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Lina20 [59]
3 years ago
15

1. For the function f(x) = x2, Find the slope of the secant line joining (1,f(1)) and

Mathematics
1 answer:
goblinko [34]3 years ago
3 0

The slope of the line connecting two points (<em>a</em>, <em>b</em>) and (<em>c</em>, <em>d</em>) is

(<em>d</em> - <em>b</em>) / (<em>c</em> - <em>a</em>)

i.e. the change in the <em>y</em>-coordinate divided by the change in the <em>x</em>-coordinate. For a function <em>y</em> = <em>f(x)</em>, this slope is the slope of the secant line connecting the two points (<em>a</em>, <em>f(a)</em> ) and (<em>c</em>, <em>f(c)</em> ), and has a value of

(<em>f(c)</em> - <em>f(a)</em> ) / (<em>c</em> - <em>a</em>)

Here, we have

<em>f(x)</em> = <em>x</em> ²

so that

<em>f</em> (1) = 1² = 1

<em>f</em> (1.01) = 1.01² = 1.0201

Then the slope of the secant line is

(1.0201 - 1) / (1.01 - 1) = 0.0201 / 0.01 = 2.01

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Simplify so that there are only positive exponents. (3^9/3^-5)?
lianna [129]

Answer:

19,683 and 1/243

Step-by-step explanation:

5 0
2 years ago
A ball is projected in to the air. Its height at time t is given by the equation
Ksju [112]
The equation gives the height of the ball. That is, h is the height of the ball. t is the time. Since we are looking for the time at which the height is 8 (h=8), we need to set the equation equal to 8 and solve for t. We do this as follows:

h=-16 t^{2} +60t+1
8=-16 t^{2} +60t+1
16 t^{2} -60t-1+8=0
16 t^{2} -60t+7=0

This is a quadratic equation and as it is set equal to 0 we can solve it using the quadratic formula. That formula is:
t= \frac{-bplus minus \sqrt{ b^{2}-4ac } }{2a}
You might recall seeing this as "x=..." but since our equation is in terms of t we use "t-=..."

In order to use the formula we need to identify a, b and c.
a = the coefficient (number in front of) t^{2} = 16.
b = the coefficient of t = -60
c = the constant (the number that is by itself) = 7

Substituting these into the quadratic formula gives us:
t= \frac{-(-60)plus minus \sqrt{ (-60)^{2}-4(16)(7) } }{2(16)}
t= \frac{60plus minus \sqrt{3600-448 } }{32}
t= \frac{60plus minus \sqrt{3152 } }{32}

As we have "plus minus" (this is usually written in symbols with a plus sign over a minus sign) we split the equation in two and obtain:
t=  \frac{60+56.1426}{32} =3.63
and
t=  \frac{60-56.1426}{32} =.12

So the height is 8 feet at t = 3.63 and t=.12

It should make sense that there are two times. The ball goes up, reaches it's highest height and then comes back down. As such the height will be 8 at some point on the way up and also at some point on the way down.


3 0
3 years ago
Plz help ASAP I will mark u branliest
-BARSIC- [3]

Answer:

Brainliest?

Step-by-step explanation:

1.

subtract 1 from both sides

divide by 2

2.

add 5 to each side

divide by 4

6 0
3 years ago
Read 2 more answers
Triangle FGH has the following side lengths: FG = 5 ft, GH = 10 ft, HF = 12 ft Triangle PQR is similar to triangle FGH. The long
7nadin3 [17]
The first thing we must do for this case is find the scale factor.
 We have then that for the larger side of both triangle, the scale factor is:
 k =  \frac{RP}{HF}
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 k = 0.6
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PQ = k * FG&#10;&#10;PQ = 0.6 * 5&#10;&#10;PQ = 3

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QR = k * GH&#10;&#10;QR = 0.6 * 10&#10;&#10;QR = 6

 Answer:
 
You have that the lengths for the other two sides of triangle PQR are:
 
PQ = 3&#10;&#10;QR = 6
3 0
3 years ago
If you guys want I’ll make it 80 points + BRAINLIEST if you help me with my previous question just please please please let me k
lesya [120]

sure dude whats the question?


8 0
3 years ago
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