The base of a triangle is shrinking at a rate of 5 cm/s and the height of the triangle is increasing at a rate of 9 cm/s. Find the rate at which the area of the triangle changes when the height is 12 cm and the base is 4 cm.

Provide your answer below:
The rate of change of the area of the triangle is ___ cm²/s.

Answers

Answer 1

Answer:

Step-by-step explanation

Area of a triangle

      A = ½bh

dA/dt = ½(b(dh/dt) + h(db/dt)

dA/dt = ½(4(9) + 12(-5))

dA/dt = ½(36 - 60)

dA/dt = ½(-24)

dA/dt = -12 cm²/s

Answer 2

The rate of change of the area of the triangle is [tex]-12 cm^2/s[/tex].

What is Area?

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to an area of an open surface or even the boundary of a three-dimensional object, whereas the area of a plane region as well as plane area refers to a area of a shape or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat. It is the two-dimensional equivalent of a curve's length.

A shape's area can be calculated by contrasting it with squares of a known size.

[tex]\frac{\mathrm{d} b(t)}{\mathrm{d} t}=-5cm/s[/tex]

[tex]\frac{\mathrm{d} h(t)}{\mathrm{d} t}=9 cm/s[/tex]

[tex]\frac{\mathrm{d}A }{\mathrm{d} t}=\frac{1}{2}\left (b\frac{\mathrm{d} h}{\mathrm{d} t} +h\frac{\mathrm{d} b}{\mathrm{d} t}\right )[/tex]

[tex]\frac{\mathrm{d} A}{\mathrm{d} t}=-12 cm^{2}/s[/tex]

Hence, The rate of change of the area of the triangle is [tex]-12 cm^2/s[/tex].

Learn more about area from link

https://brainly.com/question/25292087

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Related Questions

A ball is thrown upward and outward from a height of 8 feet. The height of the ball, f(x), in feet, can be modeled by
f(x) = -0.1x² +0.6x+8
where x is the ball's horizontal distance, in feet, from where it was thrown. Use this model to solve parts (a) through (c).
WEB
a. What is the maximum height of the ball and how far from where it was thrown does this occur?
The maximum height is feet, which occurs feet from the point of release.
(Round to the nearest tenth as needed.)

Answers

Check the picture below.

let's change the decimal values to fractions, say 0.1 to 1/10 and 0.6 to 6/10 = 3/5, so then

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-\frac{1}{10}}x^2\stackrel{\stackrel{b}{\downarrow }}{+\frac{3}{5}}x\stackrel{\stackrel{c}{\downarrow }}{+8} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{~~ \frac{3}{5}~~}{2\frac{-1}{10}}~~,~~8-\cfrac{\left( \frac{3}{5} \right)^2}{4\left(-\frac{1}{10} \right)} \right)\implies \left(\cfrac{~~ \frac{3}{5}~~}{\frac{1}{5}}~~,~~8+\cfrac{\frac{9}{25}}{\frac{2}{5}} \right)[/tex]

[tex]\left( \cfrac{3}{5}\cdot \cfrac{5}{1}~~,~~8+\left[ \cfrac{9}{25}\cdot \cfrac{5}{2} \right] \right)\implies \left(3~~,~~8+\cfrac{9}{10} \right)\implies \stackrel{\stackrel{\textit{maximum height}}{\qquad \downarrow }}{\underset{\underset{\textit{horizontal distance}}{\uparrow \qquad \quad }}{\left( 3~~,~~8\frac{9}{10} \right)}}[/tex]

Identify the function as a power function, a polynomial function, or neither.


[tex]fx=\frac{x^2}{x^2-1}[/tex]

Answers

Answer:

I think this is neither. As you can see the value of x reaches infinity and negative infinity, the value gets infinetly closer to 1.

A bag contains 4 red balls and 6 blue balls. If 3 balls are selected at random, find the probability of selecting 3 red balls?

Answers

The probability is 4⋅3⋅2⋅1/10•9•8•7=(4/4)(6/0)/(10/4)=1/210 so the probability of selecting 3 red balls would be 1/210

ABCD is a parallelogram. Determine the value of a.

Answers

Answer:

a = 6

Step-by-step explanation:

The opposite sides of a parallelogram are congruent , so

BA = CD , that is

7a - 3 = 3 + 6a ( subtract 6a from both sides )

a - 3 = 3 ( add 3 to both sides )

a = 6

Answer:D

Step-by-step explanation:

I took the test

Hep help help help help math math

Answers

Answer:

5(37)+10

10(17.5)+5

Step-by-step explanation:

5x+10=180

-10 -10

5x=170

divide by 5

x=37

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

10x+5=180

-5 -5

10x=175

divide by 10

x=17.5

What is the value of 40 1/2÷3 1/2

Answers

11.57142857142857 Is the answer

Answer:

81/7 (11.57, 11 4/7)

Step-by-step explanation:

Lets rewrite these mixed fractions

[tex]40\frac{1}{2}=\frac{81}{2}[/tex]

[tex]3\frac{1}{2} =\frac{7}{2}[/tex]

Here we can do divide these two numbers:

[tex]\frac{\frac{81}{2} }{\frac{7}{2} }=\frac{81}{7}[/tex]

The answer therefore is 81/7, or 11.571 (11 4/7)

[tex]3^{2x+1} -4.9^{x} =-9[/tex]

Answers

Ok done. Thank to me :>

Which expression shows a way to find 20% of 950

1/20 / 950

1/20 • 950

1/5 • 950

1/5 / 950

Answers

Answer:

C

Step-by-step explanation:

20% x 950

Calculate 20% x 950 = 190

Match the options one by one and there

Answer:

C: 1/5 · 950

Step-by-step explanation:

I got it correct on I-ready.

Hope this helps!!

Please help me will give brainliest

Answers

Answer:

f(x) = 8.917x³ + 2x² + 0.083x - 7

Step-by-step explanation:

f(x)= y

Let the coefficients of x³, x², x be a, b, c and the constant be d

y= ax³ + bx² + cx + d

When y = -65, x = -2

-65= a(-2)³ + b(-2)² + c(-2) + d

-65= -8a + 4b - 2c + d ...eq. 1

When y = -14, x = -1

-14= a(-1)³ + b(-1)² + c(-1) + d

-14= -a + b - c + d ...eq. 2

When y = -7, x = 0

-7= a(0)³ + b(0)² + c(0) + d

-7 = d ...eq.3

When y = 4, x = 1

4= a(1)³ + b(1)² + c(1) + d

4= a + b + c + d ...eq. 4

when y = 78, x = 2

78 = a(2)³ + b(2)² + c(2) + d

78= 8a + 4b + 2c + d ...eq. 5

From eq. 3, d is - 7

putting d as - 7 in equations 1, 2, 4 and 5

In eq. 1,

-65= -8a + 4b - 2c - 7

-58= -8a + 4b - 2c ...eq. 6

In eq. 2

-14= -a + b - c - 7

-7= -a + b - c ...eq. 7

In eq. 4,

4= a + b + c - 7

11= a + b + c ...eq. 8

In eq. 5

78= 8a + 4b + 2c - 7

85= 8a + 4b + 2c ...eq.9

Subtracting eq. 9 from eq. 6

-143 = -16a - 4c... eq 10

subtracting eq. 8 from eq 7

-18= -2a - 2c

9= a + c

a = 9 - c ...eq 11

putting a as 9 - c in eq. 10

-143 = -16(9 - c) - 4c

-143 = -144 + 16c - 4c

1= 12c

c = 1/12 or 0.083

putting c as 1/12 in eq. 11

a = 9 - 1/12

a = 107/12 or 8.917

Putting a as 107/12 and c as 1/12 in eq. 8

11= 107/12 + b + 1/12

multiplying through by 13

132 = 107 + 12b + 1

132 - 108 = 12b

24= 12b

b = 24/12

= 2

Therefore, a= 8.917, b= 2, c= 0.083 and d = -7

f(x) = 8.917x³ + 2x² + 0.083x - 7

What is the area of a triangle with the Base of √10 and a height of √13

Answers

Answer:

5.70

Step-by-step explanation:

[tex] a = \frac{1}{2} bh \\ \frac{ \sqrt{10} \sqrt{13} }{2} \\ \frac{ \sqrt{130} }{2} [/tex]

[tex]a = \frac{11.401}{2} \\ = 5.70[/tex]

Answer:

5.70

Step-by-step explanation:

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Answers

Answer:

2x³ + 4x² cub. inches

3x³ + 36x² + 105x cub. inches

x³ + 32x² + 105x cub. inches

Step-by-step explanation:

Volume of the small box = x × 2x × (x + 2)

= 2x²(x + 2)

= 2x³ + 4x² cubic inches

Volume of the large box = (x + 5)(x + 7) × 3x

= (x² + 12x + 35) × 3x

= 3x³ + 36x² + 105x cubic inches

Difference between Volume of large box and small box = 3x³ + 36x² + 105x - (2x³ + 4x²)

3x³ + 36x² + 105x - 2x³ - 4x²

x³ + 32x² + 105x cubic inches

math problem need help give 5 stars and good rating if do

Answers

Answer:

The answer is A, 20%.

Step-by-step explanation:

If you find 30 out of 150, it is 20%. A simple way to do it is add 30 up until you get 150. So in this case it is 5 times. Then you do 100% divided by 5 which is 20%. Hope this helps!

(giving brainlelist if answered correctly!) which of the following inequalities is -4
?

Answers

-5 is always smaller than -4. So, x might be -4. So, A is an option you should select.2 is greater than -4. So, x might be -4. So, B is an option you should select.If we place -4 in x, we get 3(-4)+4, i.e., -12 + 4 = -8. So, 3x + 4 = -8. Therefore, you cannot select C because it cannot be greater than, it should be always equal to.5(-4) = -20, 2(-4) - 3 = -8 -3 = -11. -11 is greater than -20 but they are never equal. So, you cannot select D.4 - 2(-4) = 4 + 8 = 12. 12 is greater than -6. Therefore, you should select E.

Answer

A, B, E.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Is 111111 divisible by 37?

Answers

Answer:

Yes

Step-by-step explanation:

3003 woooow

Answer:

yes

Step-by-step explanation:

A is divisible by  B, if after dividing them, A ÷ B, the remainder is zero.

A train travels 150 miles in three hours at the same rate how many miles will it travel in eight hours

Answers

Answer:400

Step-by-step explanation:

150 / 3 = 50 so 50 x 8= 400

If a batch of cookies uses
2
2
3
cups of sugar, then how much sugar is needed to make 5 batches of cookies

Answers

Answer:

13 1/3 cups of sugar

Step-by-step explanation:

John made 357$ for 17 hours of work.
At the same rate, how many hours would he have to work to make $237???

Answers

Answer: 14 hours

Step-by-step explanation: First I found the unit rate of how much money per hour. So, 357 divided by 17 = 21. So know I know that she earns 21$ per hour. Then, I did 237 divided by 17 which would be 13 remainder 16. Since he only get paid if he works for a full hour, I think the answer would be 14.

[tex]\begin{array}{ccll} \$&hrs\\ \cline{1-2} 357&17\\ 237&x \end{array}\implies \cfrac{357}{237}=\cfrac{17}{x}\implies \implies \cfrac{119}{79}=\cfrac{17}{x}\implies 119x=1343 \\\\\\ x = \cfrac{1343}{119}\implies x = \cfrac{79}{7}\implies x = 11\frac{2}{7}\leftarrow \textit{11 hours, 17 minutes and 8 seconds}[/tex]

Please help. Will give brainliest.

Answers

Answer:

i am going to but 11 bagels but i am going to buy them for a price under 5$

i am also going to buy 4 extra if we are still hungry

Step-by-step explanation:

i dunno you prob need a anwser with little thought like this becuase of auto grading systems hope this helps

Help me plz NO LINKS


Thanks

Answers

Answer:

please I am tired texting and answering questions.

write clearly please

Answers

Answer: this is 4

Step-by-step explanation: A+b=2+2=4

The price of an item has risen to $152 today. Yesterday it was $95. Find the percentage increase.

Answers

Answer:

60% increase

Step-by-step explanation:

152 - 95 = -57

57 / 95 = 0.6

0.6 x 100 = 60

Find the domain of the graphed function.

Answers

Answer:

A

Step-by-step explanation:

the domain is all the possible numbers that the x can be, so to find this from the graph you find the x-value of the leftmost point, which is -1 in this case, and the x-value of the rightmost point, which is 3. this means the range of values would be -1 <= x <= 3

suppose we want to choose 2 colors, without replacement from 3 colors red,bule and green

Answers

Then U Would Choose Blue And Red

What is 3894 x 6? Use the distributive property to solve.

Answers

Answer: 23,364

Step-by-step explanation:6 x 3000 + 6 x 800 + 6 x 90 + 6 x 4

Which is the equation of a parabola with Vertex (0,0) and directrix x=-2?

Answers

Answer:

y^2 = 8x

or

x = 1/8 y^2.

Step-by-step explanation:

The general form for this type of parabola is

y^2 = 4ax where the focus is at (a, 0) and the directrix  is x = -a

So the equation is y^2 = 4*2x

that is y^2 = 8x.

I need help on this question pls​

Answers

Answer:

t = 17.5 f = 12

Step-by-step explanation:

If MNOP is a square, you know that each angle is going to be 90°. To solve, let's first set each equation equal to 90°:

[tex]90 = 4t + 20[/tex]

and

[tex]90 = 7f + 6[/tex]

Then solve both equations:

[tex]90 = 4t + 20 \\ 70 = 4t \\ 17.5 = t[/tex]

and

[tex]90 = 7f + 6 \\ 84 = 7f \\ 12 = f[/tex]

I hope that helps!

harold bought 3 pounds of red apples

Answers

Answer:

what's your question?  

yesssssssssssssssssssssssssssssssssssssss

4/k =8/3 ​ what is k?

Answers

Answer:

1.5

Step-by-step explanation:

4 x 2 = 8, so k x 2 = 3

3 / 2 = 1.5

19. Ram and Rahim are partners in a firm sharing profits in the ratio of 3: 2. Kabir is admitted as a partner for 1/5th share of profits. Machinery would be appreciated by 10% (Book Value of 80,000) and Building would be depreciated by 20% (Book Value of 2,00,000). Unrecorded Debtors of 1,250 would be brought to books. There is a liability of 2,750 included in Sundry Creditors that is not to be paid. What will be the Gain (Proñt Loss on revaluation? (a) Loss of 28,000. (c) Profit 28,000. (6) Loss 40,000. (d) Profit of 40,000.​

Answers

Answer:

make me brainlist

Step-by-step explanation: firm sharing profits and losses in the ratio of 3

2. From Ist April, 2020 they decided to share the future profits equally. On this date, the General Reserve

showed a balance of 1,60,000; Revaluation of fixed assets resulted into a gain of "1,02,000 and stock resulted

to a loss of 22,000. On this date, the goodwill of the firm was valued at $3,60.000

Pas necessary journal entries for the above transactions on reconstitution of the form

Bolutions

I need help asap
Please help me!!
contains ordered pairs

Answers

Answer:

which question ?

Step-by-step explanation:

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