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Solnce55 [7]
3 years ago
13

Use the differential to approximate the expression. Then use a calculator to approximate the quantity, and give the absolute val

ue of the difference in the two results to four decimal places.
√
53
Mathematics
1 answer:
scoray [572]3 years ago
7 0

9514 1404 393

Answer:

   0.0056

Step-by-step explanation:

  f(x) = √(49 +x)

  f'(x) = 1/(2√(49 +x))

A linear approximation of f(x) expanded about x=0 is ...

  f(x) ≈ f(0) + f'(0)x = 7 +x/(2·7)

Then for √53, we have x=4

  f(4) ≈ 7 +4/14 = 7 2/7 . . . . . approximate √53 using differentials

__

The calculator value of √53 is about 7.280110, so the difference in results is ...

  approx - actual ≈ 7.285714 -7.280110 = 0.005604 ≈ 0.0056

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A car costs 20% less this year than last year. Last year, the car cost 5% less than the year before. The price of the car this y
Tems11 [23]

Answer:

The answer is 11,374

Step-by-step explanation:

First we find 5% of 9,400 is.

9,400 * 5% = 470

Next we add 9,400 with 470 then multiply by 20%

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Hope this helps! :)

3 0
3 years ago
What are the solutions to the equation (x + 2)^2 = 49?
Mekhanik [1.2K]

Answer:

X= 5, -9

Step-by-step explanation:

(X+2)² =49

Expand the bracket,


(X+2) (X+2)= 49

Apply the distributive property;

X(X+2) +2 (X+2) =49

X²+2X+2X+4=49

X²+4X+4=49

Move 49 to the left side of the equation;

X²+4X+4-49=0

X²+4X-45=0

Apply Factorisation method;

Consider the form

a²+bx+c=0  

Find two numbers whose sum is equal to b and whose product is equal to c.
Comparing with our equation;

B =4 and C =45

We can use 9 and -5, this is because ;

9+(-5)=4 and 9*(-5)= 45.

Replace X +4X-45=0 with (X-5) (X+9)=0

Therefore;

X-5=0

X+9=0

Moving to the left side of the equation;

Therefore X= 5 and -9

8 0
3 years ago
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