Suppose sarah is trying to design a metal box (a rectangular prism), which will hold 450 cubic centimeters of liquid. the length of the box must be 2 times as large as the width. define a function j j that gives the height of the metal box, h h, measured in centimeters in terms of the width of the metal box, w w, measured in centimeters.

Answers

Answer 1

So, the volume of a container can also be thought of as the amount of liquid that the container is capable of holding. It follows that 450=(length)(width)(height). The constraints of the problem say that the length of the box must be twice as large as the width, so it follows that j(height)=(2w)(w)(height)-450. This then implies that j(height)=(2w^2)(height)-450. In simpler terms, the height is defined as 450/(2w^2), or j(w)=450/(2w^2).

Related Questions

Solve for y: 10y + 3.8 = 38.8

Answers

The solution for ( y ) is ( y = 3.5 ).

To solve for y in the equation [tex]$ 10y + 3.8 = 38.8 $[/tex], follow these steps:

Start with the given equation:

[tex]\[ 10y + 3.8 = 38.8 \][/tex]

Subtract 3.8 from both sides to isolate the term with y:

[tex]\[ 10y + 3.8 - 3.8 = 38.8 - 3.8 \][/tex]

[tex]\[ 10y = 35 \][/tex]

Divide both sides by 10 to solve for y :

[tex]\[ \frac{10y}{10} = \frac{35}{10} \][/tex]

y = 3.5

So, the solution for ( y ) is ( y = 3.5 ).

How many yards equals 765 inches?

Enter your answer, as a decimal.

Answers

The amount of yards that equals 765 inches is 21.25 yards.

One inch equals 0.0277778.
So, in order to see how many yards equals 765 inches, all you have to do is multiply 765 by 0.0277778.
765 * 0.0277778 = 21.25.

The correct answer is 21.25

The base of a triangle is 7 inches more than its height. If the area of the triangle is 60 square inches, find the base and height of the triangle.

Answers

144.5 square cmWhat is the area of the triangle on the flag of Bosnia and Herzegovina?17.5 square unitsDetermine the area of the triangle.58.065 square metersWhat is the area of the triangle?576 square inchesJoseph is painting the flag of Brunei (a country in Southeast Asia) for a geography project at school. How many square inches will he cover with white paint?81 square ftAhmad just bought a used sailboat with two sails that need replacing. How much sail fabric will Ahmad need if he replaces sail A?14 inchesCindy made a triangular shaped sculpture with an area of 63 square inches. The height of the sculpture is 9 inches. What is the base length of the sculpture?80 square kilometersFind the area of the triangle.175 square centimetersFind the area of the triangle.28 square centimetersFind the area of the triangle.78 square metersFind the area of the triangle.9 square milesA wildlife conservation group buys a plot of land. How much land does it buy?1,620 square inchesFind the area of the triangle.1,125 square centimetersFind the area of the triangle.189 square millimetersFind the area of the triangle.132 square metersFind the area of the triangle.35 square centimetersFind the area of the triangle.105 square metersFind the area of the triangle.225 square feetFind the area of the triangle.1 acreYou live on a triangular piece of land with a base of 121 yards and a height of 80 yards. One acre of land is equal to 4840 square yards. Find the area of
your piece of land in acres.16 square feetYour neighbor adds a triangular section to his driveway with a base of 4 feet and a height of 8 feet. What is the area of the new section of driveway?2What is the area of a right triangle 2 cm by 4 cm?15What is the area of a right triangle 6 cm by 5 cm?10What is the area of a right triangle 5 cm by 4 cm?12What is the area of a right triangle 4 cm by 6 cm?1/2 base x heightWhat is the formula for the area of a triangle?6What is the area of a right triangle above?48What is the area of the rectangle above in cm^2?30What is the perimeter of the right triangle above?24How many cm is the perimeter of the triangle above?28What is the perimeter of the rectangle above in cm?Look at the drawing of a triangle within a rectangle. The triangle and the rectangle have the same base, b, and height, h.

If the area of the triangle is 48 square units, what is the total area of sections 1 and 2?48 sq unitsThe base (b) of the triangle is ____units.
The height (h) of the triangle is ____ units.

The area of the triangle is ____square units.3
5
7.5Triangle
Find the area of the triangle.

The area of the triangle is
_____ square units40Renee has a triangular garden with an area of 24 square feet. Which drawing shows Renee's garden?A triangular garden has an area of 9 square yards. Which figure could represent the garden?

A polygon has an area of 144 square inches and one of its sides is 10 inches long. If a second similar polygon has an area of 64 square inches, what is the length of the corresponding side in the second polygon?

Answers

Area is proportional to (side length)^2.
or, put it in another way,
side length is proportional to sqrt(area).

so for the given case,
area = 144, sqrt(area)=12, side length = 10.
area = 64, sqrt(area)=8, side length = X

By proportion,
X/8 = 10/12
solve for X
X=(10/12)*8=20/3 = 6 2/3 = 6.67 (approx.)

So side length of second polygon is approx. 6.67 in., or 6 2/3 inches.

James built a small electric car and recorded the distance it traveled. The table below shows the distance traveled (n) during the first 4 seconds after starting (f). Elapsed Time (seconds) Distance Traveled (feet) 1 6.2 2 12.4 3 18.6 4 24.8 Which of the following equations represents the relationship between the distance traveled and the elapsed ti

Answers

Table

Elapsed Time (seconds) Distance Traveled (feet)

1 6.2

2                                        12.4

3                                        18.6

4                                         24.8

Explanation:

You can check that 6.2 / 1 = 12.4 / 2 = 18.6 / 3 = 24.8 / 4 = 6.2

So, the relationship between the distance traveled and the time elapsed is a constant:

distance traveled / time elapsed = 6.2

n / f = 6.2

=> n = 6.2 f

Answer: n = 6.2 f

Answer:

n = 6.2f

Step-by-step explanation:

Given right triangle def what is the value of sin e

Answers

right triangle
10^2 - 8^2 = 100 - 64 = 36
DF = √36
DF = 6
so
sinE = Opp / Hypo
sinE = 6/10
sinE = 3/5

Answer:

Step-by-step explanation:

From the given triangle DEF, we have

[tex](EF)^{2}=(ED)^{2}+(DF)^{2}[/tex]

[tex](10)^{2}=(8)^{2}+(DF)^{2}[/tex]

[tex]100-64=(DF)^2[/tex]

[tex]DF=6[/tex]

Now, we know that SinE=[tex]\frac{Perpendicular}{Hypotenuse}[/tex], thus

[tex]SinE=\frac{DF}{EF}[/tex]

[tex]SinE=\frac{6}{10}=\frac{3}{5}[/tex]

Therefore, the value of SinE is [tex]\frac{3}{5}[/tex].

5.5-x=-4.5-x. how do you solve this?

Answers

Final answer:

The equation 5.5 - x = -4.5 - x has no solution. After cancelling out the variable x, we are left with 5.5 = -4.5, which is a contradiction.

Explanation:

To solve the equation 5.5 - x = -4.5 - x, we first notice that the variable x is present on both sides of the equation. We can simply subtract or add x to both sides to cancel it out. This will give us an equation without variables:

5.5 - x + x = -4.5 - x + x

5.5 = -4.5

This equation suggests that 5.5 is equal to -4.5, which is not true. Therefore, we can conclude that there is no solution to the equation since the two sides of the equation do not balance.

Moreover, this type of equation is an example of a contradiction, meaning that it presents a statement that is inherently false regardless of the value of x. As there is no value of x that can make the equation true, we say that the equation has no solution.

Final answer:

The equation 5.5 - x = -4.5 - x simplifies to 5.5 = -4.5 when the x terms are cancelled out. Since 5.5 does not equal -4.5, the equation has no solutions.

Explanation:

To solve the equation 5.5 - x = -4.5 - x, we can first try to simplify it by adding or subtracting the same value from both sides. This method is based on the principle that whatever you do to one side of the equation, you must do to the other to maintain balance.

In this case, if we add x to both sides of the equation, the x terms will cancel out on both sides, which leaves us with 5.5 = -4.5. Here, we notice that both sides of the equation represent constant values and no longer contain the variable x.

Therefore, since 5.5 and -4.5 are not equal, we can conclude that there is no value of x that can satisfy this equation. This equation is a contradiction, which means there are no solutions.

Please help guys im stuck. THanks

Answers

Angle 3 = 70 ( opposite angles equal each other)

Angle 1 = 90-70 = 20 ( angle 1 plus 70 = 90 )

angle 3 - angle 1 = 70 -20 = 50

Answer is B

Hi guys can I plz get some help I don't understand and can I plz get the answers so I can get a 4 on this paper thx

Answers

so, Deanna starts with 15 bucks in her pocket, and if she plays 1 game, she then has 15 - 0.75(1), if she plays two games, 15 - 0.75(2), if she plays 3, 15 - 0.75(3), if she plays say "g" amount of games, since each game costs 75 cents, then she would have after "g" games, 15 - 0.75(g) or 15 - 0.75g.

Now, Lise has 13 bucks and her game is 50 cents or $0.50, after say 3 games again she has 13 - 0.5(3) and so on, so after "g" games, she would have 13 - 0.5(g) or 13 - 0.5g.

When with both gals have the same amount?

[tex]\bf \stackrel{Deanna}{15-0.75g}=\stackrel{Lise}{13-0.5g}\implies 15-13=0.75g-0.5g\implies 2=0.25g \\\\\\ \cfrac{2}{0.25}=g[/tex]

and surely you know how much that is, since both quantities equal each other, then after that many games, both girls will have the same amount in their pocket.

The height, s, of a ball thrown straight down with initial speed 64 ft/sec from a cliff 80 feet high is s(t) = -16t2 - 64t + 80, where t is the time elapsed that the ball is in the air. What is the instantaneous velocity of the ball when it hits the ground? (2 points)
Select one:
a. 256 ft/sec
b. -96 ft/sec
c. 0 ft/sec
d. 112 ft/sec

The surface area of a right circular cylinder of height 4 feet and radius r feet is given by S(r)=2πrh+2πr2. Find the instantaneous rate of change of the surface area with respect to the radius, r, when r = 4. (2 points)
Select one:
a. 24π
b. 16π
c. 64π
d. 20π

Answers

b. -96 ft/sec
For the first part, solve the equation you were given to find the time at which the height of the ball is 0. Sos(t) = -16t^2 - 64t + 800 = -16t^2 - 64t + 80
This is a standard quadratic equation that you can solve using the quadratic formula with a = -16, b = -64, and c = 80, so the roots are: 1 and -5.We can ignore the -5 root since that's what the situation would have looked like if we went back in time 5 seconds and launched the ball upwards from the ground. But since we're not doing time travel, the solution of interest is the 1. So the ball hits the ground one second after throwing it.The formula for distance under constant acceleration is d = 1/2 A T^2. That formula accounts for the -16t^2 term, so A is 32. So during that 1 second it takes for the ball to hit the ground, it will be accelerated 1 * 32 = 32 ft/sec. That is added to the initial velocity the ball was given. So at the moment it hits the ground it's going-64 ft/sec - 32 ft/sec = -96 ft/sec.
For the second problem, the key thing to note is "instantaneous rate of change". When you see that phrase you should immediately think "first derivative". So let's calculate the first derivative of the equation given.S(r)=2πrh+2πr^2S'(r)=2πh+4πr
Now substitute the value 4 for r, givingS'(4)=2πh+4π4 = 2πh+16π
And we have a problem. That value isn't one of the available options, so something is wrong. The problem is choice "b" takes into account the increase in surface area for the end caps on the cylinder, but it doesn't take into account the increase in surface area for the side of the cylinder which is what the 2πh term accounts for. Please show this to your teacher.

The instantaneous velocity of the ball when it hits the ground is found by deriving the height function and solving for the time of impact. The instantaneous rate of change of the surface area of a cylinder with respect to its radius when r = 4 is found by differentiating the surface area function and evaluating at r = 4.

The student's question involves two separate parts of physics and calculus related to kinematics and surface area calculations.

Part 1: Instantaneous Velocity of the Ball

The height, s, of a ball thrown straight down with initial speed 64 ft/sec from a cliff 80 feet high is given by s(t) = -16t2 - 64t + 80. The instantaneous velocity when the ball hits the ground is the derivative of position with respect to time, s'(t), evaluated at the time t when s(t) = 0 (when the ball hits the ground).

First, we find t by solving -16t2 - 64t + 80 = 0. Then, we find the derivative s'(t) = -32t - 64 and evaluate it at the found time, which gives us the instantaneous velocity.

Part 2: Rate of Change of Surface Area

The surface area of a right circular cylinder of height 4 feet and radius r feet is given by S(r) = 2πrh + 2πr2. The instantaneous rate of change of the surface area with respect to the radius, when r = 4, is the derivative dS/dr evaluated at r = 4. This is done by differentiating S(r) with respect to r and substituting r = 4 into the resulting expression.

You purchased 8 pounds 10 ounces of candy from a candy shop. You want to split it equally among 3 classrooms at a local school./7425116/3d9f02b9?utm_source=registration

Answers

they will each get 2 pounds and 7 ounces

If you have 8 punds and 10 oz then we would convert everything into one term/oz.

Since 16 oz are in a pund you would end up with a total of 138 ounces and divide that by 3 and you would get 46.

So each class of the 3 would get 46 ounces/oz.

How do you simplify sqrt of x^20?

Answers

[tex]\bf \sqrt{x^{20}}\implies \sqrt{x^{10\cdot 2}}\implies \sqrt{(x^{10})^2}\implies x^{10}[/tex]

Analyze the diagram below and complete the instructions that follow.
Find the value of x and the value of y.

A.x = 15, y = 10
B.x = 20, y = 50
C.x = 50, y = 10
D.x = 50, y = 20
Answer is C x=50 y=10

Answers

Answer:

C. [tex]x=50[/tex], [tex]y=10[/tex]

Step-by-step explanation:

We have been given an image of two intersecting lines. We are asked to find the value of x and y for our given diagram.

We know that when two line intersect each other, then vertical angles are congruent.

Using vertical angles theorem, we will get a system of equations as sown below:

[tex]3y=x-20...(1)[/tex]

[tex]5x-100=y+140...(2)[/tex]

From equation (1), we will get:

[tex]x=3y+20[/tex]

Upon substituting this value in equation (2), we will get:

[tex]5(3y+20)-100=y+140[/tex]

[tex]5*3y+5*20-100=y+140[/tex]

[tex]15y+100-100=y+140[/tex]

[tex]15y=y+140[/tex]

[tex]15y-y=y-y+140[/tex]

[tex]14y=140[/tex]

[tex]\frac{14y}{14}=\frac{140}{14}[/tex]

[tex]y=10[/tex]

Therefore, the value of y is 10.

To find the value of x, we will substitute [tex]y=10[/tex] in equation (1) as:

[tex]3*10=x-20[/tex]

[tex]30=x-20[/tex]

[tex]30+20=x-20+20[/tex]

[tex]50=x[/tex]

Therefore, the value of x is 50 and option C is the correct choice.

Answer:

Option C) x = 50, y = 10

Step-by-step explanation:

We are given a two pairs of vertically opposite angle in the image.

Vertically opposite angle is formed when two lines intersect anf they are always equal.

Thus, we can write:

[tex]3y = x -20\\\Rightarrow x - 3y = 20\\5x-100 = y +140\\\Rightarrow 5x - y =240[/tex]

Solving the two equations in two variable, we get:

[tex]x - 3y = 20\\5x - y =240\\\text{Multiplying first equation by 5}\\5x - 15y = 100\\\text{Subtracting the equations}\\5x - 15y-(5x-y) = 100-240\\-14y = -140\\y = 10\\ x - 3(10) = 20\\x = 20 + 30\\x =50[/tex]

The value of x is 50 and y is 10.

What the answer to this

Answers

To round a number to the nearest hundreds, you will need to check the number in the tens position:
(1) If the number in the tens position is less that 5, then, all you will do is convert the tens and units of the original number to zeros and that's it.
(2) If the number in the tens position is 5 or more, then you will add one to the hundreds and then convert the tens and units to zeros.

Taking a look at the number we have (12,000), we will find that the number in the hundreds position is a zero, which means that the second case is invalid here.
This means that, the number might be any number whose tens is less than 5.
Examples:
12,010
12,019
12,045
12,049
12,022

Witch set of orderd pairs contains only points that are on the graph of the function y=12-3x

A.(-3,-27),(0,0),(6,54)
B.(-18,10),(-6,6),(18,-2)
C(-5,27),(-1,15),(8,-12)
D(-7,-9),(-4,0)(2,18)

Answers

You can try then by plotting the points in.
The answer is C

Make sure by plotting in the points, lets take (-5,27)
y = 12 -3(-5)
y = 12 + 15
y = 27
27 = 27
This is correct

Lets try (-1,15)
y = 12 -3(-1)
y = 12 + 3
y = 15
15 = 15
This is correct

Lets try (8,-12)
y = 12 -3(8)
y = 12 - 24
y = -12
-12 = -12
This is correct too.

The correct ordered pairs are C(-5,27),(-1,15),(8,-12)

A town's population has been growing linearly. In 2003, the population was 60000, and the population has been growing by 2700 people each year.

Write an equation for the population x years after 2003.

Answers

y=2700x+60000 hope that helps ;)

Find the derivative of the function y = sin(tan 4x)

Answers

[tex]\bf y=sin[tan(4x)]\implies \cfrac{dy}{dx}=\stackrel{chain~rule}{cos[tan(4x)]\cdot sec^2(4x)\cdot 4} \\\\\\ \cfrac{dy}{dx}=4cos[tan(4x)]sec^2(4x)[/tex]

1 mile is equal to 5280 feet. You've walk 0.20 mile on a track. How many feet have you watched?

Answers

0.20 is 1/5 of 1 mile, so a fifth of 5,280 feet would be 1,056

I had that like on my pre test in 5th grade I think that's math right

Steven bagged 52 pounds of potatoes. About what is that measure in kilograms? Round to the nearest hundredth

Answers

1 pound = 0.454 kilogram

52 x 0.454 = 23.608

Rounded to nearest hundredth:
23.61 kilograms

The formula A=P(1+r)t is used to show the total amount owed for a loan with a simple annual interest rate.

Solve for r.

Answers

We are asked to express r in terms of A, P, and t.

We first divide both sides of the equation by t, which gives us

[tex]\displaystyle{ \frac{A}{t}=P(1+r) [/tex],

then, dividing both sides by P, we have

[tex]\displaystyle{ \frac{A}{Pt}=1+r [/tex].

Swap the sides:

[tex]\displaystyle{ 1+r= \frac{A}{Pt}[/tex]

Finally subtracting 1 from both sides gives us

[tex]\displaystyle{ r=\frac{A}{Pt}-1[/tex].

Answer: [tex]r=(\frac{A}{P})^{\frac{1}{t}}-1[/tex]

Step-by-step explanation

Compound interest is the addition of interest to the principal sum of a deposit or a loan.

Let P = principal amount which was taken as a loan then the accumulated amount A is given by

[tex]A=P(1+r)^t[/tex].......(1)

where, r is the rate of simple annual interest in decimal.

t is the time applied for interest.

For solving r divide both sides of equation by P in (1),we get

[tex]\frac{A}{P}=(1+r)^t\\\Rightarrow(\frac{A}{P})^{\frac{1}{t}}=1+r\\\Rightarrow\ r=(\frac{A}{P})^{\frac{1}{t}}-1[/tex].

Jack has 5 craft sticks he needs four times that number for a project how many craft sticks does Jack need all together

Answers

Solving this problem simply only requires us the knowledge of multiplication.

So we are initially given that there are 5 craft sticks. So if we need four times that amount, that is written as:

5 x 4

Which is equal to 20

So Jack needs 20

Determine the slope and y-intercept of the line. y = 8.5x + 6

Answers

the slope is 8.5, the y-intercept is 6, y=mx+b was the original formula and m=slope and b=y-intercept :)

Answer: Slope = 8.5 and y-intercept = 6

Step-by-step explanation:

The intercept form of a linear equation is given by :_

[tex]y=mx+c[/tex], where m( coefficinet of x ) is the slope and c (constant term) is the y-intercept.

The given equation in intercept form : [tex]y = 8.5x + 6[/tex]

Here , the coefficient of c = 8.5

thus , the slope = 8.5

Also, the constant term = 6

Thus, the y-intercept =6

the calendar shows the number of days carlota rides her bike each month. each time ahe rides her bike, she travels 10 miles.is it rwasonable to say that carlota will bike more than 500 miles in 6 months?

Answers

Yes if she rides her bike around 9 days each month she’ll be more than 500 miles in 6 months. (10 miles x 9 day x 6 months = 560miles)

cory earns 52.50 in 7 hours. find the unit rate

Answers

divide them:

52.50 / 7 = 7.50 dollars per hour

It actually equals $7.46 to be precise

write a trinomial expression equivalent to (2x+5)(3x-2)

Answers

The required trinomial expression that is equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.

According to the question, we have to determine the trinomial expression that is equivalent to the (2x+5)(3x-2).

What is a polynomial function?

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.

Here,
Given expression in the question,
= (2x+5)(3x-2)
Following the distributive property
= 2x (3x - 2) + 5 (3x - 2)
= 6x² - 4x + 15x - 10
= 6x² - 11x - 10

Thus, the required trinomial expression that is equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.

Learn more about polynomial function here:

https://brainly.com/question/12976257
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Final answer:

The trinomial expression equivalent to (2x+5)(3x-2) is calculated using the FOIL method, resulting in 6x² + 11x - 10.

Explanation:

To write a trinomial expression equivalent to the product of two binomials, (2x+5)(3x-2), we perform the multiplication by using the distributive property (also known as the FOIL method).

Multiply the first terms: 2x × 3x = 6x²

Multiply the outside terms: 2x × (-2) = -4x

Multiply the inside terms: 5 × 3x = 15x

Multiply the last terms: 5 × (-2) = -10

Combine like terms:

6x² + (15x - 4x) - 10 = 6x² + 11x - 10

The trinomial expression equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.

The sum of two binomials is 3z-6. If one binomial is z+4, what is the other binomial?

Answers

The answer is 2z-10. Hope it helps.

To do this subtract 3z-6 and z+4.

3z-6 -(z+4)
3z - 6-z-4
2z - 10

So, your answer is 2z - 10.
Please rate this brainliest if this helped :)

What can a doctor use to determine a patient's body fat percentage?
Bioelectrical impedance machine
MRI machine
Waist measurement
Weight measurement

Answers

Bioelectrical impedance machine

Bioelectrical impedance machine can be used to determine a patient's body fat percentage

What is Fat percentage?

The body fat percentage of a human or other living being is the total mass of fat divided by total body mass, multiplied by 100

A doctor can use a bioelectrical impedance machine to determine a patient's body fat percentage.

This machine works by sending a small electrical current through the body and measuring how quickly it travels through different types of tissue.

Since fat and muscle have different electrical conductivity, the machine can estimate the amount of fat in the body based on the resistance to the current.

Hence, Bioelectrical impedance machine can be used to determine a patient's body fat percentage

To learn more on Fat percentage click:

https://brainly.com/question/14457888

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17,325 round to the nearest thousand

Answers

To help us round, let's look at the two thousands 17,325 is in between, 17,000 and 18,000. Which one of those two is 17,325 closer to? The closer number is where you'll want to round to.

—
Is 1.0227 a rational number?

Answers

Yes it is, because it can be calculated by dividing two integers.

Please someone help me this is the second time I posted this question....

What is the equation, in point-slope form, for a line that goes through (8, −4) and has a slope of −5/6 ?

A. y−4=−5/6(x−8)
B. y+4=−5/6(x−8)
C. y−4=−5/6(x+8)
D. y+4=−5/6(x+8)
Please provide an explanation on how to do this.

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 8}}\quad ,&{{ -4}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -\cfrac{5}{6} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-4)=-\cfrac{5}{6}(x-8) \\\\\\ y+4=-\cfrac{5}{6}(x-8)[/tex]

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