The sides of an equilateral triangle are increasing at a rate of 10 cm/min. at what rate is the area of the triangle increasing when the sides are 30 cm long?

Answers

Answer 1

Area of a triangle is given by

[tex]Area= \frac{1}{2} ab\sin C= \frac{1}{2} s^2\sin C[/tex]

Since the sides of an equilateral triangle are equal.

Differentiating the area of the triangle, we have:

[tex] \frac{dA}{dt} = \frac{dA}{ds} \cdot \frac{ds}{dt} =(s\sin C) \frac{ds}{dt} [/tex]

where

[tex] \frac{ds}{dt} =10\,cm/min \\ s=30 \, cm[/tex]

[tex]\therefore \frac{dA}{dt} =(30\sin60)\times10=300\sin60=259.8\, cm^2/min[/tex]

Therefore, the rate is the area of the triangle increasing when the sides are 30 cm long is 259.8 cm^2 / min

Related Questions

The current diameter of a tree trunk is 10 inches. the trunk diameter increases at a rate of 2 inches per year. an insect burrows into the trunk and lays its eggs in the secondary xylem, 1 inch out from the center of the tree. how far from the center will the dormant eggs be located in two years?

Answers

The answer is 1 because tree trunks grow wider because of cell divisions that occur only in the vascular and cork cambia (both located underneath the bark). Secondary xylem (wood) remains in place once it is formed. Therefore, the eggs will remain in their current position (1 inch out from the center).

the answer would be "1".

Can someone please help me with an algebra 1 problem. I'm really stuck.
Write each interval as an inequality. Then graph the solutions
24. [-4, 5]
please help, thank you so much.

Answers

[ -4, 5 ]

notice the brackets, as opposed to parentheses.

the brackets mean, -4 is a bound and it is included in the range, and 5 is the other bound and 5 is also included in the range too.

so, whatever number "x" is, we know that is between -4 and 5, so it could be -3, -2, 1, 4 or such.

keeping in mind that, for the negative side of the numbers, the closer to 0, the greater the number, therefore, -4 is greater than -5 and is also greater than -1,000,000, because -4 is closer to 0 than those two.

so, "x" is greater than -4, and includes it, but is also less than 5, but it can be 5 too.

check the picture below.

Frederick needs to borrow $3000 for a down payment on a new car. His uncle decided to loan him the money as a 4.5% loan. Frederick doesn't want to pay more than $810 in interest. How many years does Frederick have to pay back the loan?

Answers

the answer is
20.2 hopes this hepls

Evaluate the expression for x = –3

Answers

Kinda confused of the question

what is f(-5) if f(x) equals |2x-1|+10?

Answers

|2(-5) - 1| + 10
|-10-1| + 10
|-11| + 10
11 + 10
21 is your answer

Hope this helped!

Answer:

The value of the function for f(-5) is 21.

Step-by-step explanation:

Consider the provided function.

[tex]f(x)=|2x-1|+10[/tex]

We need to find the value of the function for f(-5).

Substitute the value of x=-5 in the above function.

[tex]f(-5)=|2(-5)-1|+10[/tex]

[tex]f(-5)=|-10-1|+10[/tex]

[tex]f(-5)=|-11|+10[/tex]

The absolute value of -11 is 11.

[tex]f(-5)=11+10[/tex]

[tex]f(-5)=21[/tex]

Hence, the value of the function for f(-5) is 21.

help me with algebra 2 homework

Answers

-10y + 9x = - 9....A
10y + 5x = - 5.....B

You should see right away that -10y and 10y cancel out.

We are left with

14x = -14

x = -14/14

x = -1

Plug x = -1 into EITHER equation A or B to find y.

I will use equation A.

-10y + 9(-1) = - 9

-10y - 9 = - 9

-10y = - 9 + 9

- 10y = 0

y = 0/-10

y = 0

Done!

Irina rode her bike to work at an average speed of 16 miles per hour. It started to rain, so she got a ride home along the same route in her coworker’s car at an average speed of 27 miles per hour. If Irina’s ride home in the car took 24 minutes (0.4 of an hour), how many hours was her bike ride to work, to the nearest tenth of an hour?

Answers

0.7 of an hour this is the correct answer if you put this in your quiz you will get a A for that question if you dont understand ask your teacher but this is the correct answer.

Answer:

0.7 an hour .

Step-by-step explanation:

Solve for y, give the slope and y intercept 5y=20, -y + 3=15x, y +1/3x=17

Answers

[tex]5y=20[/tex] Equation

[tex]y=4[/tex] Divide by 5 on both sides

[tex]5(4)=20[/tex] Plug in for y

[tex]20=20[/tex] Simplify

y=4
slope= 0
y-intercept= 4

[tex]^{-}y+3=15x[/tex] Equation

[tex]^{-}y=15x-3 [/tex] Subtract 3 from both sides

[tex]y=-15x+3[/tex] Divide both sides by -1

[tex]- (^{-}15x+3) +3=15x[/tex] Plug in for y

[tex]15x-3+3=15x[/tex] Distribute -1 into the parenthesis

[tex]15x=15x[/tex] Further simplified

y= -15x+3
slope= -15
y-intercept= 3

[tex]y+ \frac{1}{3}x=17 [/tex] Equation

[tex]y=^{-}\frac{1}{3}x+17 [/tex] Subtract 1/3x from both sides

[tex](^{-}\frac{1}{3}x+17 )+\frac{1}{3}x =17[/tex] plug in for y

[tex]17=17 [/tex] Simplify

y= -1/3x+17
slope= -1/3
intercept= 17

WHAT IS 7.06 DIVIDED BY 0353

Answers

The answer to this would be 0.02 !!

Transitive property: if 3x plus y equals 7 and 7 equals 5x minus 2y then

Answers

3x + y = 7
7 = 5x - 2y

THEN 3x + y = 5x - 2y ... it's like you're taking out the middle man "7"

Transitive property states that if x = y and y = z then x = z.

3x + y = 7 and 7 = 5x - 2y

Using the transitive property we get,

3x + y = 5x - 2y.

What is transitive property?

It states that if x, y and z are the three quantities, and if x is related to y by a rule, and y is related to z by the same rule, then we can say x is related to z by the same rule.

Example:

x + 1 = 2 and 2 = x + 9 then x + 1 = x + 9

We have,

3x + y = 7 and 7 = 5x - 2y

Using transitive property we can say that,

3x + y = 5x - 2y

Thus using the transitive property we have,

3x + y = 5x - 2y.

Learn more about the transitive property here:

https://brainly.com/question/2437149

#SPJ5

How to calculate confidence interval for population standard deviation?

Answers

go to google and search up "Online calculator"

and you got your answer

What is the degree of 12x⁴-8x+4x²-3
A)12
B)4
C)3
D)8

Answers

The answer to your question is B: 4

If x y z are positive integers and 3x = 4y = 7z, then the least possible value of x + y + z is

Answers

The least possible value of x+y+z is 61.
this is how we find this,
if we find the LCM of 3,4 and 7 we get 84
= 3 x (4x7) = 4x(3x7) = 7x (3x4)
x+y+z = (4x7) + (3x7) + (3x4)
=28 +21+12
=61

What is the order of the set A= (-1,20,3,17,5)
A. 3
B. 5
C. -1, 20, 3, 17, 5
D. -1,3, 5, 17, 20

Answers

letter D, because the letter D is the order of set A.

The correct answer is actually C on enginuity.

3(x−7)=6(x−10)
Solve For X
3x-21=6x-60

Answers

3(x-7)=6(x-10)
3x-21=6x-60
3x-21+21=6x-60+21
3x=6x-39
3x-6x=6x-39-6x
-3x=-39
-3x/-3=-39/-3
x=13

Hello,

Let's look at the equation: 3(x−7)=6(x−10). Let's distribute the 3 and 6 to the parenthesis. After you distribute, the equation should look like:
3x - 21 = 6x - 60. Then add 21 to both sides and that should leave you with
3x = 6x - 39. Let's then get 6x to the other side by subtracting 6x to both sides. That'll leave you with -3x = -39, then divide each side by -3 to get x by itself. The equation would now be: x = 13. Hope this helps =).

PLEASE HELP!

Translate each phrase into a numerical expression.

Twice the opposite of eleven.

Answers

2*(-11) if its multiple choice but im not sure

Twice the opposite of eleven will be 2(-11).

What is an expression?

An expression is a combination of some mathematical symbol such that arithmetic operator and variable such that all are constrained and create an equation.

In other meaning, expression is very useful to determine the end or root value of constraint.

For example 3x +5y

The constraint of expression is represented as = or <, >.

Opposite of eleven = negative of eleven

Opposite of eleven = -11

Twice = multiply by two

So,

Twice the opposite of eleven = 2(-11) = -22

Hence "Twice the opposite of eleven will be 2(-11)".

To learn more about expression,

https://brainly.com/question/14083225

#SPJ2

Hank's pickup can travel 42 miles on 3 gallons of gas. How many gallons will Hank's pickup need to travel 28 miles?

Answers

2 gallons of gas

hope it helps

brainliest pls

Answer:

The person is right it's 2 gallons of gas to travel 28 miles

Step-by-step explanation:

What is the side length b in the triangle below

Answers

12^2 +b^2 = 20^2 because of the Pythagorean theorem
144 + b^2 =400
B^2 =256
B=16

Answer:

Option B : 16

Step-by-step explanation:

Refer the attached file

Given :

In ΔABC , AB = b , BC = 12 , AC= 20

To Find : value of b i.e. Length of AB

Solution:

Since we are given a right angles triangle so we can use Pythagoras theorem i.e.

[tex](Hypotenuse)^{2} =(Perpendicular)^{2} +(Base)^{2} [/tex] ---(a)

Now in a given triangle AB is Perpendicular , BC is Base and AC is Hypotenuse.

So, putting values in (a)

[tex](AC)^{2} =(AB)^{2} +(BC)^{2} [/tex]

[tex](20)^{2} =(b)^{2} +(12)^{2} [/tex]

[tex]400 =(AB)^{2} +144 [/tex]

[tex]400-144 =(b)^{2} [/tex]

[tex]256 =(b)^{2} [/tex]

[tex]\sqrt{256} =b[/tex]

[tex]16=b[/tex]

Thus the value of b is 6

Hence Option B is correct.

Which set of integers is a pythagorean triple?
a. 2, 3, 6
b. 3, 4, 5
c. 4, 5, 9
d. 5, 7, 12?

Answers

H^2 = P^2 + B^2

a. 6^2 = 2^2 + 3^2
36 = 4 + 9
36 = 13
Therefore this is not a Pythagorean triple

b.5^2 = 4^2 + 3^2
25 = 16 + 9
25 = 25
Therefore this is a phythagorean triple

3tens 12ones= —— tens 2 ones

Answers

3 tens and 12 ones = 4 tens and 2 ones

If two lines don’t intersect, then is it parrell (( true or false ))

Answers

The definition of parallel lines states that they don't intersect, so that would always be true. (In Euclidean geometry, anyway.)

The product of two numbers is 44. find the sum of the two numbers s(x) as a function of one of the numbers, x. s(x)

Answers

Call the numbers x and y. According to the first sentence, xy = 44. You can rearrange to solve for y: y = 44/x. The sum of the numbers, s(x), is x + y, but we just found a way of expressing y in terms of x. Therefore: the sum expressed as a function of one of the numbers (x) is:

s(x) = x + 44/x

What is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=x4+5 ? Enter your answer in the box.

Answers

y = x/4 + 5, slope = 1/4

perpendicular lines, slope is opposite and reciprocal
so slope = -4

passes through the point (2, 7)
y = mx + b
b = y - mx
b = 7 - (-4)(2)
b = 7 + 8
b = 15

equation
y = -4x + 15

answer
y = -4x + 15

what is m Help Please

Answers

I don't know I forgot

I think the equation would look something like this:
M+k=180°
Now plug the equations for m and k into that equation.
Hope this helped, have a nice day.

Write a linear model for the cost of tickets based on the number of tickets a fan buys.

Answers

y = mx + b

y = 2x + 7

Simplify (x3+ 8x + 5) − (2x2− 3x − 12). −x2+ 11x + 17 x3− 2x2+ 11x + 17 −x2+ 5x − 7 x3− 2x2+ 5x − 7

Answers

x^3 + 8x + 5 - (2x^2 - 3x - 12) =
x^3 + 8x + 5 - 2x^2 + 3x + 12 =
x^3 - 2x^2 + 11x + 17 <===

What is the value of x?

x−25=7

Enter your answer in the box in simplest form.
x =

Answers

that answer is -18 dfffdffdf

x would equal 32 because 32 - 25 = 7. if you add 25 to 7 the sum would be 32.

Mayumi is constructing a line through point P that is perpendicular to RS←→. A horizontal line segment R S and a point P are drawn. The point P is above the horizontal line segment R S. She places her compass on point P to construct an arc. What must be true about the width of the compass opening when Mayumi draws the arc? It must be greater than 12RS. It must be equal to PS . It must be wide enough so that the arc intersects RS←→ in two points. It must be equal to PR .

Answers

Width of the compass should be more than the smallest space between P and RS, so that it cuts RS at two distinct points. Therefore, it must be wide enough so that the arc intersects RS←→ in two points. The photo is attached so that you can understand it more.

Hola fellow K12 kiddos!

Correct answer:

It must be wide enough so that the arc intersects RS←→ in two points.

at the start of his diet kerrin weighed 15 stone 10 pounds three months later he weighed 14 stone 8 pounds there are 14 pounds in a stone

Answers

Kerrie lost 16 pounds and weighed 204 pounds

What 8 letter word can have a letter taken away and it still makes a word. take another letter away and it still makes a word. keep on doing that until you have one letter left - that is still a word. what is the 8 letter word...and what are the other smaller words?

Answers

The word in question is "starting." Taking away the second "t" gives "staring." Next, taking away the "a" gives "string," and taking away the "r" gives "sting." Further, dropping the second "t" gives "sing." Next, removing the "g" leads to "sin," the "s" gives "in," and finally taking away the "n" leaves the word "I."

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