In a triangle, the base is increasing at a constant rate of 2.8 cm per second, while the height is decreasing at a constant rate of 0.7 cm per second. At the instant when the base of the triangle is 6 cm and the height of the triangle is 10 cm, what is the rate of change of the area of the triangle?

Answers

Answer 1

Answer:

Step-by-step explanation:

Area of a triangle = 1/2bh

b is the base

h is the height

dA/dt = dA/db * db/dt + dA/dh * dh/dt

h = 10cm

b = 6cm

dA/db = h/2 = 10/2

dA/db = 5cm

dA/dh = b/2

dA/dh = 6/2 = 3cm

db/dt = 2.8cm/s

dh/dt = 0.7cm/s

Substitutte into the formula;

dA/dt = 5(2.8) + 3(0.7)

dA/dt = 14 + 2.1

dA/dt = 16.1cm²/s

Hence the rate of change of the area of the triangle is 16.1cm²/s


Related Questions

What is the next term in this sequence? t, q, p, h, h, o, n, ?

Answers

d! for decagon:
triangle, quadrilateral, pentagon, hexagon, heptagon, nonagon, decagon <3

Hi, I am confused on this question:


The sequence 12, 15, 18, 21, 51, 81, ... consists of all positive multiples of 3 that contain at least one digit that is a 1. What is the 50th term of the sequence?


(Source: 2006 National Target #5)

Answers

Answer:

321.

Step-by-step explanation:

The next term after 81 is 102 .

Between  102 and 198 inclusive we have  (198-102)  / 5  + 1 = 96/3 + 1 = 33 terms - these will all have at least one 1 and be divisible by 3.

So 198 = 6 + 33 = 39th term.

After 198 we have 201, 210, 213, 219, 231, 261, 291, 312, 315, 318, 321

The answer is 321..

Is 0.18 a rational number

Answers

Answer:

Yes, it is a rational number.

Step-by-step explanation:

Find the y - intercept of the line:
8
y=-3 -
7
Select one:
O a. 5/3
O b. - 5/3
O c.8/7.
O d. - 877

Answers

Answer:

d. [tex] -\frac{8}{7} [/tex]

Step-by-step explanation:

The y-intercept value in a given equation in the slope-intercept form, y = mx + b sis represented by b.

Thus, given the line [tex] y = \frac{-5x}{3} - \frac{8}{7} [/tex], the value of b (y-intercept) is represented as [tex] -\frac{8}{7} [/tex].

It is the value of y when x = 0.

Therefore, the y-intercept of the line is [tex] -\frac{8}{7} [/tex].

Please Help..., This Is Due Tomorrow
I need 385 X 445 step by step

Answers

The answer is 171, 325 just use a calculator

Answer:

32725

Step-by-step explanation:

             385

            x445      

            1925

          15400

        +15400

         32725

Hope this helps :)

HELP WIT THIS IF U CAN

Answers

I think it A I am not sure

Answer:

I am also think that the answer is A.

Step-by-step explanation:

hope it's helpful..

:-befrank

A number decreased by 23 is 44 . Find the number
Which equation can be used to solve this problem?

A) x - 23 = 44
B) 23 - x = 44
C) x- 44 = 23
D) 44 - x = 23

Answers

Answer:

A

x = 67

Step-by-step explanation:

the number is being reduced by 23 which means x-23 = 44 and x = 44+23 =67

Is this function linear or nonlinear​

Answers

Answer:

Nonlinear

Step-by-step explanation:

There is an exponent so the equation will not be linear.

Hope this helps! If you have any questions on how I got my answer feel free to ask. Stay safe!

Answer:

non linear

Step-by-step explanation:

A glacier travels 10 kilometers in 20 years, what is its speed?

Answers

Answer:

To change from meters per day into kilometers per year, you just have to change from meters to kilometers and from days to years.  You just multiply/divide by the unit conversions (for example, 1000 meters per kilometer) in a way that cancels out the units and leaves just kilometers and years:

Step-by-step explanation:

Use the drop-down menus to locate integers on the number line.

A number line going from negative 5 to 7. A is at negative 4, B is at negative 1, C is at 2, D is at 6.

A -4. -1 , 6, 2
B -4, -1, 6 , 2
C -4, -1, 6, 2
D -4, -1, 6, 2

Answers

A is -4

B is -1

C is +2

D is +6

( example: +3 is positive 3

                 -3 is negative 3 )

Hope this helped!

Suppose Huston deposit $600 into a savings account with a simple interest rate of 2.5%. How many years would he have to keep his money in the bank in order to earn at least $120 in interest?

Answers

Answer:

At least 8 years

Step-by-step explanation:

Deposit = $600

Interest rate = 2.5% simple

Time = x years

Target interest amount ≥ $120

600*0.025*x ≥ 12015x ≥ 120x ≥ 120/15x ≥ 8 years

At least 8 years

Please help me ive got a limited amount of time

Answers

Answer:

The third option

Step-by-step explanation:

Since the function is a constant function, all labeled points will have the same slope

PLEASE HELP FAST Owo​

Answers

Answer:

Obtuse triangle

Right triangle

Acute triangle

Acute triangle

Step-by-step explanation:

When given 3 triangle sides, to determine if the triangle is acute, right or obtuse:

1) Square all 3 sides.

2) Sum the squares of the 2 shortest sides.

3) Compare this sum to the square of the 3rd side.

if sum > 3rd side:  Acute Triangle

if sum = 3rd side:  Right Triangle

if sum < 3rd side:   Obtuse Triangle

Answer:

Obtuse triangle

Right triangle

Acute triangle

Acute triangle

Step-by-step explanation: ug im sorry i am not good at school uwu but this should be the answer also, uwu hehe

If a conditional statement is written in the form "if p then q", how is the contrapositive of the conditional statement written?

A.) If not q then p.
B.) If not p, then not q.
C.) If not q, then not p.
D.) If not p then q.

Answers

Answer:

3.  

If a conditional statement is written in the form “If p then q”, how is the inverse of the conditional statement written?

If not q, then not p

If not p, then not q  

If not q then p

If not p then q

To write the inverse of a conditional statement, you use the "opposite" of the hypothesis and the conclusion in a conditional statement.

Step-by-step explanation:

Contrapositive statement of "if p then q" written as If not q, then not p which is correct option (C).

What is the contrapositive conditional statement ?

Contrapositive of the conditional statement is defined as interchange the hypothesis and the conclusion of the inverse statement.

Contrapositive statement of "if p then q" written as If not q, then not p

Learn more about the contrapositive statement

https://brainly.com/question/7066208

#SPJ2

elana can swim 12 laps in 4 minutes. fill in the blank in the double number line to show this relationship between laps and minutes/

Answers

Answer:

3 laps per 1 minute

Step-by-step explanation:

Hope this helps :)

Tanner scored 12 more points than Jason in a basketball game. If p represents the number of points that Tanner scored?​

Answers

Answer: p-12 would find how many points Jason scored

Step-by-step explanation

P-12 would be the answer

Work out the mean for the data set below:
2, 3, 2, 3, 3, 5, 5
Give your answer as a fraction.

Answers

Answer:

[tex]\frac{23}{7}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Statistics

Mean: [tex]\frac{total}{amount}[/tex]

Step-by-step explanation:

Step 1: Define

Total:   2 + 3 + 2 + 3 + 3 + 5 + 5 = 23

Amount:   7 numbers

Step 2: Find mean

Substitute:                    [tex]\frac{23}{7}[/tex]

And we have our final answer!

What is the equation of the line shown in this graph?

Answers

Answer:

x=-2

Step-by-step explanation:

It is a straight line when x=-2 :)

help please on all :/

Answers

1. 100 minus 5 times a number
2.0.25 multiplied by a number plus 0.6 multiplied by a number
3. 3 times m minus 8 times n divided by 13

Please help... what is the domain of this graph?

Answers

Answer:-8,4 is ur answer

Practice Finding the Area of a Polygon
> Stacy example showing how to find the area of a polygon
Then solve problems 1-5.
151
Example
The polygon represents the floor space of a
ciaching store inamall. How many square feet
of foor space does the store have?
Decompose the polygon into tovo rectangles
andatangle
Area of top rectangle
bh= 25720 = 500
Are of bottom rectangle
bih=50/15 = 750
Are of triangle
= 250
*
20
1
150
=
Total area: 500 - 750 - 250 = 1.500
The store has 1.500 ft- of floor space.
Show another way to find the number of square feet of floor space for the store in
the Example

Answers

Answer:

ebbbbbbbbvc gdf

Step-by-step explanation:

Someone please help me i’ll give brainlest

Answers

Answer:

15.5 (B)

Hope this helps

A diver descended 20 feet in 5 seconds. What is the average rate per second that he traveled? Explain how you can use integer tiles to solve the problem and find the answer.

Answers

The diver is moving down, so he moved -20 feet. Start with 20 negative tiles and separate them into 5 equal groups. There are 4 negative tiles in each group, so he has traveled at a rate of -4 feet per second

hope this helps(°▽°)

Answer: Look Below (-v-) it’s the sample response..

Step-by-step explanation: The diver is moving down, so he moved −20 feet. Start with 20 negative tiles and separate them into 5 equal groups. There are 4 negative tiles in each group, so he traveled at a rate of −4 feet per second.

the product of four and a number is negative twelve

Answers

Answer:

4x=-12

Step-by-step explanation:

Let a number = X

So

The product of four and a number is negative twelve

4x=-12

The length of the diagonal of a square is 12 inches. Find the length of the square.

Please help! I’ll give brainliest!

Answers

Answer:

Hope this helps

Step-by-step explanation:

Screenshot 2020-1...9 08

So it must be 12 inches on each side since all sides on a square are equal so if we do it we can probably get an answer leading to me to not really know the answer so meaning the guy above might have correct answer

convert to find equivalent rate.


36,192 meters/years= ———— meters/months

PLEASE HELP!!! WILL MARK BRAINLIEST!!!!!! HELP!!!

Answers

Answer:

The answer to this question is 3016. If you use mathematical proportions (or just simply divide 36,192 by 12) the answer will come out as 3016. I hope I helped.

Hi I need someone to help me. :)

Answers

Answer:

D and B are similar to A

Step-by-step explanation:

B and E . E is just rotated it’s not D it is a little longer that A

......................................................................... (5)²=....................................................................

Answers

Answer:

the answer is 25

Step-by-step explanation:

(5)^2 would equal 25

Bridget goes to the mall and buys a shirt for $15.50, a pair of jeans for $32.00, and a belt for $24.30. She has a coupon and ends up getting $14.36 off her purchase. What percent off was her coupon for?

Answers

Answer:

20%

Step-by-step explanation:

Cost of Shirt = $15.50

Cost for a pair of jeans = $32.00

Cost for a belt = $24.30

Total cost = $15.50 + $32.00 + $24.30 = $ 71.8

Given that, coupon discount = $14.36

To find:

The percentage off on the coupon.

Solution:

The percentage off will be calculated on the total cost.

[tex]\text{Percentage\ off} = \dfrac{Coupon\ discount}{Total\ Cost}\times 100\\\Rightarrow \text{Percentage\ off}= \dfrac{14.36}{71.8}\times 100\\\Rightarrow \text{Percentage\ off} = 0.2\times 100\\\Rightarrow \text{Percentage\ off} = \bold{20\%}[/tex]

Therefore, the answer is:

20%

does anyone know what the output is​

Answers

The input is the x value. Replace x with 5 and solve:

2x = 2(5) = 2 x 5 = 10

The output would be 10

Answer:

10

Step-by-step explanation:

Replace x with 5. 2 multiplied by 5 is 10.

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