How do you find the derivative of h(t)=sqrt(t)(1-t^2)

Answers

Answer 1
Answer:

Answer:

Step-by-step explanation:

h(t)=√((t)(1-t^2))\nh^(2)(t)=t(1-t^2)=t-t^3\n diff. w.r.t.,\n2 h(t)h'(t)=1-3t^2\nh'(t)=(1-3t^2)/(2 h(t)) \nh'(t)=(1-3t^2)/(2√((t)(1-t^2)) )


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Suppose that the equation of motion for a particle (where s is in meters and t in seconds) is s = 5 t^2 - 8 t + 3
find the acceleration at the instant when the velocity is at 0

Answers

Differentiate equation
v = 10t - 8
Differerentiate again
a = 10

Accelleration will always be 10m/s^-2

Why do both ways of writing the numbers as ten and ones describe the same number?

Answers


its just the form of counting and not necessarily the different number

Final answer:

Both ways of writing numbers as tens and ones describe the same number because our counting system is based on powers of ten. This means that each place in our numbering system is ten times greater than the place to its right. Scientific and exponential notations simplify arithmetic, making it easier to multiply and divide large and small numbers.

Explanation:

The reason why both ways of writing the numbers as tens and ones describe the same number is because our counting system is essentially based on powers of ten. This powers-of-ten notation effectively means that each place in our numbering system is ten times greater than the place to its right. This principle all stems from human beings starting to count with their ten fingers.

For example, if we consider a number such as 34, this can be expressed as 3 tens and 4 ones. Alternatively, it could also be written in exponential notation as 3x10^1 + 4x10^0, which is still 34. This is because the power (exponent) of 10 correlates with the number of places the decimal point is shifted to give the digit number.

In scientific notation, this makes arithmetic simpler. To multiply two numbers expressed as powers of ten, you only need to multiply the numbers out front and then add the exponents. This way of counting and doing arithmetic is not only easier to write but also simplifies the multiplication and division of large and small numbers.

Learn more about Powers of Ten here:

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Keshawn is asked to compare and contrast the domain and range for the two functions.f(x) = 5x
g(x) = 5

Answers

For the function 5x, the range is the value of f(x) which is five times the x and the domain is the value of x which can be the ratio of f(x) and 5. For the second function which is g(x) = 5, the range is 5 all through out the graph while the domain is infinity.

The equation shows the relationship between x and y:y = 9x − 2

What is the slope of the equation?

−9
−2
7
9

Answers

The slope of the equation is 9.

The correct option is D.

What is a slope?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

The equation shows the relationship between x and y:

y = 9x − 2.

The slope-intercept form of the equation:

y = mx + b,

where m is the slope and b is the y-intercept.

Comparing the slope-intercept form with the given linear equation,

we get,

m = 9 and b = -2

Therefore, slope m = 9.

To learn more about the slope;

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9

Explanation:
For a general equation of a line, y= mx +c
m represents the slope.
In this case 9 is the slope of the line

Please help! forgot how to subtract integers!

Answers

Answer: -15

Step-by-Step Explanation:
1) Reorder the terms
36-51
2) Use the rule: a-b=-(b-a)
-(51-36)
3) Use the algorithm method
51
-36
——
15
4) After simplification, we have:
-(51-36)=-15
5)Therefore, -51+36=-15
-15

Sheila bought burgers and fries for her children and some friends. the burgers cost $2.05 each and the fries are $.85 each. she bought a total of 14 items, fir a total cost if $19.10. how many of each did she buy?

Answers

Let's have B stand for burgers, and F stand for fries.
2.05B+0.85F=$19.10  - This equation is set equal to total price.
B+F=14  - This equation is set equal to total number of items.
Subtract the F in the bottom equation.
B=14-F
Put this in place of B in the first equation.
2.05(14-F)+0.85F=19.10
Make sure you distribute the 2.05 properly, over both the 14 and the F.
28.7 - 2.05F+0.85F=19.10
Collect like terms for the F values.
28.7 - 1.2F=19.10
Subtract 28.7 from both sides.
-1.2F=-9.6
Divide by -1.2 on both sides.
F=8
Put this value in place of F in either equation.
B+8=14
B=6
So F=8 and B=6.