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3 years ago

L'Hospital's Rule Lim X approaches 0 cot2x•sin6x

1 answer:

3 0

$\bf \lim\limits_{x\to 0}\ cot(2x)sin(6x)\implies \lim\limits_{x\to 0}\ \cfrac{cos(2x)}{sin(2x)}sin(6x)\\\\
-----------------------------\\\\
\underline{LH}\qquad \cfrac{-2sin(2x)sin(6x)+cos(2x)6cos(6x)}{2cos(2x)}
\\\\\\
\lim\limits_{x\to 0}\ \cfrac{-2sin(2x)sin(6x)+cos(2x)6cos(6x)}{2cos(2x)}
\\\\\\
\lim\limits_{x\to 0}\ \cfrac{-0\cdot 0+1\cdot 6\cdot 1}{2\cdot 1}\implies \cfrac{6}{2}\implies 3$

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Nathan and his brother Zach love to play video games. Right

Monica [59]

Answer:

$N=2Z-11$

$\begin{array}{cc}\text{Zac's score}&\text{Natan's score}\\ 6&1\\7&3\\8&5\\9&7\end{array}$

Step-by-step explanation:

Nathan's score is 11 less than 2 times Zac's score.

Let Z points be Zac's score and N points be Natan's score. then

2 times Zac's score = 2Z

11 less than 2 times Zac's score = 2Z -11

So, N = 2Z - 11

1. If Z=6, then $N=2\cdot 6-11=12-11=1$

2. If Z=7, then $N=2\cdot 7-11=14-11=3$

3. If Z=8, then $N=2\cdot 8-11=16-11=5$

4. If Z=9, then $N=2\cdot 9-11=18-11=7$

Thus, four other possibilities are

$\begin{array}{cc}\text{Zac's score}&\text{Natan's score}\\ 6&1\\7&3\\8&5\\9&7\end{array}$

3 0

3 years ago

Help please i need answers fast if you help or try to help tysm *hearts*

Tanzania [10]

Answer:

C. 3rd one Fraction 10/24

Step-by-step explanation:

3/4 - 2/6 = 0.41 or = 10/24 or it could be equal to 5/12 are 10/24, 15/36, 20/48 and 25/60 or as Decimal 0.41

Step-by-step explanation:

Hope This Helped

7 0

2 years ago

The height h in feet of a ball thrown vertically upward from the top of a 288-foot tall building is given by h=288+48t-16t^2 whe

mr Goodwill [35]

6 sec can take penny to strike the ground.

Solution:

Given data:

$H_0=288$ feet

$V_0=48$ feet

$h(t)=288+48t-16t^2$

Re-arrange the terms from greatest degree to smallest degree.

$h(t)=-16t^2+48t+288$

We can solve it by applying quadratic formula,

$$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here a = –16, b = 48, c = 288

$$t=\frac{-48\pm \sqrt{48^2-4(-16)(288)}}{2(-16)}$

$$t=\frac{-48\pm \sqrt{2304+18432}}{-32}$

$$t=\frac{-48\pm \sqrt{20736}}{-32}$

$$t=\frac{-48\pm144}{-32}$

Now, write find two t's using plus and minus operation.

$$t=\frac{-48+144}{-32},\ \ t=\frac{-48-144}{-32}$

$$t=\frac{96}{-32},\ \ t=\frac{-192}{-32}$

t = –3 (or) t = 6

We cannot write time is negative. so neglect t = –3.

Therefore t = 6.

Hence 6 sec can take penny to strike the ground.

8 0

3 years ago

Show whether or not y=x+3 is tangential to the curve y^2=x

wolverine [178]

The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.

y² = x

Take the derivative of both sides with respect to x, assuming y = y(x) :

2y dy/dx = 1

dy/dx = 1/(2y)

Solve for y when dy/dx = 1 :

1 = 1/(2y)

2y = 1

y = 1/2

When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.

This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :

x = y² ⇒ y = y² + 3 ⇒ y² - y + 3 = 0

has no real solution for y.

3 0

2 years ago

How to generate a Venn diagram to compare the following numbers 318,274 and 138,524

Agata [3.3K]

In the middle/Alike: 3,1,8,2,4
Outside for 318,274: Doesnt have 5
Outside for 138,524: Doesnt have 7

3 0

3 years ago