Ask question

Ask question

All categories

2 years ago

5

A 15-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 14 feet

from the base of the building. How high up the wall does the ladder reach?
The ladder reaches feet up the wall. (Round to the nearest hundredth.)
HELPP!!

1 answer:

Finger [1]2 years ago

6 0

Answer:

Step-by-step explanation:

Well certainly friction alone will not hold it there.

c² = a² + b²

15² = 14² + b²

15² - 14² = b²

b² = 29

b = √29 = 5.385164... = 5.39 ft

You might be interested in

Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = yzi + 4xzj + ex

natima [27]

Answer:

The result of the integral is 81π

Step-by-step explanation:

We can use Stoke's Theorem to evaluate the given integral, thus we can write first the theorem:

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S curl \vec F \cdot d\vec S$

Finding the curl of F.

Given $F(x,y,z) = < yz, 4xz, e^{xy} >$ we have:

$curl \vec F =\left|\begin{array}{ccc} \hat i &\hat j&\hat k\\ \cfrac{\partial}{\partial x}& \cfrac{\partial}{\partial y}&\cfrac{\partial}{\partial z}\\yz&4xz&e^{xy}\end{array}\right|$

Working with the determinant we get

$curl \vec F = \left( \cfrac{\partial}{\partial y}e^{xy}-\cfrac{\partial}{\partial z}4xz\right) \hat i -\left(\cfrac{\partial}{\partial x}e^{xy}-\cfrac{\partial}{\partial z}yz \right) \hat j + \left(\cfrac{\partial}{\partial x} 4xz-\cfrac{\partial}{\partial y}yz \right) \hat k$

Working with the partial derivatives

$curl \vec F = \left(xe^{xy}-4x\right) \hat i -\left(ye^{xy}-y\right) \hat j + \left(4z-z\right) \hat k\\curl \vec F = \left(xe^{xy}-4x\right) \hat i -\left(ye^{xy}-y\right) \hat j + \left(3z\right) \hat k$

Integrating using Stokes' Theorem

Now that we have the curl we can proceed integrating

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S curl \vec F \cdot d\vec S$

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S curl \vec F \cdot \hat n dS$

where the normal to the circle is just $\hat n= \hat k$ since the normal is perpendicular to it, so we get

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S \left(\left(xe^{xy}-4x\right) \hat i -\left(ye^{xy}-y\right) \hat j + \left(3z\right) \hat k\right) \cdot \hat k dS$

Only the z-component will not be 0 after that dot product we get

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S 3z dS$

Since the circle is at z = 3 we can just write

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S 3(3) dS\\\displaystyle \int\limits_C \vec F \cdot d\vec r = 9\int \int_S dS$

Thus the integral represents the area of a circle, the given circle $x^2+y^2 = 9$ has a radius r = 3, so its area is $A = \pi r^2 = 9\pi$ , so we get

$\displaystyle \int\limits_C \vec F \cdot d\vec r = 9(9\pi)\\\displaystyle \int\limits_C \vec F \cdot d\vec r = 81 \pi$

Thus the result of the integral is 81π

5 0

3 years ago

How would you solve this equation? Please show steps

Serhud [2]

Simple....

you have: $3x= \sqrt{12-12x}$

So...first you know you're trying to find x..

But, you have a square root on one side...to remove this you'd have to square both sides--->>>

$(3x)^{2} = \sqrt{12-12x} ^{2}$

Leaving you with....

$9x^{2} =12-12x$

Move the terms over and set it equal to zero.

-->>

$9x^{2}+12x-12=0$

Factor out a 3...

$3( 3x^{2} +4x-4=0)$

What multiplies to -12 and adds to 4?

6*-2=-12

6+-2=4

Leaving you with...

$3(3x-2)(x+2)=0$

Remember you're solving for 0....

3x-2=0

3x-2=0
+2 +2

3x=2

$\frac{3x}{3} = \frac{2}{3}$

x= $\frac{2}{3}$

Then-->>

x+2=0

x+2=0
-2 -2

x=-2

Thus, your answer.

4 0

3 years ago

What is the value of c?

yulyashka [42]

Answer:

71

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Triangles ABC and DEF are similar triangles. What are the lengths of the unknown sides?<br>

pantera1 [17]

Answer:

A)

Step-by-step explanation:

In the first image, AC=13, and in the second image, DE=26. so basically, every measurement is simply doubled.

12(2)= 24, DE=24

5(2)=10, EF= 10

Let me know if you need further explanation!

8 0

3 years ago

Find the slope of the line <br> Y=-3x - 4

Dimas [21]

Let y=0 to find the x-intercept(s).
0=−3x−4

Add 4 to both sides.
4=−3x

Divide both sides by -3
-4/3 =x (fraction)

Switch sides.
x=−4/3 (fraction)

Let x=0 to find the y-intercept(s).
y=−3×0−4

Simplify
y=−4

6 0

3 years ago