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2 years ago

Write the following equation without using an absolute value sign. |y-x|, if y>x

Mathematics

1 answer:

Vera_Pavlovna [14]2 years ago

4 0

Answer:

y-x $\leq$ 0 and y-x $\geq$ 0

Step-by-step explanation:

As we know,

Absolute value of any given number is the positive number itself. Therefore,

y-x $\leq$ 0 and y-x $\geq$ 0

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If a 20 ft tree casts a 15ft shadow, how long a shadow is cast

Irina-Kira [14]

Answer:

25 ft

Step-by-step explanation:

c = √a^2 + b^2 = √20^2 + 15^2 = 25ft

Hooke me up with a 5 star and a thanks :)

4 0

2 years ago

the perimeter of this quarter circle with radius, r = 32mm. Give your answer as an expression in terms of π.

djverab [1.8K]

Answer:

16π + 64

Step-by-step explanation:

So the whole circumference is 64π

A quarter is 16π

Then you just have to account for the two radii.

16π + 64

3 0

3 years ago

Read 2 more answers

Help for a brainliest lol

Sergio [31]

Step-by-step explanation:

The answer is option b.

Explanation in the pic.

Need any other maths, feel free!!

6 0

3 years ago

Read 2 more answers

Determine whether LINE AB and LINE CD are parallel, perpendicular, or neither. A(−1, −4) , B(2, 11) , C(1, 1) , D(4, 10) ( write

Luba_88 [7]

Step-by-step explanation:

Hey there!

The points of line AB are; (-1,-4) and (2,11).

Note:

Use double point formula and simplify it to get two eqaution.
Use condition of parallel lines, perpendicular lines to know whether the lines are parallel or perpendicular or nothing.

~ Use double point formula.

$(y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)$

~ Keep all values.

$(y + 4) = \frac{11 + 4}{2 + 1} (x + 1)$

~ Simplify it.

$y + 4 = \frac{15}{3} (x + 1)$

$y + 4 = 5x + 5$

$5x - y + 1 = 0$

Therefore this is the equation of line AB.

Now, Finding the equation of line CD.

Given;

The points of line CD are; (1,1) and (4,10).

~ Using formula.

$(y - y1) = \frac{y2 - y1}{x2 - x1}(x - x1)$

~ Keep all values.

$(y - 1) = \frac{10 - 1}{4 - 1} (x - 1)$

~ Simplify it.

$y - 1 = 3 x - 3$

$3x - y - 2 = 0$

Therefore, 3x - y- 2 = 0 is the eqaution of line CD.

Use condition of parallel lines.

m1= m2

Slope of equation (i)

$m1 = \frac{ - coeff. \: of \: x}{coeff \: of \: y}$

$m1 = \frac{ - 5}{ - 1}$

Therefore, m1 = 5

Slope of second equation.

$m2 = \frac{ - coeff \: .of \: x}{coeff \: .of \: y}$

$m2 = \frac{ - 3}{ - 1}$

Therefore, m2 = 3.

Now, m1≠m2.

So, the lies are not parallel.

Check for perpendicular.

m1*m2= -1

3*5≠-1.

Therefore, they aren't perpendicular too.

So, they are neither.

Hope it helps...

6 0

3 years ago

R leaks out of a barrel so that the rate of change in the water level is proportional to the square root of the depth of the wat

Irina-Kira [14]

Let y(t) represent the level of water in inches at time t in hours. Then we are given ...
y'(t) = k√(y(t)) . . . . for some proportionality constant k
y(0) = 30
y(1) = 29

We observe that a function of the form
y(t) = a(t - b)²
will have a derivative that is proportional to y:
y'(t) = 2a(t -b)

We can find the constants "a" and "b" from the given boundary conditions.
At t=0
30 = a(0 -b)²
a = 30/b²
At t=1
29 = a(1 - b)² . . . . . . . . . substitute for t
29 = 30(1 - b)²/b² . . . . . substitute for a
29/30 = (1/b -1)² . . . . . . divide by 30
1 -√(29/30) = 1/b . . . . . . square root, then add 1 (positive root yields extraneous solution)
b = 30 +√870 . . . . . . . . simplify

The value of b is the time it takes for the height of water in the tank to become 0. It is 30+√870 hours ≈ 59 hours 29 minutes 45 seconds

5 0

3 years ago