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3 years ago

Pls lmk what the vertex of this is ?

Mathematics

1 answer:

Darya [45]3 years ago

4 0

Answer:

Point U

Step-by-step explanation:

The center point of the angle

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Please help Ladder question!!

PIT_PIT [208]

Answer:

Step-by-step explanation:

This is a related rates problem from calculus using implicit differentiation. The main equation is going to be Pythagorean's Theorem and then the derivative of that. Pythagorean's Theorem is

$x^2+y^2=c^2$ where c is the hypotenuse and is a constant. Therefore, the derivative of this with respect to time, and using implicit differentiation is

$2x\frac{dx}{dt}+2y\frac{dy}{dt}=0$ and dividing everything by 2 to simplify a bit:

$x\frac{dx}{dt}+y\frac{dy}{dt}=0$ . Upon analyzing that equation, it looks like we need values for x, y, $\frac{dx}{dt}$ , and $\frac{dy}{dt}$ . And here's what we were given:

$\theta=45$ and $\frac{dx}{dt}=.5$ In the greater realm of things, that's nothing at all.

BUT we can use the right triangle and the angle we were given to find both x and y. The problem we are looking to solve is to

Find $\frac{dy}{dt}$ at the instant that $\frac{dx}{dt}$ = .5.

Solving for x and y:

$tan45=\frac{x}{6}$ and

6tan45 = x ( and since this is a 45-45-90 triangle, y = x):

$6(\frac{\sqrt{2} }{2})=x=y$ so

$x=y=3\sqrt{2}$ and now we can fill in our derivative. Remember the derivative was found to be

$x\frac{dx}{dt}+y\frac{dy}{dt}=0$ so

$3\sqrt{2}(\frac{1}{2})+3\sqrt{2}\frac{dy}{dt}=0$ and

$\frac{3\sqrt{2} }{2}+3\sqrt{2} \frac{dy}{dt}=0$ and

$3\sqrt{2}\frac{dy}{dt}=-\frac{3\sqrt{2} }{2}$ and multiplying by the reciprocal of the left gives us:

$\frac{dy}{dt}=-\frac{3\sqrt{2} }{2}(\frac{1}{3\sqrt{2} })$ so

$\frac{dy}{dt}=-\frac{1}{2}\frac{m}{s}$

8 0

3 years ago

Line JK passes through points J(–4, –5) and K(–6, 3). If the equation of the line is written in slope-intercept form, y = mx + b

andrey2020 [161]

(-4,-5)(-6,3)
slope(m) = (3 - (-5) / (-6 - (-4)
slope(m) = (3 + 5) / (-6 + 4)
slope(m) = 8/-2 = -4

y = mx + b
slope(m) = -4
u can use either of ur points...I will use (-6,3)
3 = -4(-6) + b
3 = 24 + b
3 - 24 = b
- 21 = b <== here ya go

3 0

3 years ago

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Simplify the following expression into simplest form with all positive exponents

Yuri [45]

3.2 x 10 ^5

Hope this helps ;)

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3 years ago

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An acrobat was launched toward a water tank, with an upward velocity of 48 feet per second. The launch point was 32 feet below t

ludmilkaskok [199]

Hello. How are you. Do u take K12