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nataly862011 [7]
3 years ago
15

Solve the system of equations using the tables below

Mathematics
1 answer:
Bezzdna [24]3 years ago
7 0

Answer:

  (x, y) = (0, 3)

Step-by-step explanation:

(x, y) = (0, 3) is in both tables. Hence, that point is a solution to the system of equations.

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Given f(x) = (lnx)^3 find the line tangent to f at x = 3
kirill [66]
Explanation

We must the tangent line at x = 3 of the function:

f(x)=(\ln x)^3.

The tangent line is given by:

y=m*(x-h)+k.

Where:

• m is the slope of the tangent line of f(x) at x = h,

,

• k = f(h) is the value of the function at x = h.

In this case, we have h = 3.

1) First, we compute the derivative of f(x):

f^{\prime}(x)=\frac{d}{dx}((\ln x)^3)=3*(\ln x)^2*\frac{d}{dx}(\ln x)=3*(\ln x)^2*\frac{1}{x}=\frac{3(\ln x)^2}{x}.

2) By evaluating the result of f'(x) at x = h = 3, we get:

m=f^{\prime}(3)=\frac{3}{3}*(\ln3)^2=(\ln3)^2.

3) The value of k is:

k=f(3)=(\ln3)^3

4) Replacing the values of m, h and k in the general equation of the tangent line, we get:

y=(\ln3)^2*(x-3)+(\ln3)^3.

Plotting the function f(x) and the tangent line we verify that our result is correct:

Answer

The equation of the tangent line to f(x) and x = 3 is:

y=(\ln3)^2*(x-3)+(\ln3)^3

6 0
1 year ago
Is it possible to form a triangle with<br> side lengths 5, 3, and 5 units?
7nadin3 [17]

Answer:

Yes

Step-by-step explanation:

Isosceles triangle with base of 3 units and sides of 5 units

8 0
2 years ago
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Help me, please!!!!!!!
navik [9.2K]

9514 1404 393

Answer:

  2

Step-by-step explanation:

Alex has 10 money units. Annie has 5 money units. The ratio of amounts is ...

  Alex : Annie = 10 : 5 = 2 : 1

Alex has 2 times as much money as Annie.

8 0
3 years ago
A print shop orders 58 T-shirts. They order 16 pink T-shirts, and six times as many blue T-shirts as white T-shirts. How many bl
Pepsi [2]
The have ordered 36 blue T-shirts.
___________________

How I got it --- So, we take away 16 from 58. You get 42. 
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So, from then, you know 36 is 6 times as many as 6, right? ( Because 6 x 6 = 36)
___________________________________________________________

So, then, you have ordered 36 blue shirts and 6 white shirts, because 36 + 6 =42.
______________________________________________________

Glad I could help, and good luck!
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3 0
2 years ago
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13,406,109 pennis into dollars
geniusboy [140]

Answer:

$134,061.09

Step-by-step explanation:

hope this helps

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