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2 years ago

What is the value of x? *

Mathematics

1 answer:

Juliette [100K]2 years ago

3 0

The value of x if YR is a perpendicular bisector of HB is 5

<h3>How to determine the value of x?</h3>

The given parameters are:

YR is a perpendicular bisector of HB.

HY = 7x + 13

HW = 8y - 15

WB = 3y + 21

YB = 12x - 12.

The statement "YR is a perpendicular bisector of HB" implies that:

The line segment YR divides the line segment HB into equal halves

So, we have the following equation

HY = YB

Substitute the known values in the above equation

7x + 13 = 12x - 12

Collect the like terms in the above equation

7x - 12x = -13 - 12

Evaluate the like terms in the above equation

-5x = -25

Divide both sides of the equation by -5

x = 5

Hence, the value of x if YR is a perpendicular bisector of HB is 5

Read more about perpendicular bisectors at

brainly.com/question/11006922

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Find the absolute extreme of the function on the closed interval. y=9e^xsinx , [0,pi]

Molodets [167]

For convenience sake, I will let $y=f(x)=9e^{x}\sin x$

First, we evaluate the function at the endpoints of the interval.

$f(0)=9e^{0}\sin(0)=0\\\\f(\pi)=9e^{\pi}\sin(\pi)=0$

Then, we need to find the critical points.

We can start by taking the derivative using the power rule.

$f'(x)=9e^{x} \frac{d}{dx} \sin x+9\sin x \frac{d}{dx} e^{x}=9e^{x}(\cos x+\sin x)$

Setting this equal to 0,

$9e^x (\cos x+\sin x)=0$

Since $9e^x > 0$ , we can divide both sides by $9e^x$ .

$\cos x+\sin x=0\\\\\sin x=-\cos x\\\\\tan x=-1\\\\x=\frac{3\pi}{4}$

$f\left(\frac{3\pi}{4} \right)=9e^{3\pi/4}\sin \left(\frac{3\pi}{4} \right)=\frac{9\sqrt{2}e^{3\pi/4}}{2}$

So, the absolute minimum is $\boxed{\left(\frac{3\pi}{4}, \frac{9\sqrt{2}e^{3\pi/4}}{\sqrt{2}} \right)}$ and the absolute minima are $\boxed{(0,0), (\pi, 0)}$

3 0

2 years ago

If a snowball melts so that its surface area decreases at a rate of 5 cm2/min, find the rate at which the diameter decreases whe

mixas84 [53]

Answer:

The diameter decreases at the rate of 0.0796 cm/min when the diameter is 10 cm.

Step-by-step explanation:

A snowball is spherical, so it's area is given by the following formula:

$A = 4\pi r^{2}$

The radius is half the diameter so:

$A = 4\pi (\frac{d}{2})^{2}$

$A = 4\pi \frac{d^{2}}{4}$

$A = \pi d^{2}$

If a snowball melts so that its surface area decreases at a rate of 5 cm2/min, find the rate at which the diameter decreases when the diameter is 10 cm.

We have to find $\frac{dd}{dt}$ when $\frac{dA}{dt} = -5, d = 10$