The altitude (i.e., height) of a triangle is increasing at a rate of 1.5 cm/minute while the area of the triangle is increasing at a rate of 3.5 square cm/minute. At what rate is the base of the triangle changing when the altitude is 10 centimeters and the area is 86 square centimeters? The base is changing at cm/min.

Answers

Answer 1

Answer:

-1.88cm/min

Step-by-step explanation:

Given

dh/dt = 1.5cm/min

dA/dt = 3.5cm²/min

Height h = 10cm

Area A = 86cm²

Required

db/dt

b is the base

h is the height.

Area of a triangle A = 1/2bh

dA/dt = dA/db•db/dt + dA/dh •dh/dt

dA/db = h/2 = 10/2 = 5cm

Get the base

86 = 1/2(10)b

5b = 86

b = 17.2cm

dA/ dh = 1/2b = 1/2(17.2)

dA/dh = 8.6cm

.substitute given values into the formula above;

dA/dt = dA/db•db/dt + dA/dh •dh/dt

3.5 = 5 db/dt + 8.6(1.5)

3.5 = 5 db/dt + 12.9

5 db/dt = 3.5-12.9

5 db/dt = -9.4

db/dt = -9.4/5

db/dt = -1.88cm/min

Hence the base is changing at -1.88cm/min


Related Questions

I really need help with this one

Answers

Answer:

a=70 b=.16 c=350

Step-by-step explanation:

50 messages is 8 dollars

A triangle has angles that measure 54.6° and 17.8°. Which equation can be used to find the value of x, the measure of the third angle in the triangle?

Answers

Answer:

58.6 + 17.8 + x = 180

Step-by-step explanation:

hope this helps

1 point
The temperature in Anchorage, Alaska was 2 degrees Celsius below zero.
The next day, the temperature dropped 10 more degrees Celsius. Thanks to
a warm front, the temperature rose by 5 degrees Celsius. On the fourth
day, the temperature decreased by 13 degrees Celsius. What was the final
temperature in Anchorage, Alaska on the fourth day? *
20

Answers

Answer:

6 degrees Celsius

Step-by-step explanation:

It started at 2 degrees Celsius below zero. The next day, it dropped to 12 degrees Celsius below zero. The next day, it rose to 7 degrees below zero. The next day, it increased to 6 degrees ABOVE zero. -7+13=6

Solve picture that I provided

Answers

I hope it helps good luck

Please help me I need help?!!!

Answers

Answer:

B

Step-by-step explanation:

If an initial amount A0 of money is invested at an interest rate i compounded times a year, the value of the investment after t years is If we let n = 8, that is referred to as the continuous compounding of interest. Use L' Hospital's Rule to show that if interest is compounded continuously, then the amount after years is A=A0eit

Answers

Answer:

Following are the solution to the given point:

Step-by-step explanation:

Please find the comp[lete question in the attached file.

Given:

[tex]\bold{ \lim_{n \to \ \infty} (1+ \frac{r}{n})^{nt} =e^{rt}}[/tex]

In point 1:

[tex]\to y = (1+ \frac{r}{n})^{nt}[/tex]

In point 2:

[tex]\to \ln (y)= nt \ln(1+ \frac{r}{n})[/tex]

In point 3:

Its key thing to understand, which would be that you consider the limit n to[tex]\infty[/tex],  in which r and t were constants!  

[tex]=lim_{n \to \ \infty} \ln (y) = lim_{n \to \ \infty} nt \ln(1+\frac{r}{n})\\\\= lim_{n \to \ \infty} \frac{\ln(1+\frac{r}{n})}{\frac{1}{nt}}\\\\= lim_{n \to \ \infty} \frac{\frac{-r}{\frac{n^2}{(1+\frac{r}{n})}}}{- \frac{1}{n^2t}}\\\\= lim_{n \to \ \infty} \frac{\frac{rn^2t}{n^2}}{(1+\frac{r}{n})}\\\\= lim_{n \to \ \infty} \frac{rt}{(1+\frac{r}{n})}\\\\= \frac{rt}{(1+\frac{r}{0})}\\\\=rt[/tex]

In point 4:

[tex]\to \lim_{n \to \ \infty} = (1+\frac{r}{n})^{nt}[/tex] and

[tex]\to \lim_{n \to \ \infty} = A_0e^{rt}[/tex]

The table below represents equivalent ratios.

X y
6= 10
12 = 20
??= 45

Answers

Answer:

27

Step-by-step explanation:

6/10=12/20 because when you cross multiply, 120=120, so then you can do wither 6/10=x/45 and when you cross multiply you get 270=10x and 270/10=27.

here is a list of number 51 38 48 36 39 40 39 47

WHAT is the median

Answers

Answer:

36

Step-by-step explanation:

Median is the Middle number in the sequence.

Hope this Helps!!

:D

First need to place in value order:
36 38 39 40 47 48 51

So 40 is the median/middle number

If 39 twice is a typo and there are 8 numbers then average the two middle numbers (the 4th and 5th numbers)

What is the multiplicative inverse of 1 2/3

Answers

Answer:

sorry if im wrong but im pretty sure -5/3

Step-by-step explanation:

Answer:

2/1

Step-by-step explanation:

A calculator showed me that this was the answer. I would give you the link but I would probably get deleted. I already got warned so yeah.

Hope this helps!

is 4.23x10^-5 greater than 1 or less than 1? explain how you know

Answers

Answer: Less than 1

Step-by-step explanation: 4.23 x 10^-5 simply translated to 0.0000423

which is less than 1.

Answer:

less than 1

Step-by-step explanation:

4.23 * 10^5 is less than 1

The Buffalo Bills football team wanted to buy new footballs. what did the team have to pay per football? Be sure to explain all of your work.​

Answers

Answer: I don't see the amount per football

Step-by-step explanation:

-2(b+5)= -6
What is b?

Answers

Answer:

-2

Step-by-step explanation:

It would be =

-2(-2 + 5) = -6

4 - 10 = -6

-10 and a positive four is a -6


Graph this line using the slope and y-intercept:
Y= 1/8X + 4

Click to select points on the graph.
10
9
8
o
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
Submit

Answers

Answer:

98765432123459 that is te answer

Step-by-step explanation:

write a linear equation in slope intercept form for a line that passes through the point 6,-2 and has a slope of -2/3

Answers

y=0.625x+1.75 is the equation for your problem.

Does f(x)=|x|+5 go up or down

Answers

Answer:

up

Step-by-step explanation:

postive, up!

Answer:

..........UP..........

If x + y = 5, then x =
1. 5y
2. 5+y
3. 5 - y

Answers

Heyyy! The answer should be x=5-y

The sales tax for an item was $18.60 and it cost $ 310 before tax. Find the sales tax rate. Write your answer as a percentage.

Answers

about 16 cent per dollar

Look at image which graph shows T (ABC)?

Answers

Answer:

A.

Step-by-step explanation:

That is a translation of 3 units left and 6 units down.

plz help out i am so confused

Answers

Answer:

Me too not trying to get the points but how are u suppose to solve this anyway

Step-by-step explanation:

I don’t know if I’m right because it’s a big number but you can probably still use it


Remove the radical by raising each side to the index of the racial .


Exact Form:b=^8 square root 357569423794.101 , - 357569423794.101


Decimal Form:b=27.80801870....,-27.8080187




8. Kim has a fever. Her temperature is 100.5 degrees Fahrenheit. Norr
temperature is 98.6 degrees Fahrenheit, How much above normal
temperature is Kim's fever?

Answers

Answer:

1.9 degrees above the normal temperture

Step-by-step explanation:

Normal temperture: 98.6 degrees Fahrenheit

100.5 - 98.6 =  1.9  

A snowboard shop charges $10, plus an additional #3 per hour to rent a snowboard. Write the equation for the line in slope-intercept form.

HURRY HELP PLS!!

Answers

Answer:

y = 3x + 10

Step-by-step explanation:

Answer:

im pretty sure it is (0,5) or (10,0)

Step-by-step explanation:

What is the polynomial of least degree with the given zeroes -2 and 4?

Answers

Answer:

-2

Step-by-step explanation:

base on my stuck knowledge

A genetic experiment with peas resulted in one sample of offspring that consisted of 438 green peas and 173 yellow peas.

Required:
a. Construct a 95â% confidence interval to estimate of the percentage of yellow peas.
b. It was expected thatâ 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is notâ 25%, do the results contradictâ expectations?

Answers

Answer:

a

The 95% confidence interval is [tex] 0.2474 < p < 0.3188 [/tex]

b

  The result obtained does not contradict expectation

Step-by-step explanation:

From the question we are told that

   The number of green peas is  k =  438

   The number of yellow peas is u =  173

Generally the sample size is mathematically represented as

       [tex]n = k + u[/tex]

=>    [tex]n = 438 + 173[/tex]

=>    [tex]n = 611[/tex]

Generally the sample proportion for yellow peas is

      [tex]\^ p = \frac{u}{n}[/tex]

=>   [tex]\^ p = \frac{173}{611 }[/tex]

=>   [tex]\^ p = 0.2831[/tex]

From the question we are told the confidence level is  95% , hence the level of significance is    

      [tex]\alpha = (100 - 95 ) \%[/tex]

=>   [tex]\alpha = 0.05[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } =  1.96[/tex]

Generally the margin of error is mathematically represented as  

     [tex]E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]

=>  [tex]E =  1.96 * \sqrt{\frac{ 0.2831 (1- 0.2831)}{611} } [/tex]

=>  [tex]E =  0.0357 [/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]\^ p -E <  p <  \^ p +E[/tex]

=>     [tex] 0.2831  -0.0357 <p< 0.2831  + 0.0357[/tex]

=>     [tex] 0.2474 < p < 0.3188 [/tex]

From the question we are told that it was expected that 25% of the offspring peas will be yellow

   Now from the 95% confidence interval obtained we see that the expected sample proportion(25% ) falls within it so  it means that the result obtained does not contradict expectation

Tom is the custodian at the local highschool. He has a circular key ring with 9 keys on it. How many different arrangements of those keys can Tom make on his key ring?

Answers

tom will have his key 10

Answer:

40,320.. took the test on USA test prep

Step-by-step explanation:

what is the answer to d- 48.60 = 80.00

Answers

Answer:

31.4

Step-by-step explanation:

You subtract 80.00 from 48.60, and you get your answer 31.4

Answer:

128.6

Step-by-step explanation:

You have to do the inverse operation.

So you add 48.60 to each side of the equation. This cancels out the -48.60 which isolates the variable. And on the other side of the equation it leaves you with 128.6. Therefore d = 128.6

True False x-sqrt6 is a factor of x^4-36

Answers

True because it wouldn’t have made since if it was false

a bowl of grapes has a total mass of 265 grams. The bowl has a mass 121 grams

Answers

Answer:

144 grams

Step-by-step explanation:

Im assuming you want to mass of grapes, do total mass subtracted by the mass of the bowl

HELP ME OUT REALL FAST PLEASEE

Answers

Answer:

The answer is C because you have to multiply them both:)

Answer:

The answer is C

Step-by-step explanation:

What I'm about to write is overkill for this question, but it works for any common denominator. Factor the denominators.

10: 2 * 5

5 : 1 * 5

You need 1 five and 1 two. The answer is 10

The correct way to go about doing the question is to multiply the 5 by 2 and the 2 on top by 2

2*2/5*2 = 4/10

1/10        1 / 10

4/10 + 1/10

discriminant of 2x2 - 4x + 7 = 0

Answers

Answer:

1

Step-by-step explanation:

The discriminant of the quadratic equation 2x2+4x-7=0 is 1

Amaia purchased two blouses and a skirt for a total of $32. The sales tax rate is 8%. How much total sales tax will Amaia pay on these items?

Answers

Answer:

2.56

Step-by-step explanation:

8% of 32 is 2.56

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