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AURORKA [14]
3 years ago
6

The position of an object at time t is given by s(t) = -9 - 3t. Find the instantaneous velocity at t = 8 by finding the derivati

ve.
Mathematics
1 answer:
Yakvenalex [24]3 years ago
6 0

Hello! There are a few ways to find the derivative. One famous formula is below:

Note, t = x = 8

\frac{f(x + h) - f(x)}{h}

To find the derivative of s(t) = -9 - 3t let insert it into our formula:

\frac{f(x + h) - f(x)}{h}

\frac{(-9 - 3(x + h)) - (-9 - 3x)}{h}

Insert x = 8

\frac{(-9 - 3(8 + h)) - (-9 - 3(8))}{h}

Do the Math

\frac{(-9 - 3(8 + h)) - (-9 - 3(8))}{h}

\frac{(-9 - 24 - 3h)) + 9 +24)}{h}

Group Like Terms

\frac{-9 + 9- 24 +24 - 3h )}{h}

Cancel Terms and Finish Doing The Math

\frac{-9 + 9- 24 +24 - 3h )}{h}

\frac{ -3h }{h}

\frac{ -3h }{h} = -3

---------------------------------------------------------------------------------------

So when t = 8 the instantaneous velocity = -3

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If the endpoints of the diameter of a circle are (−8, −6) and (−4, −14), what is the standard form equation of the circle?
kondaur [170]

Equation of the circle is (x+6)^{2}+(y+10)^{2}=20.

Solution:

The endpoints of the diameter of a circle are (–8, –6) and (–4, –14).

Center of the circle = Mid point of the diameter

Mid point formula:

$P(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)

Here, x_1=-8, y_1=-6, x_2=-4, y_2=-14

$P(x, y) =\left(\frac{-8-4}{2}, \frac{-6-14}{2}\right)

$P(x, y) =\left(\frac{-12}{2}, \frac{-20}{2}\right)

$P(x, y) =(-6, -10)

Center of the circle = (–6, –10)

Radius is the distance between center and any endpoint of the diameter.

To calculate the radius using distance formula.

r=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}

Here, x_1=-6, y_1=-10, x_2=-8, y_2=-6

r=\sqrt{\left(-8-(-6)\right)^{2}+\left(-6-(-10)}\right)^{2}}

r=\sqrt{(-8+6)^{2}+(-6+10)^{2}}

r=\sqrt{(-2)^{2}+(4)^{2}}

r=\sqrt{20} units

The standard form of the equation of a circle is

(x-a)^{2}+(y-b)^{2}=r^{2}, where (a, b) are center and r is the radius.

Here, center = (–6, –10) and r=\sqrt{20}

(x-(-6))^{2}+(y-(-10))^{2}={(\sqrt{20})} ^{2}

(x+6)^{2}+(y+10)^{2}=20

Equation of the circle is (x+6)^{2}+(y+10)^{2}=20.

4 0
3 years ago
What is 4²(4²)? <br> 2. 5⁴(5)÷2¹? <br> 3. (5+3)²? <br> Solve the following expressions
Nat2105 [25]

Answer:

256, 3125/2, 64

Step-by-step explanation:

4^2(4^2)=16(16)=256

5^4(5)/2^1=625(5)/2=3125/2

(5+3)^2=8^2=8*8=64

7 0
3 years ago
The ratio of boys to girls is 3:4 and the ratio of girls to adults is 5:7 what is the ratio of children to adults
Ilya [14]

Answer:

the ratio is 12:7 but im not 100% sure

6 0
3 years ago
Calculate simple interest earned on a deposit of $500 at a rate of 5% for 5 years. $125 $500 $625 $12,500
Sergio [31]

Answer:

$125

Step-by-step explanation:

Given:

deposit, P=  $500

rate,i =  5%

time,t= 5 years

I=P*i*t

where P is principal amount

i is interest rate

t is time

I is simple interest

Putting values we get:

I=500*0.05*5

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8 0
3 years ago
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Task: E = mc2
Afina-wow [57]

Answer:

$c=\left(\frac{E}{m} \right)^{\frac{1}{2} }$

Step-by-step explanation:

E = mc^2

$c^2=\frac{E}{m} $

$c=\sqrt{\frac{E}{m} } $

or

$c=\left(\frac{E}{m} \right)^{\frac{1}{2} }$

3 0
3 years ago
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