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2 years ago

Use the image below to answer the following question:

Mathematics

1 answer:

Ksju [112]2 years ago

5 0

Answer: The ratios are both identical. (Choice A)

Why does this answer work?

Well let's refer to the diagram below.

Angle x has side 12 opposite it and the hypotenuse is 13.

This means sin(x) = opposite/hypotenuse = 12/13

Also, angle y has side 12 adjacent to it, meaning,

cos(y) = adjacent/hypotenuse = 12/13

Both trig ratios result in 12/13 and we can say sin(x) = cos(y)

One last thing to notice is that x+y = 90

In other words, if x+y = 90, then sin(x) = cos(y)

Phrased a slightly different way: if x+y = 90, then sin(y) = cos(x)

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Calculate dy/dx if Ln (x + y) = ex/y

Margaret [11]

Assuming that the given expression is $ln(x+y)= e^{x/y}$

You calculate dy / dx = y' as:

1
-------. y' = e^(x/y) * (-x/y^2)
x + y

=> y' = e^(x/y) * (-x/y^2) * (x + y).

Answer dy / dx = - e^(x/y) (x/y^2) (x+y)

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3 years ago

What's 25% of $130,000

weeeeeb [17]

100% = 1

25% = 0.25

25% * 130,000 = 0.25*130,000 = 32,500

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4 years ago

-2.105 as a fraction?

Bezzdna [24]

The easiest way is if it doesn't need to be simplified. Multiply -2.105 by $\frac{1000}{1000}$ . You get the fraction $-\frac{2105}{1000}$ . While this is technically the answer, you can simplify this down to $\frac{421}{200}$ . Because 421 is a prime number, this can not be simplified any further. Therefore, the solution is $\frac{421}{200}$ .

$\frac{421}{200}$ .

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3 years ago

What is 16 : 24 in simplest form

REY [17]

2/3

16/24 and divide the greatest common factor (8)

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4 years ago

Read 2 more answers

Phil's shadow is half as long as Phil is tall. If he were 4 inches taller and his shadow were 3 inches

insens350 [35]

Answer:

Phil is 16 inches tall and his shadow is 8 inches tall

Step-by-step explanation:

this is an algebra word problem.

1. Find the unknown and label it x.

Let Phil's shadow be x inches.

2. find other unknown quantities and define them with

Phil's height= 2x (phil is shadow is half as long as Phil is tall)

3. FInd the equation

if he was 4 inches taller (2x+4)

and his shadow was three inches shorter (x-3)

his height ( 2x+4) times the shadow's height (x-3) would be 100 square inches.

(2x+4) ×(x-3)=100

(2x+4)(x-3)=100

this is a quadratic equation and there are a number of ways to solve these. the two main ways are

1. quadratic equation

2. expanding and factorising

3. graphing

we will use 2. expanding and factorising for this problem. We need to make the right hand side = 0 by first factorising then rearranging.

(2x*x)+(2x*-3)+(x*4) +(4*-3)=100

2x^2 -6x+4x-3x-12=100

2x^2 -2x=112

2x^2 -2x-112=0

once factorised take out the common factor of 2

2(x^2-x-56)=0

now factorise what's in the brackets ( two numbers multiply to make 56 but add to make -1.

2(x-8)(x+7)=0

x-8=0 => x=8

x+7=0 x=-7 not possible

the shadow is 8 inces long. Phil is 16 inches tall.

Hope this is of help :)

5 0

3 years ago