

$=x\ln(x)^2-2(x\ln(x)-x)$

Now, we just have to simplify :)

Distribute the -2:

$=x\ln(x)^2-2x\ln(x)+2x$

And if preferred, we can factor out a x:

$=x(\ln(x)^2-2\ln(x)+2)$

And, of course, don't forget about the constant of integration!

$=x(\ln(x)^2-2\ln(x)+2)+C$

And we are done :)

8 0

3 years ago

Which of the following equations have exactly

Anestetic [448]

Answer:

-5x + 12 = –12x – 12

-5x + 12 = 5x + 12

-5x + 12 = 5x – 5

Step-by-step explanation:

First degree equations

A first degree equation has the form

ax + b = 0

There are some special cases where the equation can have one, infinitely many or no solution

If $a\neq 0$ , the equation has exactly one solution

If a=0 and b=0 the equation has infinitely many solutions, because it doesn't matter the value of x, it will always be true that 0=0

If a=0 and $b\neq 0$ the equation has no solution, because it will be equivalent to b=0 and we are saying it's not true. No matter what x is, it's a false statement.

We have been given some equations, we only need to put them in standard form

-5x + 12 = –12x – 12

Rearranging

7x + 24 = 0

It has exactly one solution because a is not zero

.......................

-5x + 12 = 5x + 12

Rearranging

-10x + 0 = 0

It has exactly one solution because a is not zero

.......................

-5x + 12 = 5x – 5

Rearranging

-10x + 17 = 0

It has exactly one solution because a is not zero

.......................

-5x + 12 = -5x – 12

Rearranging

0x + 24 = 0

It has no solution, no matter what the value of x is, it's impossible that 24=0

Answer: These are the equations with exactly one solution

-5x + 12 = –12x – 12

-5x + 12 = 5x + 12

-5x + 12 = 5x – 5

6 0

3 years ago

Find the surface area of a sphere with a radius of 12 cm. Approximate 3.14 and round your answer to the nearest hundredth

attashe74 [19]

The equation to find a spheres surface area is 4 pi R ^2
and this works in any order

4 * 12 is 48 (4 * R)

48^2 is 2304 ((4 * R)^2)

the exact answer is 2304 $\pi$

the full answer is 7234.56 (((4 * R)^2) $\pi$ )

5 0

3 years ago

Read 2 more answers

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Nikolay [14]

Answer:

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Step-by-step explanation

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3 years ago