What is the slope of the line that contains these points?

The position equation for a particle is s of t equals the square root of the quantity t cubed plus 1 where s is measured in feet

vladimir1956 [14]

$\bf s(t)=\sqrt{t^3+1}
\\\\\\
\cfrac{ds}{dt}=\cfrac{1}{2}(t^3+1)^{-\frac{1}{2}}\cdot 3t^2\implies \boxed{\cfrac{ds}{dt}=\cfrac{3t^2}{2\sqrt{t^3+1}}}\leftarrow v(t)
\\\\\\
\cfrac{d^2s}{dt^2}=\cfrac{6t(2\sqrt{t^3+1})-3t^2\left( \frac{3t^2}{\sqrt{t^3+1}} \right)}{(2\sqrt{t^3+1})^2}\implies 
\cfrac{d^2s}{dt^2}=\cfrac{ \frac{6t(2\sqrt{t^3+1})-1}{\sqrt{t^3+1}} }{4(t^3+1)}$

$\bf \cfrac{d^2s}{dt^2}=\cfrac{6t[2(t^3+1)]-1}{4(t^3+1)\sqrt{t^3+1}}\implies 
\boxed{\cfrac{d^2s}{dt^2}=\cfrac{12t^4+12t-1}{4t^3+4\sqrt{t^3+1}}}\leftarrow a(t)\\\\
-------------------------------\\\\a(2)=\cfrac{215~ft^2}{44~sec}$

8 0

3 years ago

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Write an equation for that graph,where y depends on x. ____

Firlakuza [10]

y = -2x + 6

Steps:

y = mx + b

m is slope

b is the y-intercept

m = -2

b = 6

plug in m and b

y = -2x + 6

5 0

3 years ago

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Can someone plz help me. How can you find the inequalities of 11/15 and 5/7. Next 5/9 and 7/13. Next 11/15 and 5/7. Lastly 5/9 a

LekaFEV [45]

To make this a little clearer, let's give the pairs of inequalities the same denominator:

Question 1:
 $\frac{11}{15}$ ? $\frac{5}{7}$
First, apply the common denominator to the first fraction:
$(\frac{11}{15})7 \\ \frac{11}{15} * \frac{7}{7} \\ \frac{11*7}{15*7} \\ \frac{77}{105}$
Do the same for the second: $15( \frac{5}{7}) \\ \frac{5}{7}* \frac{15}{15} \\ \frac{5*15}{7*15} \\ \frac{75}{105}$
Nest, compare the two fractions:
$\frac{77}{105} \ \textgreater \ \frac{75}{105}$
Therefore:
$\frac{11}{15}$ > $\frac{5}{7}$

Question Two:
$\frac{5}{9}$ ? $\frac{7}{13}$
Apply the common denominator to fraction one:
$13( \frac{5}{9}) \\ \frac{5}{9} * \frac{13}{13} \\ \frac{5*13}{9*13} \\ \frac{65}{117}$
Fraction two:
$9(\frac{7}{13}) \\ \frac{7}{13} * \frac{9}{9} \\ \frac{7*9}{13*9} \\ \frac{63}{117}$
Evaluate:
$\frac{65}{117}$ > $\frac{63}{117}$
Therefore:
 $\frac{5}{9}$ > $\frac{7}{13}$

Hope this helps!

5 0

3 years ago

A store is having a sale on trail mix and jelly beans. For 6 pounds of trail mix and 5 pounds of jelly beans, the total cost is

-Dominant- [34]

6t + 5j= 34
2t + 3j = 16

12t + 10 j = 68
12t + 18j = 96
-8j = -28
j = 3.5

jelly beans= 3.5 and trail mix = 2.75

8 0

4 years ago

Solve the equation for y: -3y - 2 = 10

slavikrds [6]

Answer y=-4

Because it's like you do if backwards

6 0

3 years ago