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Alex787 [66]
2 years ago
14

The plot below shows the volume of vinegar used by each of 171717 students in their volcano experiments.

Mathematics
1 answer:
iren [92.7K]2 years ago
4 0
What’s the question?
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The derivative of y with respect to x, when y = 3e^5x - 2 is:
Ede4ka [16]
Answer: 15e^5x

Step - by - step

y=3e^5x - 2

By the sum rule, the derivative of 3e^5x - 2 with respect to x is d/dx [ 3e^5x ] + d/dx [-2].

d/dx [ 3e^5x ] + d/dx [ -2 ]

Evalute d/dx [ 3e^5x ]

Since 3 is constant with respect to x , the derivative of 3e^5x with respect to x is
3 d/dx [ e^5x ].

3 d/dx [ e^5x ] + d/dx [ -2 ]

Differentiate using the chain rule, which states that d/dx [ f(g(x))] is f' (g(x)) g' (x) where f(x) = e^x and g(x) = 5x.

To apply the Chain Rule, set u as 5x.
3 ( d/du [ e^u] d/dx [5x] ) + d/dx [ -2]

Differentiate using the Exponential rule which states that d/du [ a^u ] is a^u ln(a) where a=e.

3( e^u d/dx[5x] ) + d/dx [ -2 ]
Replace
3(e^5x d/dx [5x] ) + d/dx [ -2 ]
3(e^5x( 5 d/dx [x] )) + d/dx [ -2 ]

Diffentiate using the Power Rule which states that d/dx [x^n] is nx^n-1 where n=1.
3(e^5x(5*1)) + d/dx [-2]
3 ( e^5x * 5 ) + d/dx [-2]

Multiply 5 by 3
15e^5x + d/dx [-2]

Since -2 is constant with respect to x, the derivative of -2 with respect to x is 0.
15e^5x + 0
15e^5x
5 0
1 year ago
A 44<br> B 5<br> C 10<br> D None of the choices are correct.
Brums [2.3K]

Answer:

D. None of the choices are correct.

Step-by-step explanation:

If <em>B</em> is the midpoint of AC, then that means that AB is congruent to BC. Because this is true, you can set 8x + 4 and 10x - 8 equal.

8x + 4 = 10x - 8

Now just solve for x. Subtract 8x from both sides and add 8 to both sides.

4 = 2x - 8

12 = 2x

Then divide by 2.

6 = x

Another way to do this problem is to set up the same equation, but instead of solving it, plug in answer choices A, B, and C independently of each other. Then simplify to see if those are right. You'll find out that none of them are.

4 0
3 years ago
Determine if a triangle can be formed with the given lengths. If it can, classify it as acute,
lisabon 2012 [21]

Answer:

steps below

Step-by-step explanation:

1. It can be formed a triangle: sum of any two sides is greater than the 3rd side

2. It can't be an obtuse triangle: 5² + 7² = 74 < 10²

   the triangle is an obtuse-angled triangle if  the square of the longest side (c²) is greater than the sum of the square of other two sides (c²>a²+b²)

6 0
3 years ago
What are the x-intercepts of the graph of the following function y = 6x to the second power minus 12x - 18
maksim [4K]

Answer:

it would be 12x 26y doe to the problem

7 0
3 years ago
Round 62,981 to the nearest thousand.
olga2289 [7]

Answer:

63,000

Step-by-step explanation:

When 981 is rounded to the nearest thousand, it is equal to 1,000. Add this to the remaining number, 62,000, and voila! you get it!

62,000 + 1,000 = 63,000

If you want this explained further, please just let me know!

Thanks!

7 0
3 years ago
Read 2 more answers
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