A trough is 10 feet long and the ends have the shape of isosceles triangles that measure 3 feet across at the top and have a height of 1 foot. If the trough is being filled with water at a rate of 12 ft3 per minute, how fast is the water level rising when the water is 6-inches deep

Answers

Answer 1

Answer:

0.8 ft³/min

Step-by-step explanation:

Assuming that the cross section formed by the water at a depth of x is b. Then, if we use the property of similar triangles we have...

See the attachment for the workings.

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Continuation of the workings

From the question, we're told that the water is 6 inches deep. Converting this inch to ft, we have

6 ft = 0.5 ft.

So we use 0.5 as our x, and then use 12 ft³/min as our dV/dt. Doing this, we have

.

12 = 30 * 0.5 dx/dt

12 = 15 dx/dt

dx/dt = 12/15

dx/dt= 0.8 ft³/min

A Trough Is 10 Feet Long And The Ends Have The Shape Of Isosceles Triangles That Measure 3 Feet Across

Related Questions

Please help me thankss

Answers

Answer:

1/2

Step-by-step explanation:

you can find the ratio by doing 12 / 6 and you will get 2 then you dump a 1 over the 2 to get 1/2 that's not how it works in all tho

Answer:

1:1

Step-by-step explanation:

if the rule was 1:2 then they would have won 4 games so its 1:1

Write an exponential function in the form y=ab^x that goes through points (0,9) and (3, 576)

Answers

Answer:

An exponential function in the form y=9(4ˣ)

Step-by-step explanation:

Step(i):-

Given that exponential function

                  y = a bˣ ...(i)

The equation (i) passes through the point (0,9)

               9 = a (b )⁰ = a

             a =9

Step(ii):-

The equation (i) passes through the point (3,576)

            576 = 9(b)³

         ⇒    [tex]\frac{576}{9} = b^{3}[/tex]

      ⇒     64 = b³

     ⇒     4³ = b³

             [tex](4^{3} )^{\frac{1}{3} } = (b^{3} )^{\frac{1}{3} }[/tex]

             b = 4

Final answer:-

An exponential function in the form y=abˣ

An exponential function in the form y=9(4ˣ)

 

Math Geniuses!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Sorry I don’t know the answer but have a great day! Hope you get the right answer!

Use the grouping method to factor the polynomial below.

x^3+4x^2-3x-12

Answers

x³+4x²-3x-12
= x²(x+4)-3(x+4)
= (x+4)(x²-3)

What is the area?Write your answer as a fraction or as a whole or mixed number

Answers

Answer:

83 3/10

Step-by-step explanation:

multiple the numbers

Sandra calculated her Taxable income as 39,250. She paid 6,000 dollars in federal withholding tax . Based on the table above , what is the amount Sandra Will receive as a refund

Answers

Answer:

i really dont even know

Step-by-step explanation:

Answer:

Sorry if it’s to late but the answer is 56:)

Step-by-step explanation:

SOLUTION
5 Salvador drives 6.5 miles to his aunt's house. For every mile Salvador drives, the
amount of gas in the car's gas tank changes by -0.04 gallon. What is the total
change in the gallons of gas in the car's tank? Show your work.
SOLUTION

Answers

Answer:

-0.26 gallon

Step-by-step explanation:

-0.04x 6.5=0.26

plz answer for 35 points​

Answers

The answer is b I think hope this helps

Answer:

The answer is B.

Step-by-step explanation:

Help me please with math

Answers

Answer:

B. 1 and 10

Step-by-step explanation:

answer is b....have a good day

7. A rectangle has a perimeter of 24 motors
and an area of 35 square meters, what is
the length in meters of the longer side?
AI
B. 3
c.5
D.7
E8

Answers

Answer:

D

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

D

why must it be more than 20 characters???

y varies inversely with x. If y = 4 when x= -6, find the constant of variation and find the value of y when x= -2

Answers

Answer:

constant of variation:  k = -24

y = 12 when x = -2

Step-by-step explanation:

y varies inversely with x equation is:  y = k/x

where 'k' if the constant of variation

plug in:

4 = k/-6

cross-multiply to get value of 'k' which is -24

plug in:

y = -24/-2

y = 12

pls i need help with the attachment its my hw

Answers

Answer:

C

Step-by-step explanation:

It has to be c by process of elimination the circle has to be filled in and on the #5 and as you can see the only one was C

Answer:

D

Step-by-step explanation:

Solving the inequality

2x + 3 ≤ 5 ( subtract 3 from both sides )

2x ≤ 2 ( divide both sides by 2 )

x ≤ 1

The required number line will have a solid circle at x = 1 and the arrow will be going left.

The only graph with these conditions is D


At the farmer's market 1 dozen eggs cost 3.75 What is the cost for 1 dozen eggs?

Answers

Answer: The cost is 3.75

Step-by-step explanation: Since you wrote, 1 dozen eggs costs about 3.75, your question was, "What is the cost for 1 dozen eggs?" So the answer should be 3.75.

x^2+19=10 solve algebraically
4x^2+3=43 solve algebraically

Answers

Answer:

[tex]a)\ x_1=-3i,\ x_2 =3i[/tex]

[tex]b)\ x_1=-\sqrt{10},\ x_2=\sqrt{10}[/tex]

Step-by-step explanation:

Given equations:

[tex]a)\ x^2+19=10\\\\b)\ 4x^2+3=43[/tex]

A. x² + 19 = 10

Step 1: Subtract 19 from both sides.

[tex]\\\implies x^2+19-19=10-19\\\\\implies x^2=-9[/tex]

Imaginary number rule: For any positive real number "k", [tex]\sqrt{-k} = i\sqrt{k}[/tex]

Note: Two imaginary (complex) solutions indicate that the graph will not intersect the x-axis. As a result, it has no real roots.

Step 2: Take the square root of both sides (positive and negative roots).

[tex]\\\implies \sqrt{x^2}=\sqrt{-9}\\\\\implies x=\pm\ i\sqrt{9}\\\\\implies x=\pm\ 3i[/tex]

Step 3: Separate the solutions.

[tex]\implies x_1=-3i,\ x_2 =3i[/tex]

----------------------------------------------------------------------------------------------------------------

B. 4x² + 3 = 43

Step 1: Subtract 43 from both sides.

[tex]\\\implies 4x^2++3-3=43-3\\\\\implies 4x^2=40[/tex]

Step 2: Divide both sides by 4.

[tex]\\\implies 4x^2=40\\\\\implies \dfrac{4x^2}4=\dfrac{40}{4}\\\\\implies x^2=10[/tex]

Step 3: Take the square root of both sides (positive and negative roots).

[tex]\\\implies \sqrt{x^2}=\sqrt{10}\\\\\implies x=\pm\ \sqrt{10}[/tex]

Step 4: Separate the solutions.

[tex]\implies x_1=-\sqrt{10},\ x_2=\sqrt{10}[/tex]

If a circle has a diameter of 24 inches, which expression gives its area in
square inches?

A. 12^2 • pi
B. 12 • pi
C. 24 • pi
D. 24^2 • pi

Answers

A= pi x r^2

radius is diameter / 2
r= 12
so your answer is
A=pi(12)^2

A cyclist travels 15 miles in 45 minutes.
What is his average speed in mph?

Answers

The cyclist’s average speed in mph is 20mph

The answer is 20 Km/hr

first : you have miles . then change it into Km .

second: 45 min to sec

finally speed is the distance per unit time


The quotient x divide 5 is a negative integer. Name two
integers that x could represent and find the quotients

Answers

Answer:

Herk in a boo

Step-by-step explanation:

Two lighthouses flash their lights every 20 seconds and 30 seconds respectively. Given that they flash together at 8 p.m, when will they next flash together?

Answers

One minute later at 8:01pm. One lighthouse will flash 3 times (at 20, 40 and 60 seconds)...the other will flash twice (at 30 and 60 seconds). So they will both flash 60 seconds later, at 8:01

Elimination method 3x + y = 14 4x - y = 7

Answers

Answer:

(3,5)

x=2 and y=5

Find the value of x.
102
146
120
124
x
158
X

Answers

Answer:

x = 70

Step-by-step explanation:

180* (n-2)

180*(6-2)

180*(4) = 720

102 + 146 + 120 + 124 + 158 = 650

720 - 650 = 70

A polygon is a planar figure characterized by a limited number of straight-line segments. The value of the x is 70°.

What is a polygon?

A polygon is a planar figure characterized by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.

The sum of the interior angles of a n-sided polygon is calculated using the formula,

Sum of the interior angles = (n-2) × 180°

For the given polygon, the number of sides is equal to 6. Therefore, the sum of the interior angles of the polygon is,

Sum of the interior angles = (6-2) × 180°

                                            = 4 × 180°

                                            = 720°

Further, the sum of the interior angles for the given polygon can be written as,

Sum of the interior angles = 102° + 146° + 120° + 124° + 158° + x°

720° = 102° + 146° + 120° + 124° + 158° + x°

x = 720° -  (102° + 146° + 120° + 124° + 158°)

x = 720° - 650°

x = 70°

Hence, the value of the x is 70°.

Learn more about Polygon here:

https://brainly.com/question/10441863

#SPJ2

Use the Distributive Property and write the sum of the number as the product of the GCF.
30 + 12

Answers

Answer:

1,2,3 and 6 is the answer

Find the perimeter of a rectangle whose one side measures 20m and diagonal is 29m​

Answers

Answer:

Option A

Step-by-step explanation:

Answer:

1.You draw the rectangle and label on one side 20m

2.Draw a diagonal line inside the rectangle an label the line as 29m

3.Extract the the newly formed right angled triangle.

4.Find the hypotenuse (a+b=c) of the right angle which will give you the value of the unknown side.

5.Calculate the perimeter which is;

P=S+S+S+S

P= 20m+9m+20m+9m

P=29m+29m

P=58m

3-2(3x+1)=19
How would I solve this equation?​

Answers

Step-by-step explanation:

3-2(3x+1)=19

[tex]3 - 6x - 2 = 19 \\ 1 - 6x = 19 \\ - 6x = 19 - 1 \\ - 6x = 18 \\ x = - 3[/tex]

Do 4x and 15+x have the same value when x is 5?
Are 4x and 15+x equivalent expressions? Explain your reasoning.

Answers

Answer:

1. yes 2. no

Step-by-step explanation:

Hi there!

When x is equal to 5, 4x and 15+x have the same value because 4*5= 20 and 15+5 = 20.

4x and 15+x are not equivalent expressions because they cannot be simplified to create the same expression nor will they produce the same answer every time.

I hope this helps!

Find the quotient 7/9 divide 5/6

Answers

Answer:

7/9 ÷ 5/6 = 42/45 as simplified as 14/15 in fraction form. 7/9 ÷ 5/6 = 0.9333 in decimal form.

Step-by-step explanation:

Answer:

14/15

Step-by-step explanation:

7/9 x 6/5 = 42/45 = 14/15

brainliest pls

Please help will give 20 points

Answers

Answer:

not sure but i think its B

Carrie got a $65 gift certificate. She plans to buy a $12 rose bush and as many seed packets as she can for $1.79 each. Which of these inequalities shows x, the number of seed packets she can buy?

Answers

Answer:

she can buy the rose bush and 29 packets of seeds. So i think X= 29

Step-by-step explanation:

Solve for x -2x -3<5

Answers

Answer:

Inequality form

x > - 8

Step-by-step explanation:

hope this helps

Answer:

i think it's

x > - 8

Step-by-step explanation:

hope this helps :)

Solve for x.

PLease need help

Answers

Answer:

x=7

Step-by-step explanation:

22x-4=7x-4+105

cancel both 4 out

22x=7x+105

15x=105

x=7

which statement best describes the graphs of the lines
A. they are parallel
B. they are the same line
C. they intersect at exactly one point
D. they intersect at exactly two points

Answers

Answer:

A

Step-by-step explanation:

Since they have the same slope and have different y-intercept they're parallel

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