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2 years ago

15

Write an equation that expresses the following relationship.

1 answer:

devlian [24]2 years ago

5 0

Answer:

Step-by-step explanation:

p = kd/u

p varies directly with d, p=md

p varies inversely with u, p=n/u

put them together

p=kd/u

as d goes up, p goes up. as u goes up, p goes down

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1. find the sum of the following numbers: -4, 7, -3, -12, 9

Leni [432]

1.

$= ( - 3 - 4 - 12) + (7 + 9)$

$= - 19 + 16$

$= - 3$

2.

$= ( - 5 - 8 - 10) + 23$

$= - 23 + 23$

$= 0$

6 0

3 years ago

Use a trigonometric function to find each value of x. Round to the nearest tenth if necessary.

Ulleksa [173]

Answer:

4.0

Step-by-step explanation:

Using trig identity Tangent, tangent is equal to opposite / adjacent side. Therefore tan30 = x/7, because x is the side opposite to 30 degrees and it is adjacent to 7, (note: adjacent side is never the hypotenuse)

To save time, tan 30 = sqrt(3)/3,

sqrt(3)/3 = x/7

x = 7*sqrt(3)/3 ~ 4.041

4 0

2 years ago

Prove that if a and b are integers, then a^2-4b egal or non-egal 2

Lera25 [3.4K]

Answer:

tex]a^2 - 4b \neq 2[/tex]

Step-by-step explanation:

We are given that a and b are integers, then we need to show that $a^2 - 4b \neq 2$

Let $a^2 - 4b = 2$

If a is an even integer, then it can be written as $a = 2c$ , then,

$a^2 - 4b = 2\\(2c)^2 - 4b =2\\4(c^2 -b) = 2\\(c^2 -b) =\frac{1}{2}$

RHS is a fraction but LHS can never be a fraction, thus it is impossible.

If a is an odd integer, then it can be written as $a = 2c+1$ , then,

$a^2 - 4b = 2\\(2c+1)^2 - 4b =2\\4(c^2+c-b) = 2\\(c^2+c-b) =\frac{1}{4}$

RHS is a fraction but LHS can never be a fraction, thus it is impossible.

Thus, our assumption was wrong and $a^2 - 4b \neq 2$ .

7 0

3 years ago

-10.7474..... as a fraction

kondaur [170]

In fraction, it would be:

-107474/10000

6 0

3 years ago

A ball is tossed between three friends. The first toss is 8.6 feet, the second is 5.8 feet, and the third toss is 7.5 feet, whic

Rainbow [258]

angles formed by these tosses are $79.45, 59.02$ and $41.53$ degrees to the nearest hundredth.

<u>Step-by-step explanation:</u>

Here , We have a triangle with sides of length 8.6 feet, 5.8 feet and 7.5 feet.

The Law of Cosines (also called the Cosine Rule) says:

$c^2 = a^2 + b^2 - 2ab (cosx)$

Using the Cosine Rule to find the measure of the angle opposite the side of length 8.6 feet:

⇒ $c^2 = a^2 + b^2 - 2ab (cosx)$

⇒ $c^2 -a^2 - b^2 = -2ab (cosx)$

⇒ $(cosx) =\frac{ c^2 -a^2 - b^2}{ -2ab}$

⇒ $(cosx) =\frac{(8.6^2 - 5.8^2 - 7.5^2)}{ ( -2(5.8)7.5)}$

⇒ $(cosx) =0.18310$

⇒ $cos^{-1}(cosx) = cos^{-1}(0.18310)$

⇒ $x = 79.45$

The Law of Sines (or Sine Rule) is very useful for solving triangles:

$\frac{a}{sin A} = \frac{ b}{sin B} = \frac{c}{sin C}$

We can now find another angle using the sine rule:

⇒ $\frac{ 8.6 }{ sin 79.45} = \frac{7.5}{ sin Y}$

⇒ $sin Y = \frac{(7.5 (sin 79.45))}{ 8.6}$

⇒ $Y = 59.02 degrees$

So, the third angle = $180 - 79.45 - 59.02 = 41.53 degrees.$

Therefore, angles formed by these tosses are $79.45, 59.02$ and $41.53$ degrees to the nearest hundredth.

4 0

3 years ago