1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
salantis [7]
3 years ago
13

Please help differentiate this!!!!!!!!!

Mathematics
2 answers:
vlada-n [284]3 years ago
5 0
\bf h=20ln(3t+2)+30\\\\
-------------------------------\\\\
\boxed{a}\\\\
\stackrel{0~years}{t=0}\qquad h=20ln[3(0)+2]+30\implies h=20ln(2)+30
\\\\\\
h\approx 43.86
\\\\\\
\boxed{b}\\\\
\stackrel{1~meter}{h=100}\qquad 100=20ln(3t+2)+30\implies 70=20ln(3t+2)
\\\\\\
\cfrac{70}{20}=ln(3t+2)\implies \stackrel{\textit{log cancellation rule}}{e^{\frac{7}{2}}=e^{ln(3t+2)}}\implies e^{\frac{7}{2}}=3t+2
\\\\\\
e^{\frac{7}{2}}-2=3t\implies \cfrac{e^{\frac{7}{2}}-2}{3}=t\implies 10.371817\approx t

\bf \boxed{c}\\\\
\cfrac{dh}{dt}=20\left(\cfrac{1}{3t+2}\cdot 3  \right)+0\implies \cfrac{dh}{dt}=20\left(\cfrac{3}{3t+2} \right)\\\\\\ \cfrac{dh}{dt}=\cfrac{60}{3t+2}
\\\\\\
\left. \cfrac{dh}{dt}  \right|_{3}\implies \cfrac{60}{3(3)+2}\implies \cfrac{60}{11}
\\\\\\
\left. \cfrac{dh}{dt}  \right|_{10}\implies \cfrac{60}{3(10)+2}\implies \cfrac{15}{8}
AveGali [126]3 years ago
5 0
H=20ln(3t +2) +30cm :

a) how tall was the shrub when it was planted. When it was planted t = 0, then

H = 20ln(0+2) +30 →→H = 20.ln(2) + 3 →→ and H = 43.86 cm

b) how long will it take for the shrub to reach a height of 1:

H = 1  or in cm, H=100→→ 100 = 20ln(3t+2) + 30 
100-30  = 20ln(3t+2) →→ 70/20 = ln(3t+2)

ln(3t+2) = 7/2 →→ 3t+2 = e⁷/² →→ t = [(e⁷/²)-2]/3 →→t = 10.37 years

c)At what rate is the shrubs height changing 3 years after being planted?
H = 20ln(3t+2) +30 
dH/dt = 20 . 3/(3t+2)  (remember d(ln(u) = u'/u)

for t =3 years , the growth (dH/dt) will be (20).(3)(3.3 + 2) = 60/11                  = 5.45 cm/year
for t = 10 , dH/dt = 1.81 cm/year

You might be interested in
Consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs show the p
frutty [35]

Answer:

y = 0.00587x +1986.406

Step-by-step explanation:

Given that the population of a city increased steadily over a ten-year span. The following ordered pairs show the population x and the year y over the ten-year span in the form (x, y) for specific recorded years.

x y

 

2500 2001

2650 2002

3000 2004

3500 2007

4200 2011

 

 

Slope 0.005865485

Intercept 1986.406413

So regression line is

y = 0.00587x +1986.406

When population = 15000

0.00587(17000)+1986.406\\=2074.389

3 0
2 years ago
Tyler is overdrawn at the bank by $180. His brother has $70 more than him. How much money does Tyler's brother have?
Lena [83]

Answer:

Tyler's brother has $250

Step-by-step explanation:

180+70 =250

8 0
2 years ago
Read 2 more answers
There are 65 pens in 3 boxes. How many pens are in 12 boxes?
Rainbow [258]

Answer:

260

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Alvin is planning to be out of town for the day, so he asks a friend to dog-sit his 3 dogs. Each dog eats 0.5 pounds of food eve
german

Answer:

2 cans

Step-by-step explanation:

Calculate how many pounds he needs for one day:

3(0.5)=1.5 pounds for each day Alvin is gone ( 3 represents his dogs, .5 is each dog's food)

Convert into ounces:

1.5*16=24 ounces for one day

Question: If dog food is sold in 12 oz cans, how many will he need?

24/12=2 cans

Thus, he will need 2 cans

6 0
3 years ago
Find the product of 5/6( 1/2) *<br> O 6/8<br> O 5/12<br> O 5/6
inysia [295]
The anser is 6/8 that what i think
6 0
3 years ago
Read 2 more answers
Other questions:
  • Does there seem to be a relationship in the age of the park guest and what type of ticket they purchase?
    6·2 answers
  • You plant a tree that is 36 inches tall. After one year, the tree is 43 inches tall. Write an expression which describes the per
    6·2 answers
  • Ted has $6.00. He will buy a notebook for $1.50 and some pencils. Each pencil costs $0.25. Write and solve an equation to determ
    8·1 answer
  • Use the following function rule to find f(28).
    12·1 answer
  • Which angle has a measure less than 60
    5·1 answer
  • What is x? x – 15 = 40
    11·2 answers
  • Find the slope of each line
    5·1 answer
  • A data set is made up of these values.
    14·2 answers
  • WHOEVER ANSWERS CORRECTLY W STEP BY STEP GETS BRAINLIEST
    6·2 answers
  • Harry is one third as old as his father. If his father is x 12 years old, how old is Harry? StartFraction x over 3 EndFraction 4
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!