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3 years ago

8

What is the value of x?

1 answer:

Pani-rosa [81]3 years ago

7 0

Answer:

x=4

Step-by-step explanation:

Length of LJ is $8\sqrt{2} * sin(30)$ which is $4\sqrt{2}$

Now, in triangle LMJ the both angles are 45 degrees,

so $x^{2} +x^{2} =(4\sqrt{2}) ^{2}$

$2x^{2} = 2*4^{2}$

x=4

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Answer:

Huh

Step-by-step explanation:

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2 years ago

maggie's brother is 3 years younger than twice her age. the sum of their ages is 24. write solve an equation to determine maggie

prohojiy [21]

Maggie =x
brother = 2x-3
x+2x-3= 24
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3 years ago

The surface area of a cylinder is increasing at a rate of 9 pi square meters per hour. The height of the cylinder is fixed at 3

Alekssandra [29.7K]

Answer:

$9\pi \text{ cubic meters per hour}$

Step-by-step explanation:

Since, the surface area of a cylinder,

$A= 2\pi r^2 + 2\pi rh$ ................(1)

Where,

r = radius,

h = height,

If $A= 36\pi\text{ square meters}, h = 3\text{ meters}$

$36\pi = 2\pi r^2 + 2\pi r(3)$

$18 = r^2 + 3r$

$\implies r^2 + 3r - 18=0$

$r^2 + 6r - 3r - 18 = 0$ ( by middle term splitting )

$r(r+6)-3(r+6)=0$

$(r-3)(r+6)=0$

By zero product property,

r = 3 or r = - 6 ( not possible )

Thus, radius, r = 3 meters,

Now, differentiating equation (1) with respect to t ( time ),

$\frac{dA}{dt}= 4\pi r\frac{dr}{dt} +2\pi(r\frac{dh}{dt} + h\frac{dr}{dt})$

∵ h = constant, ⇒ dh/dt = 0,

$\frac{dA}{dt} = 4\pi r \frac{dr}{dt} +2\pi h \frac{dr}{dt}$

We have, $\frac{dA}{dt}=9\pi\text{ square meters per hour}, r = h = 3\text{ meters}$

$9\pi = 4\pi (3) \frac{dr}{dt}+2\pi (3)\frac{dr}{dt}$

$9\pi = (12\pi + 6\pi )\frac{dr}{dt}$

$9\pi = 18\pi \frac{dr}{dt}$

$\implies \frac{dr}{dt} =\frac{1}{2}\text{ meter per hour}$

Now,

Volume of a cylinder,

$V=\pi r^2 h$

Differentiating w. r. t. t,

$\frac{dV}{dt}=\pi ( r^2 \frac{dh}{dt}+h(2r)\frac{dr}{dt})=\pi ((3)(6) (\frac{1}{2})) = 9\pi \text{ cubic meters per hour}$

6 0

3 years ago

Solve the inequality and graph the solution<br> 7x ≥ -91

Alex Ar [27]

The solution is $x \geq 13$ .

Solution:

Given inequality:

$7 x \geq 91$

Divide by 7 on both sides.

$$\frac{7 x}{7} \geq \frac{91}{7}$

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The image of the graph is attached below.

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3 years ago

Which expression is equivalent to 5(w+4) when w=9

erica [24]

Answer: Should be 5(9)+4

Step-by-step explanation:

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3 years ago

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