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Liono4ka [1.6K]

3 years ago

8

What are the slope and the y-intercept of the linear function that is represented by the graph?

1 answer:

amm18123 years ago

3 0

Answer:

the slope is 4 and the y intercept is 12

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Explain why you can use πr2 to find the area of the base of a cone

olga nikolaevna [1]

The base of a cone is a circle.

The area of a circle is $\pi r^2$ .

Thus, the area of the base of a cone $\pi r^2$ .

The derivation of the formula for the area of a circle involves a bit of calculus, but if you'd like, I can walk you through it.

8 0

3 years ago

In 2000 the population of a country reached 1 billion, and in 2025 it is projected to be 1.2 billion. (a) Find values for C an

Mice21 [21]

Answer:

(a) The value of C is 1.

(b) In 2010, the population would be 1.07555 billions.

(c) In 2047, the population would be 1.4 billions.

Step-by-step explanation:

(a) Here, the given function that shows the population(in billions) of the country in year x,

$P(x)=Ca^{x-2000}$

So, the population in 2000,

$P(2000)=Ca^{2000-2000}$

$=Ca^{0}$

$=C$

According to the question,

$P(2000)=1$

$\implies C=1$

(b) Similarly,

The population in 2025,

$P(2025)=Ca^{2025-2000}$

$=Ca^{25}$

$=a^{25}$ (∵ C = 1)

Again according to the question,

$P(2025)=1.2$

$a^{25}=1.2$

Taking ln both sides,

$\ln a^{25}=\ln 1.2$

$25\ln a = \ln 1.2$

$\ln a = \frac{\ln 1.2}{25}\approx 0.00729$

$a=e^{0.00729}=1.00731$

Thus, the function that shows the population in year x,

$P(x)=(1.00731)^{x-2000}$ ...... (1)

The population in 2010,

$P(2010)=(1.00731)^{2010-2000}=(1.00731)^{10}=1.07555$

Hence, the population in 2010 would be 1.07555 billions.

(c) If population P(x) = 1.4 billion,

Then, from equation (1),

$1.4=(1.00731)^{x-2000}$

$\ln 1.4=(x-2000)\ln 1.00731$

$0.33647 = (x-2000)0.00728$

$0.33647 = 0.00728x-14.56682$

$0.33647 + 14.56682 = 0.00728x$

$14.90329 = 0.00728x$

$\implies x=\frac{14.90329}{0.00728}\approx 2047$

Therefore, the country's population might reach 1.4 billion in 2047.

3 0

2 years ago

Drinking 6 fluid ounces of milk provides 202.5 milligrams of calcium. how many fluid ounces of milk provide 85.5 milligrams of c

Alona [7]

$\frac{85.5}{202.5} \times 6 = 2.53\ ounces\ of\ milk$

3 0

2 years ago

Read 2 more answers

A rectangular garden is 5 ft longer than it is wide. Its area is 300 ft2. What are its dimensions?

topjm [15]

Answer:

width=x

length=5x

area= 300ft2

area=lxb

300=5x(x)

300=5x^2

x^2=60

x=7.74

7.74(5)=38.7

dimensions are 38.7ft by 7.74 ft

<u><em>Please mark as brainliest</em></u>

5 0

1 year ago

Read 2 more answers

What’s 4/5 divided by 3

Valentin [98]

Answer:

$\frac{4}{15}$

Step-by-step explanation:

remember when dividing with fractions, you are multiplying by the reciprocal.

this means

$\frac{4}{5} \div3=\frac{4}{5}*\frac{1}{3}=\frac{4}{15}$

6 0

3 years ago

Read 2 more answers