MATHEMATICS HIGH SCHOOL

2.The length of the shortest wavelength of visible light is approximately 4 x 10-7 meter. Which
is an equivalent length?
A
0.00000004 meter
B
0.0000004 meter
C 4,000,000 meters
D
40,000,000 meters

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

B. 0.0000004 metres

4÷10000000

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By definition, future value is?

Answers

Answer:

Future value is the value of an item calculated after certain years on a given value at a given certain interest rate.

Future value is always increasing in nature and when future value is decreasing it is know as Depreciate value.

And is calculated using the formula as stated

$FV=P(1+(r)/(100) )^n$

Where P is the principal amount that is the given amount for which we have t calculate the future value.

r is the rate of interest and it is the rate at which the given principal value is increasing.

n is the time period for which the principal value is kept.

Future value is the value of an asset at a specific date. It measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest rate, or more generally, the rate of return; it is the present value multiplied by the accumulation function.

A cylindrical glass of soda has a mass of 700g. The glass itself has a mass of 80g. If the glass has a radius of 4cm and a height of 8cm, what is the density of the soda?

Answers

The density of the soda is 3.6 g/cm³

What is density?

Density is the measurement of how tightly a material is packed together. It is defined as the mass per unit volume.

Given that, a cylindrical glass of soda has a mass of 700g. The glass itself has a mass of 80g, the glass has a radius of 4 cm and a height of 8 cm,

We are asked to find the density of the soda,

Density = mass / volume

Volume = 2π×radius×height

Therefore,

Density = 700/2π×4×8 [we will not add the mass of glass because we need to find the density of soda only]

Density = 700/194.68

= 3.59

= 3.6

Hence, the density of the soda is 3.6 g/cm³

Learn more about density, click;

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How do you divide 15 pounds of rice into 4 unequal measuring using ounces

Answers

you have to cut 15 pounds into 3.75 four times

C(x) = 0.000002x3 − 0.03x2 + 400x + 80,000 where C(x) denotes the total cost incurred in producing x sets. Find the level of production that will yield a maximum profit for the manufacturer. Hint: Use the quadratic formula

Answers

Answer:

The producer will have maximum profit when x is 5000.

Step-by-step explanation:

Given C(x) = 0.000002x³ - 0.03x² + 400x + 80000

To find the level of production that will yield the maximum profit for the manufacturer, firstly, we differentiate C(x) to obtain C'(x), we then set the resulting quadratic expression to zero and solve. Whichever of the two values obtained from the quadratic equation will be tested to see what we want to find.

Differentiate C(x)

C'(x) = 3(0.000002)x² - 2(0.03)x + 400

= 0.000006x² - 0.06x + 400

Set C'(x) = 0

0.000006x² - 0.06x + 400 = 0

Solve using quadratic formula.

x = [-b ± √(b² - 4ac)]/2a

a = 0.000006

b = -0.06

c = 400

x = [-(-0.06) ± √((-0.06)² - 4(0.000006 × 400)]/2(0.000006)

= [0.06 ± √(0.0036 - 0.0096]/0.000012

= (0.06/0.000012) ± i√(0.006)/0.000012

= 5000 ± 6454.97i

x = 5000 + 6454.97i

x = 5000 - 6454.97i

The height of a balloon is given by the fucntion s(t)= -960t^2+26400t , where t= hours since lift-off and s= feet . Find the velocity of the balloon 5 hours after lift off

Answers

v is slope of graph s-t
v(t) = s'(t) = -1920t + 26400
v(5) = -1920(5) + 26400

16800 metres

Working
i) Differentiate the given function to get the velocity function:
ds/dt = =1920t+ 26400
Then replace the value of t with 5 hours
v(t)= -1920(5)+26500
v(t)= -9600+26500
V(5)= 16800 m

What is the value of the function f(x)=3(4-x) when x=7?

Answers

f(x) = 3(4 - x)
= 3(4 - 7)
= 3(-3)
= -9

Final answer:

The value of the function f(x)=3(4-x) when x=7 is -9. This is calculated by substituting x=7 into the function and simplifying.

Explanation:

To find the value of the function f(x)=3(4-x) when x=7, you should insert x's value into the equation. Therefore, the function takes the form: f(7)=3(4-7). Then you simplify it to: f(7)=3(-3) and further simplification gives: f(7)=-9.