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maks197457 [2]
3 years ago
6

Test the convergence of 011xx dx .

Mathematics
1 answer:
Slav-nsk [51]3 years ago
6 0

Step-by-step explanation:

eggfdddfgggfseeedhhggh

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A 10-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate
Alex777 [14]

Answer:

The area is changing at 15.75 square feet per second.

Step-by-step explanation:

The triangle between the wall, the ground, and the ladder has the following dimensions:

H: is the length of the ladder (hypotenuse) = 10 ft

B: is the distance between the wall and the ladder (base) = 6 ft

L: the length of the wall (height of the triangle) =?

dB/dt = is the variation of the base of the triangle = 9 ft/s        

First, we need to find the other side of the triangle:  

H^{2} = B^{2} + L^{2}

L = \sqrt{H^{2} - B^{2}} = \sqrt{(10)^{2} - B^{2}} = \sqrt{100 - B^{2}}

Now, the area (A) of the triangle is:            

A = \frac{BL}{2}  

Hence, the rate of change of the area is given by:

\frac{dA}{dt} = \frac{1}{2}[L*\frac{dB}{dt} + B\frac{dL}{dt}]      

\frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - B^{2}}*\frac{dB}{dt} + B\frac{d(\sqrt{100 - B^{2}})}{dt}]        

\frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - B^{2}}*\frac{dB}{dt} - \frac{B^{2}}{(\sqrt{100 - B^{2}})}*\frac{dB}{dt}]  

\frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - 6^{2}}*9 - \frac{6^{2}}{\sqrt{100 - 6^{2}}}*9]      

\frac{dA}{dt} = 15.75 ft^{2}/s  

     

Therefore, the area is changing at 15.75 square feet per second.

I hope it helps you!                                    

5 0
3 years ago
Find the distance between A (-3,<br> - 4) and B (5. – 10).
Kamila [148]

Answer:

16.13

Step-by-step explanation:

Sorry!! if I am wrong....

7 0
3 years ago
Evaluate the function when x=5<br> F(5)=?
kenny6666 [7]

Step-by-step explanation:

When evaluating piecewise function, make sure the x value satisfies the function we use.

since 5>3, we use the second equations

That function is a constant function, this means at any x>3, exclusive, we will have a y value of -1.

So

f(5) =  - 1

7 0
2 years ago
Find the 4th term of the expansion of (2a - b)^7.
ankoles [38]

Answer:

-560a^4b^3

Step-by-step explanation:

Given:

(2a - b)^7

By using Binomial theorem:

128a^7 - 448a^6b + 672a^5b^2 - 560a^4b^3 + 280a^3b^4 - 84a^2b^5 + 14ab^6-b^7

Here the fourth term is -560a^4b^3 !

4 0
3 years ago
Read 2 more answers
In ΔJKL, j = 890 cm, k = 260 cm and l=740 cm. Find the measure of ∠K to the nearest degree.
vova2212 [387]

Answer: 47

Step-by-step explanation: I’m smart

5 0
2 years ago
Read 2 more answers
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