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monitta
3 years ago
15

Simplify 16-3(8-3)^2÷5

Mathematics
2 answers:
Darina [25.2K]3 years ago
6 0

Answer:

1

Step-by-step explanation:

PODMAS:-

16-3(8-3)²/5

=16-3(5)²/5

=16-3(25)/5

=16-3(5)

=16-15

= 1

Sunny_sXe [5.5K]3 years ago
6 0

Answer:

65

Step-by-step explanation:

=> \frac{16-3(8-3)^2}{5}

=> \frac{13(5)^2}{5}

=> \frac{13(25)}{5}

=> 13 × 5

=> 65

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Suppose that we don't have a formula for g(x) but we know that g(3) = −5 and g'(x) = x2 + 7 for all x.
Leni [432]

Answer:

a)

g(2.9) \approx -6.6

g(3.1) \approx -3.4

b)

The values are too small since g'' is positive for both values of x in. I'm speaking of the x values, 2.9 and 3.1.

Step-by-step explanation:

a)

The point-slope of a line is:

y-y_1=m(x-x_1)

where m is the slope and (x_1,y_1) is a point on that line.

We want to find the equation of the tangent line of the curve g at the point (3,-5) on g.

So we know (x_1,y_1)=(3,-5).

To find m, we must calculate the derivative of g at x=3:

m=g'(3)=(3)^2+7=9+7=16.

So the equation of the tangent line to curve g at (3,-5) is:

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y+5=16(x-3)

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y=16(x-3)-5

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g(x) \approx 16(x-3)-5.

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g(2.9) \approx 16(-.1)-5

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g(3.1) \approx 16(.1)-5

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b) To determine if these are over approximations or under approximations I will require the second derivative.

If g'' is positive, then it leads to underestimation (since the curve is concave up at that number).

If g'' is negative, then it leads to overestimation (since the curve is concave down at that number).

g'(x)=x^2+7

g''(x)=2x+0

g''(x)=2x

2x is positive for x>0.

2x is negative for x.

That is, g''(2.9)>0 \text{ and } g''(3.1)>0.

So 2x is positive for both values of x which means that the values we found in part (a) are underestimations.

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