The price of an item yesterday was $115. Today, the price rose to $161. Find the percentage increase

Mathematics

1 answer:

mamaluj [8]3 years ago

4 0

Answer:

14%

Step-by-step explanation:

161/115 = 1.4 which you times by 100

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Three less than the quotient of ten and a number, increased by six” when n = 2?

Musya8 [376]

(10/n +6) -3
10/2+6-3
5+6-3
11-3
8
Hope this helped!

3 0

3 years ago

Read 2 more answers

A firework is launched at the rate of 10 feet per second from a point on the ground 50 feet from an observer. to 2 decimal place

Kazeer [188]

The rate of change of the angle of elevation when the firework is 40 feet above the ground is 0.12 radians/second.

First we will draw a right angle triangle ΔABC, where ∠B = 90°

Lets, assume the height(AB) = h and base(BC)= x

If the angle of elevation, ∠ACB = α, then

tan(α) = $\frac{AB}{BC} = \frac{h}{x}$

Taking inverse trigonometric function, α = tan⁻¹ ( $\frac{h}{x}$ ) .............(1)

As we need to find the rate of change of the angle of elevation, so we will differentiate both sides of equation (1) with respect to time (t) :

$\frac{d\alpha}{dt}=[\frac{1}{1+ \frac{h^2}{x^2}}]*(\frac{1}{x})\frac{dh}{dt}$

Here, the firework is launched from point B at the rate of 10 feet/second and when it is 40 feet above the ground it reaches point A,

that means h = 40 feet and $\frac{dh}{dt}$ = 10 feet/second.

C is the observer's position which is 50 feet away from the point B, so x = 50 feet.

$\frac{d\alpha}{dt}= [\frac{1}{1+ \frac{40^2}{50^2}}] *\frac{1}{50} *10\\ \\ \frac{d\alpha}{dt} = [\frac{1}{1+\frac{16}{25}}] *\frac{1}{5}\\ \\ \frac{d\alpha}{dt} = [\frac{25}{41}] *\frac{1}{5}\\ \\ \frac{d\alpha}{dt}= \frac{5}{41} =0.1219512$

= 0.12 (Rounding up to two decimal places)

So, the rate of change of the angle of elevation is 0.12 radians/second.

5 0

3 years ago

Help please logarithms

DochEvi [55]

Answer:

Simplified: 40

Step-by-step explanation:

To simplify this, we need to first separate the terms in this expression. There is a property of exponents that says: $x^{a+b} =x^ax^b$ We can do this same thing to simplify this expression. Next, we can simplify each of these terms. $2^2$ simply becomes 4. In the other term, the $2^{log_2}$ simply cancel each other and leave the 10. This means that we're left with 4*10, which is 40