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3 years ago

Solve for v in terms of s, t, v. u=-tsv

1 answer:

6 0

Suppose an object starts moving at u and gains an acceleration of a. After time t, it gets a speed v after travelling a distance of s.

a = (v - u) / t => v - u = at

v = u + at

s = ut + 1/2(v - u) t

s = ut + 1/2 (at) t

s = ut + 1/2 at2

v2 = (u + at)2

v2 =u2 + 2uat + a2t2

v2 = u2 + 2a (ut + 1/2 at2)

v2 = u2 + 2as

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Factor the expression below.

Sonbull [250]

Answer:

(3x -1) (3x+1)

Step-by-step explanation:

9x^2 - 1

Rewriting

(3x)^2 -1^2

This is the difference of squares a^2 -b^2 = (a+b) (a-b)

(3x -1) (3x+1)

3 0

3 years ago

Read 2 more answers

A soup can in the shape of a right circular cylinder is to be made from two materials. The material for the side of the can cost

Advocard [28]

Answer:

Radius = 1.12 inches and Height = 4.06 inches

Step-by-step explanation:

A soup can is in the shape of a right circular cylinder.

Let the radius of the can is 'r' and height of the can is 'h'.

It has been given that the can is made up of two materials.

Material used for side of the can costs $0.015 and material used for the lids costs $0.027.

Surface area of the can is represented by

S = 2πr² + 2πrh ( surface area of the lids + surface are of the curved surface)

Now the function that represents the cost to construct the can will be

C = 2πr²(0.027) + 2πrh(0.015)

C = 0.054πr² + 0.03πrh ---------(1)

Volume of the can = Volume of a cylinder = πr²h

16 = πr²h

$h=\frac{16}{\pi r^{2}}$ -------(2)

Now we place the value of h in the equation (1) from equation (2)

$C=0.054\pi r^{2}+0.03\pi r(\frac{16}{\pi r^{2}})$

$C=0.054\pi r^{2}+0.03(\frac{16}{r})$

$C=0.054\pi r^{2}+(\frac{0.48}{r})$

Now we will take the derivative of the cost C with respect to r to get the value of r to get the value to construct the can.

$C'=0.108\pi r-(\frac{0.48}{r^{2} })$

Now for C' = 0

$0.108\pi r-(\frac{0.48}{r^{2} })=0$

$0.108\pi r=(\frac{0.48}{r^{2} })$

$r^{3}=\frac{0.48}{0.108\pi }$

r³ = 1.415

r = 1.12 inch

and h = $\frac{16}{\pi (1.12)^{2}}$

h = 4.06 inches

Let's check the whether the cost is minimum or maximum.

We take the second derivative of the function.

$C"=0.108+\frac{0.48}{r^{3}}$ which is positive which represents that for r = 1.12 inch cost to construct the can will be minimum.

Therefore, to minimize the cost of the can dimensions of the can should be

Radius = 1.12 inches and Height = 4.06 inches

5 0

3 years ago

3/4^2 + 1^2 = x2<br><br> solve for x with work shown! pls help!

photoshop1234 [79]

Answer:

X=19/32

Step-by-step explanation:

3/4^2+1^2=2*x

3/4^2+1=2x

3+(4^2)/4^2=2x

3+16/4^2=2x

19/4^2=2x

19/(2^2)^2=2x

19=16(2x)

19=16*2x

32x=19

32x/32=19/32

x=19/32

This took alot of time goodluck!

8 0

2 years ago

Read 2 more answers

Easton wants to put a variety of donuts in a display case. The case is large enough to hold 100 donuts. Complete the table below

shutvik [7]

The amounts for each donut are given as follows:

Strawberry: 15.

Chocolate: 45.

Sprinkle: 40.

<h3>How to obtain the amounts?</h3>

The amounts for each donut are found applying the proportion, multiplying the decimal equivalent of each percentage by the total number of donuts.

From the problem, the total number of donuts is given as follows:

100 donuts.

The percentages of each type of donuts are given as follows:

Strawberry: 15%.

Chocolate: 45%.

Sprinkle: 40%.

The decimal equivalent of each percentage is given as follows:

Strawberry: 0.15.

Chocolate: 0.45.

Sprinkle: 0.4.

Hence the amounts are given as follows:

Strawberry: 15, as 0.15 x 100 = 15.

Chocolate: 45, as 0.45 x 100 = 45.

Sprinkle: 40, as 0.4 x 100 = 40.

More can be learned about proportions at brainly.com/question/24372153

#SPJ1

3 0

1 year ago

Darnell starts the month $952.43 in his checking account. Darnell buys an iPhone 7 for $217.49 with tax included, and two kindle

ki77a [65]

Answer:

Therefore his new balance=$712.95

Therefore his new balance is =$ 930.44

Step-by-step explanation:

Darnell starts the month $ 952.43 in his checking account.

He buys an iPhone 7 for $ 217.49 with tax included and two kindle books that each $7.99.

The price of two books is =$(7.99× 2)= $ 15.98

Total amount that he paid for iPhone 7 and two books is =$(217.49+15.98)

=$233.47

Therefore his new balance = $(952.43- 233.47)

=$712.95

The new iPhone 7 is not as awesome as promised , and Darnell returns it.

He will get the price of iPhone refund.

Therefore his new balance is $(712.95+217.49)

=$ 930.44

8 0

3 years ago