Find the function y = f(t) passing through the point (0, 18) with the given first derivative.
dy/dt = 1/8 t

y = ?

Answers

Answer 1

Answer:

[tex]\displaystyle y = \frac{t^2}{16} + 18[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

FunctionsFunction NotationCoordinates (x, y)

Calculus

Derivatives

Derivative Notation

Antiderivatives - Integrals

Integration Constant C

Integration Rule [Reverse Power Rule]:                                                                   [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Property [Multiplied Constant]:                                                             [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

Point (0, 18)

[tex]\displaystyle \frac{dy}{dt} = \frac{1}{8} t[/tex]

Step 2: Find General Solution

Use integration

[Derivative] Rewrite:                                                                                         [tex]\displaystyle dy = \frac{1}{8} t\ dt[/tex][Equality Property] Integrate both sides:                                                        [tex]\displaystyle \int dy = \int {\frac{1}{8} t} \, dt[/tex][Left Integral] Integrate [Integration Rule - Reverse Power Rule]:                 [tex]\displaystyle y = \int {\frac{1}{8} t} \, dt[/tex][Right Integral] Rewrite [Integration Property - Multiplied Constant]:           [tex]\displaystyle y = \frac{1}{8}\int {t} \, dt[/tex][Right Integral] Integrate [Integration Rule - Reverse Power Rule]:              [tex]\displaystyle y = \frac{1}{8}(\frac{t^2}{2}) + C[/tex]Multiply:                                                                                                             [tex]\displaystyle y = \frac{t^2}{16} + C[/tex]

Step 3: Find Particular Solution

Substitute in point [Function]:                                                                         [tex]\displaystyle 18 = \frac{0^2}{16} + C[/tex]Simplify:                                                                                                             [tex]\displaystyle 18 = 0 + C[/tex]Add:                                                                                                                   [tex]\displaystyle 18 = C[/tex]Rewrite:                                                                                                             [tex]\displaystyle C = 18[/tex]Substitute in C [Function]:                                                                                [tex]\displaystyle y = \frac{t^2}{16} + 18[/tex]

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Integration

Book: College Calculus 10e


Related Questions

please answer it soon

Answers

Hey dude we’re both from Nepal so here’s the written worksheet hope it helps :)

Find the distance between the points (4,0) and (0, 3).

Answers

Step-by-step explanation:

Given points are (4,0) and (0,3)

The distance between these two points =√(0-4)^2+(3-0)^2

=√16+9

=√25

=5 units

Answer:

(4,0) = ([tex]x_{1}[/tex],[tex]y_{1}[/tex])

(0,3)=([tex]x_{2} ,y_{2}[/tex])

distance between the points = [tex]\sqrt{(x_{1}-x_{2})^2 + (y_{1}-y_2 )^2 }[/tex]

distance=5

Step-by-step explanation:

Tara uses 8.8 pints of white paint and blue paint to paint her bedroom walls. 4 5 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?

Answers

Answer:

the blue paints of 1.76 pints is used to paint her bedroom walls

Step-by-step explanation:

Given that

Tara uses 8.8 pints of white paint

And, the 4 by 5 of this amount represent the white paint

We need to find out the number of paint used by the blue paint

So,

= 8.8 - (8.8 × 4 ÷ 5)

= 8.8 - 7.04

= 1.76 pints

Hence, the blue paints of 1.76 pints is used to paint her bedroom walls

A middle school took all of its 6th grade students on a field trip to see a ballet at a theater that has 1300 seats. The students filled 1001 of the seats in the theater. What percentage of the seats in the theater were filled by the 6th graders on the trip?

Answers

77%

I like to use ratios and cross multiply for problems like this. Take the part (1001) over the whole (1300), and that equals x percent of 100 percent.

1001/1300 = x/100
100100 = 1300x
x = 77

RS 1000 was distributed equally a anmong certain number of people. If there were 5 people more each would have received RS 20 less .Among how many people was the amount distributed? Find it.

Answers

Answer:

is answer 13.50781059 ?

someone help i'll give brainliest to right answer!

QUESTION: A pentagon has angles that measure 110°, 90°, 80°, 115°, and v. What is v?

Answers

Answer:

145

Step-by-step explanation:

angles in a pentagon add up to equal 540

Hence, 110 + 90 + 80 + 115 + v = 540

( note that we just created an equation that we can use to solve for v )

We now solve for v using the equation created

110 + 90 + 80 + 115 + v = 540

step 1 combine like terms

110 + 90 + 80 + 115 = 395

we now have 395 + v = 540

step 2 subtract 395 from each side

540 - 395 = 145

395 - 395 cancels out

we're left with v = 145

The parabola in the image has its focus at (4,3). Its directrix is the line y=1. The point (8,6) is on the parabola.
4
3
2
ol

Answers

Answer

:

Step-by-step explanation:

Could you help me with one of those two questions, please? Please

Answers

Answer

Step-by-step explanation:

Hope it helps you!

You have started keeping track of your spending habits. You have noticed that after 12 days you have
$1281 left in your account. You check again after 17 days have passed and your account is now at $861.
How many days will it take before you run out of money (assume you are spending money at a constant
rate)? Marks will be awarded only for the use of equations where t is the time elapsed in days and m is
the money left in your account in dollars.

Answers

Answer:

Time taken to elapse the remaining $861  = 10.25 days

Step-by-step explanation:

Assuming that I am spending at a rate of -x dollars per day

Let initial amount be A

The rate of expenditure = 1281-861/5 = 84 dollars per day

Time taken to elapse the remaining $861 = $861/$84 per day

= 10.25 days

50 POINTS

Show work for both questions.

Pleaseee don’t answer if you don’t know, I need this really soon.

Answers

Step-by-step explanation:

a)

[tex]\sin^{2}x + \cos^{2}x = 1[/tex]

Dividing both sides by sin^2x, we get

[tex]1 + \frac{\cos^{2}x }{ \sin^{2}x} = \frac{1}{\sin^{2}x } [/tex]

The 2nd term on the LHS is simply cot^2x and the RHS is simply csc^2x

[tex]1 + \cot^{2}x = \csc^{2}x[/tex]

b)

[tex]2 \sin x = 1[/tex]

[tex] \sin x = \frac{1}{2} [/tex]

[tex]x = \sin^{ - 1} (\frac{1}{2}) = \frac{\pi}{6} [/tex]

You can also graph it to arrive at the solution.

Did u get help

On you question?

which ones plsss help

Answers

they are not the same shape or size. hope this helps!
The answer is they are not the right shape and size

Type the expression that results from the following series
of steps:
Start with x and multiply by itself.

Answers

Answer: x^2 (the ^ represents that the next number is an exponent)

Step-by-step explanation:

Any number squared (to the power of 2) is just itself multiplied by itself. Remember, multiplication is repeated addition and exponents are repeated multiplication.

HELP ME PLEASEEEEEEEEE

Answers

[tex](11 + x) \div 2 = 7 \\ 11 + x = 14 \\ x = 14 - 11 \\ x = 3[/tex]

[tex](4 + y) \div 2 = 5 \\ 4 + y = 10 \\ y = 10 - 4 \\ y = 6[/tex]

[tex](3,6) - option \: a[/tex]

What are the coordinates of vertex ?

Answers

Answer:

(0, -8)

Step-by-step explanation:

What is the inverse of the function f(x) = 64x2 when x 2 0?

Answers

Answer:

The answer is A.

Y=64x²

X=64y²

X/64=y2

Then y = + or - root of x /8

Barry wants to make a drawling this is 1/2 the size of the original. If a tree in the original drawling is 11 inches tall and 7 inches wide, what will be the length and width of the tree in Barry's drawling?

Answers

Answer: 5.5 inches, 3.5 inches

Step-by-step explanation:

Given

Barry wants to make a drawing i.e. half the size of original

The length and width of the original drawing are  11 inches and 7 inches respectively.

So, the intended drawing is obtained by multiplying the original dimensions by [tex]\frac{1}{2}[/tex]

The length of barry's drawing is

[tex]\Rightarrow 11\times \frac{1}{2}\\\\\Rightarrow 5.5\ \text{inches}[/tex]

The breadth of barry's drawing

[tex]\Rightarrow 7\times \frac{1}{2}\\\\\Rightarrow 3.5\ \text{inches}[/tex]

Por favor alguien que me ayude ( es un examen final) :(​

Answers

Answer:

A) 24

Step-by-step explanation:

Answer:

m = 24

Step-by-step explanation:

Write the word sentence as an equation.

The sum of nine and one-fourth of a number g is equal to a number h.

Answers

Answer:

9+1/4g = h

Step-by-step explanation:

Aaron is a chocolate vendor. He finds that he needs 25 identical sweet boxes to pack all the chocolates he has if he puts 24 chocolates per box. How many sweet boxes will he need to pack all the chocolates, if he puts only 30 chocolates in a box?Immersive Reader (1 Point)

Answers

Answer: 20 boxes of chocolates

Step-by-step explanation:

First find out the total number of chocolates he has:

= 25 boxes * 24 chocolates per box

= 600 pieces of chocolate

The number of boxes needed if the chocolates are packed 30 in a box is:

= Total number of chocolates / Number of chocolates per box

= 600 / 30

= 20 boxes of chocolates

7m²(4-3m²)
this one is algebra question and multiply so plzz plzz replyy ​

Answers

Answer:

ok so the answer is 28² - 21 to the power of 4

Step-by-step explanation:

Simplify 4^3(3^2+11)(7^4-7^4)(10^10) show work

Answers

put that in photo math

will give brainiest!!
Find the volume of the cone.
9 cm
r = 6 cm
V = [?] cm3
Round to the nearest tenth.

Answers

Volume of a cone is equal to pi * r^2 * h/3.

In this case:

pi * 6^2 * 9/3

pi * 36 * 3

108pi

Answer: 339.3

Answer: 339.292006588 or V ≈ 339.29

Step-by-step explanation:  Here is the formula that you need...

V = π [tex]r^{2}[/tex] [tex]\frac{h}{3}[/tex]

1. Multiply π (pi or approximately 3.14) by  [tex]6^{2}[/tex] (36).

2. Multiply your answer from the last step which is 113.097335529 by [tex]\frac{9}{3}[/tex] or 3.

3. Final Answer should be 339.29 for the nearest tenth.

V = π [tex]6^{2}[/tex] [tex]\frac{9}{3}[/tex] which gives you...

V = 339.29

I hope this helped you!!

1. Complete the following table for the proportional relationship:
Hot Dogs
I Total Price
1
2
$3.00
3
$7.50
12
$31.50
55
What is the constant of proportionality for the relation above?

Answers

Add 1.50 to each time the price goes up

Step-by-step explanation: Multiply by two each time and you will have your answer 1 hot dog is 1.50 two are 3.00 use that method and you will have the correct answer

The histogram represents the time it takes employees to get to work each morning.
Which statement correctly describes the data?

A.The data is skewed left because the time it takes employees to get to work tails off to the left.

B.The data is skewed left because the time it takes employees to get to work tails off to the right.

C.The data is skewed right because the time it takes employees to get to work tails off to the right.

D. The data is skewed right because the time it takes employees to get to work tails off to the left.

Answers

Answer:  The Real answers are 1) ✔ skewed left and 2) ✔ 1-3

Step-by-step explanation:

Please mark me brainliest

I need 3 more to move to a higher level but

i'm just glad to help.

TRUE or FALSE
(a) In a scatterplot, the response is shown on the horizontal axis with the explanatory variable
on the vertical axis.
(b) If all of the data lie along a single line with nonzero slope, then the r
2 of the regression is
1. (Assume the values of the explanatory variable are not identical).
(c) If the correlation between the explanatory variable and the response is zero, then the slope
will also be zero.
(d) The use of a linear equation to describe the assocation between price and sales implies
that we expect equal differences in sales when comparing periods with prices $10 and $11
and periods with prices $20 and $21.
(e) The linear equation (estimated from a sequence of daily observerations):
Estimated shipments = b0 + 0.9*(Orders Processed) implies that we expect twice as many
shipments when the number of orders processed doubles only if b0 = 0.
(f) The intercept estimates how much the response changes on average with changes in the
predictor.

Answers

I'll do parts (a) through (c) to get you started

(a) False. The explanatory variable is always along the x axis, and the response variable is along the y axis. The response variable reacts to whatever the input explanatory variable is, hence the name "response".

---------

(b) True. If all data lie along a single straight line with nonzero slope, then either r = -1 or r = 1. If we have all data points on a line with some negative slope, then r = -1. If the regression slope is positive, then r = 1. Either way, it will lead to r^2 = 1 because (1)^2 = 1 and (-1)^2 = 1. In other words, there are two solutions to r^2 = 1 and they are r = -1 or r = 1. In the case of r = -1, we say the data has perfect negative linear correlation. With r = 1, the data has perfect positive linear correlation.

---------

(c) True. If r > 0, then we have some level of positive correlation which means the regression slope is positive in some way. If r < 0, then the regression slope is negative in some way. That must mean r = 0 leads to the regression slope having a flat horizontal line. This could mean one of two things: i) The points are all on or near the same curve such as a parabola, ii) The points are completely randomly scattered about. If case (i) happens, then it's better to use nonlinear regression instead of linear regression.

pleaseeeeeeeeeeeeeeeeeee answer

Answers

Answer:

The answer is y=x-5

Step-by-step explanation:

y=x-5

A TV is priced at $475.25. There is a 7% sales tax rate. What is the sales tax for the TV in dollars and cents?

Answers

Answer:

$33.27

Step-by-step explanation:

The correct answer is 33.79 dollars

5.) James is 4 feet 7 inches tall? How tall is James in inches? A 55 inches B. 54 inches C. 47 inches D. 11 inches ?​

Answers

Answer:

55 inches

Step-by-step explanation:

4 feet x 12 inches per foot = 48 inches + 7 inches = 55 inches

If f(x) = 8x2-5, what is f(-1)

Answers

Answer:3

Step-by-step explanation:

Simply plug in -1 for anywhere you see x in the equation so...

8(-1)^2-5

8(1)-5

8-5

3

Hope this helps

Step-by-step explanation:

Remember math is a language

f(x) : A function of x where x can be any number including a number you choose

when you see f(-1), this tells you what the function is at this given x value. So you substitute - 1 wherever you see x

8(-1)2 - 5

A truck is bought at the price of $60,000. The value decreases at the rate of .25 every year (t). The exponential expression 60,000(0.75)t describes this situation. Find the value of the truck at 2 years.

Answers

Answer:

$33750

Step-by-step explanation:

Replace t with 2.  The correct formula is

[tex]60000(.75)^t[/tex]   (t is an exponent)

With t = 2, the value of the truck is

[tex]60000(.75)^2=33750[/tex]

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