1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Margarita [4]
4 years ago
15

How to evaluate question number 4

Mathematics
1 answer:
ANTONII [103]4 years ago
5 0

There are 2 ways that spring to mind.

One is to use the definition of the derivative at a point:

f'(c)=\displaystyle\lim_{x\to c}\frac{f(x)-f(c)}{x-c}

In this case, c=0 and f(x)=\sqrt{5-x}. Then

f'(x)=-\dfrac1{2\sqrt{5-x}}\implies f'(0)=\displaystyle\lim_{x\to0}\frac{\sqrt{5-x}-\sqrt5}x=-\dfrac1{2\sqrt5}

- - -

If you don't know about derivative yet (I would think you do, considering this is for a midterm in AP Calc, but I digress), the other way is to rely on algebraic manipulation. Multiply the numerator and denominator by the conjugate of the numerator to get

\dfrac{\sqrt{5-x}-\sqrt5}x\cdot\dfrac{\sqrt{5-x}+\sqrt5}{\sqrt{5-x}+\sqrt5}=\dfrac{\left(\sqrt{5-x}\right)^2-\left(\sqrt5\right)^2}{x\left(\sqrt{5-x}+\sqrt5\right)}=-\dfrac x{x\left(\sqrt{5-x}+\sqrt5\right)}=-\dfrac1{\sqrt{5-x}+\sqrt5}

This is continuous at x=0, so the limit is the value of the expression at x=0:

\displaystyle\lim_{x\to0}\frac{\sqrt{5-x}-\sqrt5}x=-\lim_{x\to0}\frac1{\sqrt{5-x}+\sqrt5}=-\frac1{2\sqrt5}

You might be interested in
The area of a book cover is 63.8 in². The width of the book is the difference of the length and 3 inches. Let x represent the bo
Mazyrski [523]
In this item, we are already given that the length of the rectangular book can be represented by the variable x. In this way, the width, which was described to be the difference of the length and 3 inches, can be expressed as x - 3. 

The area of the triangle is rectangle is calculated by multiplying the length, x, and the width, which was derived to be x - 3.

                 Area = Length x width
                 Area = (x)( x - 3)

Putting in the value of the area, we have the final answer as,
               x(x - 3) = 63.8 in²

Hence, the final answer is the first answer. 
3 0
4 years ago
5. Solve: 16 * 22 / 2
bixtya [17]

Answer:

176

Step-by-step explanation:

Usually you'll follow PEMDAS & the left->right rule, however, as you are only multiplying and dividing, it does not matter.

22/2 = 11

11 * 16 = 176

176 is your answer.

~

5 0
3 years ago
Read 2 more answers
A regular hexagon has an apothem of 14.7 inches and a perimeter of 101.8 inches. what is the area of the hexagon? square inches
WINSTONCH [101]

Answer:

748.23 in^2.

Step-by-step explanation:

Area = 1/2 * apothem * perimeter

        = 1/2 * 14.7 * 101.8

        =  748.23 in^2.

3 0
2 years ago
Read 2 more answers
The speed of the current in a certain stream is 6 mph. If a boat travels 94 miles
Katyanochek1 [597]

Answer: The trick to this question is twofold:

Spot that 94 is double 47. Therefore when going downstream, the speed of the boat relative to the earth is double it's speed going upstream as it covers double the distance in the same time.

Understand that whatever the speed of the boat is, when going downstream it's speed relative to the earth is 6mph greater than speed relative to the water, and conversely when going upstream, earth speed is 6mph less than water speed.

So, if the speed through the water is X, upstream speed is (X-6) and downstream speed is (X+6).

Now, we know that upstream speed is double downstream speed, so:

Double (x-6) is equal to (X+6)

Or:

2(x-6)=(X+6)

5 0
2 years ago
Write an expression with five different terms that is equivalent to 8x^2 + 3x^2 + 3y
Misha Larkins [42]

▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪

An expression having five terms which is equivalent to above term is :

  • 5x {}^{2}  + 3 {x}^{2}  + 3{x}^{2}  +4y - y

3 0
3 years ago
Other questions:
  • Write 3 + 2 x 1/10 +4 x 1/1000 in standard form
    8·1 answer
  • To prove that VWZ ~ YXZ by SAS similarity theorem, which other side or angle should be used
    5·2 answers
  • The number of gallons of water in a tank, that already has 400 gallons in it, after being filled at 15 gallons per minute for m
    15·1 answer
  • Find the equation of the circle whose center and radius are given.
    15·2 answers
  • What is the name of an investment in which deposits are made in fixed dollar amounts at regular intervals?
    9·2 answers
  • Niki typed a 500- word essay in 8 minutes. How many words per second did she type?
    6·2 answers
  • Solve for x, show all work please :)
    13·1 answer
  • Which expressions are equivalent?
    14·2 answers
  • What is 4 a whole number as a fraction<br><br> note: this is for my little sister!
    8·1 answer
  • Need help plzzz 10 points
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!