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3 years ago

7

A cone is 6 cm in height and its vertical angle is 54° calculate the radius of its base.

1 answer:

Romashka [77]3 years ago

8 0

Answer:

7cm

Step-by-step explanation:

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solve the problem related to population growth.A city had a population of 23,900 in 2007 and a population of 25,100 in 2012.(a)

Finger [1]

Solution

a)

To find the exponential growth function, we apply the exponential growth formula which is

$N(t)=a(1+k)^t$

Where

$\begin{gathered} a\text{ is the }initial\text{ population} \\ k\text{ is the growth rate} \\ t\text{ is the number of time intervals} \end{gathered}$

Given that

$\begin{gathered} a=23,900 \\ N(5)=25,100 \\ t=2012-2007=5 \end{gathered}$

Substitute the variables into the exponential growth formula

$\begin{gathered} 25100=23900(1+k)^5 \\ \text{Divide both sides by 23,900} \\ \frac{25100}{23900}=\frac{23900(1+k)^5}{23900} \\ 1.05021=(1+k)^5^{} \\ \sqrt[5]{1.05021}=1+k \\ 1.00984=1+k \\ \text{Collect like terms} \\ k=1.00984-1 \\ k=0.00984 \end{gathered}$

Hence, the exponential growth function is

$\begin{gathered} N(t)=23900(1+0.00984)^t_{} \\ N(t)=23900(1.00984)^t \end{gathered}$

Hence, the exponential growth function is

$N(t)=23900(1.00984)^t$

b)

For the population of the city in 2022,

$\begin{gathered} t=2022-2007=15 \\ t=15 \end{gathered}$

Substitute for t into the exponential growth function

$\begin{gathered} N(t)=23900(1.00984)^t \\ N(15)=23900(1.00984)^{15} \\ N(15)=27700\text{ (nearest hundred)} \end{gathered}$

Hence, the population is 2022 is 27700 (nearest hundred)

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1 year ago

A recipe for quinoa calls 2 2/3 cups of milk. Conner wants to makes 4 batches of quinoa. How much milk does he needs

krek1111 [17]

10 2/3 cups of milk for 4 batches

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4 years ago

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Martha recieved a commission of 7% for every car she sells. She sold a car for $5,625. What was her commission?

lubasha [3.4K]

Answer: $393.75.

Step-by-step explanation:

Multiply 5,625 by 0.07 to find the comission amount.

4 0

3 years ago

What is the surface area of the rectangular prism

anastassius [24]

340 you were right

Step-by-step explanation:

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3 years ago

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In quadrilateral ABCD, BN and DM are drawn perpendicular to AC such that BN = DM. Prove that O is the midpoint of BD

GaryK [48]

Answer:

Step-by-step explanation:

Given :

In the given quadrilateral ABCD,

BN and DM are the perpendiculars drawn to AC such that,

BN = DM

To prove:

Point O is the midpoint of segment BD.

Or

OD = OB

Solution:

In ΔOMD and ΔONB,

∠MOD ≅ NOB [Vertical angles]

∠M ≅ ∠N ≅ 90° [Given]

Therefore, by AA property of similarity,

ΔOMD ~ Δ ONB

Therefore, their corresponding sides will be proportional,

$\frac{DM}{BN}=\frac{OD}{OB}$

Since BN = DM,

OD = OB

Hence O is the midpoint of BD.

4 0

4 years ago