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

#SPJ2


Related Questions

The dot product of u ∙ u = 45 what is the length of u?

Answers

Answer:

67 hah why you solve this

[tex]\textbf{u} \cdot \textbf{u} = 45\\\\\implies |\textbf{u}|^2 =45\\\\\implies |\textbf{u}| = 3\sqrt{5}[/tex]

The mass of a an atom of helium is 6.65 x 10−24. Use scientific notation to express the mass of 250 helium atoms. A) 1.6625 x 10−21 B) 1.6625 x 10−22 C) 1.6625 x 10−24 D) 1.6625 x 10−26

Answers

Answer: its A

Step-by-step explanation:

i know this is it

please get this done asap

Answers

Answer:

1)2 2)2y=4  y=2 x=1

Step-by-step explanation:

For what values of k

Answers

If y = cos(kt), then its first two derivatives are

y' = -k sin(kt)

y'' = -k² cos(kt)

Substituting y and y'' into 49y'' = -16y gives

-49k² cos(kt) = -15 cos(kt)

⇒   49k² = 15

⇒   k² = 15/49

⇒   k = ±√15/7

Note that both values of k give the same solution y = cos(√15/7 t) since cosine is even.


For what value of x does 32X – 9^3x-4?

Answers

Answer: X = 4/61

Step-by-step explanation

It takes 4/5 of an hour to fill 1/2 tank.how many tanks can she fill in an hour

Answers

Answer:

5/8 of a tank

Step-by-step explanation:

Divide 1/2 by 4 to get how much of a tank you would be able to fill in 1/5 of an hour.  1/2 ⁒ 4 is 1/8 so she can fill 1/2+1/8 of a tank or 5/8 of a tank.

Evaluate ( f/g)(x) if f(x) = 2x and g(x) = 3x – 2 when x = 2.

Answers

Answer:

1

Step-by-step explanation:

(f/g)(x)

= [tex]\frac{f(x)}{g(x)}[/tex]

= [tex]\frac{2x}{3x-2}[/tex] ← substitute x = 2 into the expression

= [tex]\frac{2(2)}{3(2)-2}[/tex]

= [tex]\frac{4}{6-2}[/tex]

= [tex]\frac{4}{4}[/tex]

= 1

Solve. x 2 = 7
pls help!!

Answers

Answer:

x = 14

Step-by-step explanation:

1) Multiply both sides by 2.

x = 7 * 2

2) Simplify 7 * 2 to 14.

x = 14

Answer:

D.

Step-by-step explanation:

when using diversions in fractions to whole numbers you will always multiply the denominator by the whole number. So 2 x 7 equals 14. :))

Would you use SSS or SAS to prove the triangles​ congruent? If there is not enough information to prove the triangles by SSS or​ SAS, write​ "not enough​ information". Explain your answer.

Write a congruence statement and give a reason why the triangles are congruent. Select the correct choice below​ and, if​ necessary, write the vertices of the second triangle in the correct order.

Answers

Answer:

option B is correct answer. ∆SVZ~=∆YVX, SSS

Step-by-step explanation:

reasons,

VY=VS, S

YX=SZ, S

VX=VZ, S

therefore, ∆SVZ~=∆YVX.

hope this helps you.

The two triangles are congruent by side angle side property. The correct option is A.

What is congruency?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.

Given that there are three triangles and these three triangles are connected to each other at the centres' A, B, and C.

The diameter of the three circles is HF, DF, and DH. The three diameters are similar in shape and are also equal to each other.

To know more about congruency follow

brainly.com/question/2938476

#SPJ2

Less than and equal to is closed or open

Answers

Less than or equal to is a closed cricke on the number line

Answer:

less than is

<

Step-by-step explanation:

equal to is =

mark me as brainliest pls

Simplify Exponents and Roots

Answers

The answer is A: 2 square root 2.

Name the triangle described

Answers

Answer:

acute angle

Step-by-step explanation:

different angles will produce different "opposite side" lenghts, so the angle has 3 distinct angles and therefore 3 distinct sides, different sides means is an Scalene.

Now, one of the angles is 90° or namely a right-angle, that makes it a Right Scalene Triangle.

B = {x|x ∈ N and 1 ≤ x < 9}

Answers

Answer:

Set membership x ∈ X means x is an element of the set X. (Non-membership is written x ∈ X.) Set inclusion X ⊆ Y means every element of X is an element of Y ; X is a subset of Y .

Step-by-step explanation:

Carry on learning

True or False (See Image)

The remainder theorem can be used to check if a binomial is a factor of a larger polynomial.

Answers

Answer: true

Step-by-step explanation:

Solve -2/3x > 8 or -2/3x < 4.

{x | x > -12 or x < -6}
{x | -12 < x < -6}
{x | x < -12 or x > -6}

Answers

Answer: Choice C

{x | x < -12 or x > -6}

=========================================================

Explanation:

Let's solve the first inequality for x.

(-2/3)x > 8

-2x > 8*3

-2x > 24

x < 24/(-2)

x < -12

The inequality sign flips when we divide both sides by a negative value.

Let's do the same for the second inequality.

(-2/3)x < 4

-2x < 4*3

-2x < 12

x > 12/(-2)

x > -6

The conclusion of each section is that x < -12 or x > -6 which points us to choice C as the final answer.

Side note: The intervals x < -12 and x > -6 do not overlap in any way. There's a gap between the two pieces. We consider these intervals to be disjoint. The number line graph is below.

please help me do this question​

Answers

Answer:

hope you understand my answer:)

Which represents the RANGE of the following relation? {(-6, 5), (-4, 3), (-1, 0), (4, 3)}

Answers

Answer:

5, 3, 0, 3 are all the ranges! Hope this helps

Step-by-step explanation:

Ranges are on the right, domains are on the left

Plot 1[tex]\frac{2}{5}[/tex] −12, and −2[tex]\frac{1}{10}[/tex] on the number line.

Answers

Answer:

1st= 2.4 on the line

2nd= -0.5 on the line

3rd=2.1 on the line

Step-by-step explanation:

1st=because each line represents 1 part so if it is split into 5 you have to treat 2 lines as one

2nd 1/2=0.5 so -1/2= -0.5

3rd if one line is one part then it is 2.1

Solve for x + (1/x):

3x + (2/x) - 4 = 2(x+9) - (7 - (1/x))

Answers

Answer:

Step-by-step explanation:

he Nassau Bahamas Community College (NBC) claims that students who take statistics spend on average 19 hours a week working. The population standard deviation is not known. Statistics students in MAT 102 believe students work more than 19 hours because they want to make more money.

Answers

Using the t-distribution, it is found that since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that the students' claim that they work more than 19 hours is correct.

At the null hypothesis, it is tested if they spend on average 19 hours a week working, that is:

[tex]H_0: \mu = 19[/tex]

At the alternative hypothesis, it is tested if they spend more than 19 hours a week working, that is:

[tex]H_1: \mu > 19[/tex]

We have the standard deviation for the sample, hence, the t-distribution is used.

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.

Searching the problem on the internet, it is found that the values of the parameters are:

[tex]\overline{x} = 24.2, \mu = 19, s = 12.59, n = 25[/tex]

Hence, the value of the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{24.2 - 19}{\frac{12.59}{\sqrt{25}}}[/tex]

[tex]t = 2.07[/tex]

The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05 and 25 - 1 = 24 df is of [tex]t^{\ast} = 1.71[/tex]

Since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that the students' claim that they work more than 19 hours is correct.

To learn more about the t-distribution, you can take a look at https://brainly.com/question/13873630

HELP ME PLEASEEEEEE I WILL GIVE BRAINLIEST

Answers

Answer:

DE, EW, WD

Step-by-step explanation:

From shortest line to longest line this would be the correct order.

8) A school community had planned to reduce the number of grade 9 students per class room by constructing additional class rooms. However, they constructed 4 less rooms than they planned. As the result, the number of students per class 10 more than they planned. If there are 1200 grade nine students in the school, determine the current number of class rooms and the number of students per class.​

Answers

Step-by-step explanation:

Let "c" be the original number of classrooms.

The 1200/c was the original number of students per classroom.

----

Equation:

1200/(c-4) = (1200/c)+10

Multiply thru by c(c-4)

---

1200c = 1200(c-4)+10c(c-4)

---

1200c = 1200c-4800 + 10c^2-40c

----

10c^2-40c-4800 = 0

c^2-4c-480 = 0

Factor:

(c-24)(c+20) = 0

---

Positive solution:

c = 24 (# of classrooms originaly planned)

The radius of a circle wheel is 35 cm. How many revolutions does it make to cover a distance of 81.40

Answers

Answer:

.37 resolutions

Step-by-step explanation:

2×22/7×35

44.5×=220

0.37 revolutions

Bill wanted to know how many times students at his middle school go to the beach each week during the summer. He surveyed every other middle school student at the mall last Saturday. After analyzing the data collected, Bill determined that the average student from his middle school goes to the beach about 2.4 times a week during the summer. What error did he make in the survey?

Answers

The survey was intended for Bill's middle school during the summer. The

survey was administered to students of other schools on a Saturday.

The type of error is the selection bias error.

Reasons:

The type of error made is a non sampling error, given that the target of the

study is the number of times in a week students at his middle school

attend the beach during the summer.

The errors are; Selection bias error.

The given that the students survey are not from his middle school.The survey was carried out once on a Saturday, where the target was during the summer.

The selection bias error is a type error that is due to the researcher

chooses what to study, such that the participant have common

characteristics rather than being random.

Learn more about selection bias error here:

https://brainly.com/question/13727092

Find
∂f
∂x
,
∂f
∂y
, and
∂f
∂z
.
f(x, y, z) = 32xyz

Answers

Answer:

what are the measurements for 1 and 2?

Step-by-step explanation:

George Washington

A 2ft-by-2ft square is divided into smaller squares and portions are shaded. What is the area of the shaded portion?

Answers

Answer:

1.5 ft^2

Step-by-step explanation:

Since the length is divided into 4 parts,

Length of a small square = 2/4

= 0.5 ft

Hence,

Area of 1 small square = (0.5)(0.5)

= 0.25 ft^2

Area of shaded portion = Area of 6 small squares

= 6(0.25)

= 1.5 ft^2

Step-by-step explanation:

The area of the shaded cubes is 3 square feet.

What is a square?

A square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is given side²

We have,

Since the 2 ft-by-2 ft square is divided into 16 smaller squares, each smaller square has an area of:

(2/4)ft = 0.5ft.

Now,

Out of the 16 smaller squares, 6 smaller cubes are shaded.

Since each smaller cube occupies the space of one of the smaller squares, the total area of the shaded cubes is 6 times the area of one of the smaller squares.

The area of the shaded cubes is:

6 x 0.5ft² = 3ft²

Thus,

The area of the shaded cubes is 3 square feet.

Learn more about squares here:

https://brainly.com/question/22964077

#SPJ2

Write an expression that is the product of two factors and is equivalent to -2x - 10

PLEASE HELP

Answers

Answer:

-2(x + 5)

Step-by-step explanation:

When a retired police officer passes away, he leaves $325,000 to be divided among his five children and three grandchildren. The will specifies that each child is to get twice as much as each grandchild. How much does each get?

Answers

grandchildren get 25,000 and child gets
50.000

HELP! Due in 5 minutes

Answers

ANSWER:

the first one: 30x+48

The second one: x y^2(10 y + 15)

The third one: 30 x y - 5 x^2

Hope this helped!

sorry if im wrong. :)

GOOD LUCK!! <3

A rock is launched from a cannon. Its height, h(x), can be represented by a
quadratic function in terms of time, x, in
seconds.

After 1 second, the rock is 94 feet in the
air; after 2 seconds, it is 176 feet in the
air.

Complete the height function, h(x), for this situation

h(x) =

Answers

Answer:

The height, in feet, of the rock after 5 seconds = 875 feet

Step-by-step explanation:

Other Questions
Adding a few more points to this one plz answer the question in the picture identify the error in the following sentence and the best way to fix it The sum of a number and negative three, multiplied by the number? A wedding venue holds no more than 185 guests. If 319 people have said they are attending, how many more people does the venue have room for? Drzewko decyzyjne o "Chopcy z Placu Broni" (dokadnie to o Gerebie) what is 3 1/3 - 1 1/2 Hassan surveyed 120 of the students in his school about their favorite color. 114 students said their favorite color was purple. What percentage of the surveyed students said their favorite color was purple? 1. What do we call the study of the earth and its structure? Explain how the linear rate spring operates? answer this pleaseas percentages civil society is a voluntary and self-mobilized social group i did the upgrade what do i do now? how many active volcanoes are there in the united states A farmer has 220 bushels of apples to sell at roadside stand. She sells an average of 14 3/5 each day. Represent the total change in the number of bushels has for sale after 6 days.The total change in the number of bushels has for sale is ???, please answer as a fraction A recipe that serves 6 people calls for 1 1/2 cups of sugar. Suppose you have 9 cups of sugar. Do you have enough to make the recipe for 40 people? Laura made 3/4 of a kilogram of trail mix. If she puts 1/4 of a kilogram into each bag, how many bags can Laura fill? A cart with an unknown mass is at rest on one side of a track. A student must find the mass of the cart by using newtons second law. The student attaches a force probe to the cart and pulls it while keeping the force constant. A motion detector rests on the opposite end of the track to record the acceleration of the cart as it is pulled. The student uses the measured force and acceleration values and determines that the carts mass is 0. 4kg. When placed on a balance, the carts mass is found to be 0. 5kg. Which of the following could explain the difference in mass?. extrano a mi sobrina, what does the underlined word mean What advice would you give to someone who is just beginning to be physically active? Omar saved the same amount ofmoney each week for 4 weeks. Hewrote the equation below to showhow much he saved. In the equation,Sis the total amount of moneysaved, in dollars, and wis thenumber of weeks.S = 2.5w