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2 years ago

How to work out 12.5% of a number

Mathematics

1 answer:

mario62 [17]2 years ago

4 0

Step-by-step explanation:

12.5÷100 × 5

=0.125×5

=0.625

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) The density of oil in a circular oil slick on the surface of the ocean at a distance of r meters from the center of the slick

Feliz [49]

Answer:

Therefore the mass of the of the oil is 409.59 kg.

Step-by-step explanation:

Let us consider a circular disk. The inner radius of the disk be r and the outer diameter of the disk be (r+Δr).

The area of the disk

=The area of the outer circle - The area of the inner circle

= $\pi (r+\triangle r)^2- \pi r^2$

$=\pi [r^2+2r\triangle r+(\triangle r)^2-r^2]$

$=\pi [2r\triangle r+(\triangle r)^2]$

Since (Δr)² is very small, So it is ignorable.

∴ $A=2\pi r\triangle r$

The density $\delta (r)= \frac{40}{1+r^2}$

We know,

Mass= Area× density

$=(2r \pi \triangle r)(\frac{40}{1+r^2}})$

Total mass $M=\sum_{i=1}^n \frac{80r_i\pi }{1+r^2}\triangle r_i$

Therefore

$\sum_{i=1}^n \frac{80r_i\pi }{1+r^2}\triangle r_i=\int_0^5 \frac{80r\pi }{1+r^2}dr$

$=40\pi[ln(1+r^2)]_0^5$

$=40\pi [ln(1+5^2)-ln(1+0^2)]$

$=40\pi ln(26)$

= 409.59 kg (approx)

Therefore the mass of the of the oil is 409.59 kg.

3 0

2 years ago

Two functions f and g represent the profit of two companies, in millions of dollars, about 13 years after they went into busines

hram777 [196]

Answer:

13.253 is correct

Step-by-step explanation:

This table shows 0.1203 and 0.1212 having the most correlation since they are the closest to each other which means 13.253 hours is the closest.

4 0

3 years ago

Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is infinite, enter '[infinity]' or

soldi70 [24.7K]

Answer:

The limit of this function does not exist.

Step-by-step explanation:

$\lim_{x \to 3} f(x)$

$f(x)=\left \{ {{9-3x} \quad if \>{x \>< \>3} \atop {x^{2}-x }\quad if \>{x\ \geq \>3 }} \right.$

To find the limit of this function you always need to evaluate the one-sided limits. In mathematical language the limit exists if

$\lim_{x \to a^{-}} f(x) = \lim_{x \to a^{+}} f(x) =L$

and the limit does not exist if

$\lim_{x \to a^{-}} f(x) \neq \lim_{x \to a^{+}} f(x)$

Evaluate the one-sided limits.

The left-hand limit

$\lim_{x \to 3^{-} } 9-3x= \lim_{x \to 3^{-} } 9-3*3=0$

The right-hand limit

$\lim_{x \to 3^{+} } x^{2} -x= \lim_{x \to 3^{+} } 3^{2}-3 =6$

Because the limits are not the same the limit does not exist.

8 0

3 years ago

I need help on these two questions

Marina86 [1]

Answer:

1. $60 2. $233.20

Step-by-step explanation:

That is the answer

4 0

2 years ago

Using t=tanx/2, write an expression for sinx and cosx in terms of t.

Dafna11 [192]

Assume 0 < x/2 < π/2. Then

tan²(x/2) + 1 = sec²(x/2) ===> sec(x/2) = √(1 - tan²(x/2))

===> cos(x/2) = 1/√(1 - tan²(x/2))

===> cos(x/2) = 1/√(1 - t ²)

We also know that

sin²(x/2) + cos²(x/2) = 1 ===> sin(x/2) = √(1 - cos²(x/2))

Recall the double angle identities:

cos(x) = 2 cos²(x/2) - 1

sin(x) = 2 sin(x/2) cos(x/2)

Then

cos(x) = 2/(1 - t ²) - 1 = (1 + t ²)/(1 - t ²)

sin(x) = 2 √(1 - 1/(1 - t ²)) / √(1 - t ²) = 2t/(1 - t ²)

7 0

2 years ago