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____ [38]
3 years ago
11

Solve this equation for a: 6a+3=45

Mathematics
1 answer:
fenix001 [56]3 years ago
3 0

Answer: 7

Step-by-step explanation:

Step 1: Subtract 3 from both sides.

6a+3−3=45−3

6a=42

Step 2: Divide both sides by 6.

6a /6 = 42 /6

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Consider functions of the form f(x)=a^x for various values of a. In particular, choose a sequence of values of a that converges
sleet_krkn [62]

Answer:

A. As "a"⇒e, the function f(x)=aˣ tends to be its derivative.

Step-by-step explanation:

A. To show the stretched relation between the fact that "a"⇒e and the derivatives of the function, let´s differentiate f(x) without a value for "a" (leaving it as a constant):

f(x)=a^{x}\\ f'(x)=a^xln(a)

The process will help us to understand what is happening, at first we rewrite the function:

f(x)=a^x\\ f(x)=e^{ln(a^x)}\\ f(x)=e^{xln(a)}\\

And then, we use the chain rule to differentiate:

f'(x)=e^{xln(a)}ln(a)\\ f'(x)=a^xln(a)

Notice the only difference between f(x) and its derivative is the new factor ln(a). But we know  that ln(e)=1, this tell us that as "a"⇒e, ln(a)⇒1 (because ln(x) is a continuous function in (0,∞) ) and as a consequence f'(x)⇒f(x).

In the graph that is attached it´s shown that the functions follows this inequality (the segmented lines are the derivatives):

if a<e<b, then aˣln(a) < aˣ < eˣ < bˣ < bˣln(b)  (and below we explain why this happen)

Considering that ln(a) is a growing function and ln(e)=1, we have:

if a<e<b, then ln(a)< 1 <ln(b)

if a<e, then aˣln(a)<aˣ

if e<b, then bˣ<bˣln(b)

And because eˣ is defined to be the same as its derivative, the cases above results in the following

if a<e<b, then aˣ < eˣ < bˣ (because this function is also a growing function as "a" and "b" gets closer to e)

if a<e, then aˣln(a)<aˣ<eˣ ( f'(x)<f(x) )

if e<b, then eˣ<bˣ<bˣln(b) ( f(x)<f'(x) )

but as "a"⇒e, the difference between f(x) and f'(x) begin to decrease until it gets zero (when a=e)

3 0
3 years ago
Please help i dont get it and its for a grade! :(
Tju [1.3M]

Answer:

y=-4x+5

Step-by-step explanation:

7 0
2 years ago
Brainly do ur magic pls.?
jok3333 [9.3K]

1. 3y

multiplying 3 and y together gets 3y

2. y-5

5 less implies that we subtract 5 from y

3. y+7

adding 7 to y, self-explanatory

4. 9y

same thing as #1

5. \frac{y}{8}

quotient of implies division, since number y is listed first, y is the numerator

8 0
3 years ago
4x^5 in verbal algebraic expression
disa [49]

Answer:

The product of 4 times the quantity x to the fifth power

6 0
3 years ago
What equation of the line that has a slope of -4 and passes through the point (-2,-5)? Answer ASAP!!
Anna11 [10]

Answer:

<em>Given </em><em>points </em><em>are </em><em>(</em><em> </em><em>-</em><em>2</em><em> </em><em>,</em><em> </em><em>-</em><em>5</em><em> </em><em>)</em><em> </em><em>and </em><em>slope </em><em>(</em><em> </em><em>m</em><em>) </em><em> </em><em>=</em><em> </em><em>-</em><em>4</em>

Step-by-step explanation:

<em>y </em><em>-</em><em> </em><em>y1</em><em> </em><em>=</em><em> </em><em>m </em><em>(</em><em> </em><em>x </em><em>-</em><em> </em><em>x1</em><em>)</em>

<em>y </em><em>+</em><em> </em><em>5</em><em> </em><em>=</em><em> </em><em>-</em><em>4</em><em> </em><em>(</em><em> </em><em>x </em><em>+</em><em> </em><em>2</em><em> </em><em>)</em>

<em>y </em><em>+</em><em> </em><em>5</em><em> </em><em>=</em><em> </em><em>-</em><em>4</em><em>x</em><em> </em><em>-</em><em> </em><em>8</em>

<em>4x </em><em>+</em><em> </em><em>y </em><em>+</em><em>5</em><em> </em><em>+</em><em> </em><em>8</em><em> </em><em>=</em><em> </em><em>0</em>

<em>4x </em><em>+</em><em> </em><em>y </em><em>+</em><em>1</em><em>3</em><em> </em><em>=</em><em> </em><em>0</em><em> </em>

<em>y </em><em>=</em><em> </em><em>-</em><em>4</em><em>x</em><em> </em><em>-</em><em> </em><em>1</em><em>3</em>

<em>which </em><em>is </em><em>the </em><em>required </em><em>equation </em>

4 0
3 years ago
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