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Lady_Fox [76]
3 years ago
10

Evaluate the following expression. cos870° - sin780º =

Mathematics
1 answer:
Yuri [45]3 years ago
8 0

Answer:

-sqrt(3)

Step-by-step explanation:

Solve each individually

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The length of the hypotenuse of a right triangle is 15 in. and one leg has length of 6 in. Find the length of the other leg.
liq [111]

Answer:

square root 189 i did the math and google says the same

Step-by-step explanation:

5 0
3 years ago
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A man starts walking north at 2 ft/s from a point P. Five minutes later a woman starts walking south at 3 ft/s from a point 500
Vedmedyk [2.9K]

Answer:

The rate at which both of them are moving apart is 4.9761 ft/sec.

Step-by-step explanation:

Given:

Rate at which the woman is walking,\frac{d(w)}{dt} = 3 ft/sec

Rate at which the man is walking,\frac{d(m)}{dt} = 2 ft/sec

Collective rate of both, \frac{d(m+w)}{dt} = 5 ft/sec

Woman starts walking after 5 mins so we have to consider total time traveled by man as (5+15) min  = 20 min

Now,

Distance traveled by man and woman are m and w ft respectively.

⇒ m=2\ ft/sec=2\times \frac{60}{min} \times 20\ min =2400\ ft

⇒ w=3\ ft/sec = 3\times \frac{60}{min} \times 15\ min =2700\  ft

As we see in the diagram (attachment) that it forms a right angled triangle and we have to calculate \frac{dh}{dt} .

Lets calculate h.

Applying Pythagoras formula.

⇒ h^2=(m+w)^2+500^2  

⇒ h=\sqrt{(2400+2700)^2+500^2} = 5124.45

Now differentiating the Pythagoras formula we can calculate the rate at which both of them are moving apart.

Differentiating with respect to time.

⇒ h^2=(m+w)^2+500^2

⇒ 2h\frac{d(h)}{dt}=2(m+w)\frac{d(m+w)}{dt}  + \frac{d(500)}{dt}

⇒ \frac{d(h)}{dt} =\frac{2(m+w)\frac{d(m+w)}{dt} }{2h}                         ...as \frac{d(500)}{dt}= 0

⇒ Plugging the values.

⇒ \frac{d(h)}{dt} =\frac{2(2400+2700)(5)}{2\times 5124.45}                       ...as \frac{d(m+w)}{dt} = 5 ft/sec

⇒ \frac{d(h)}{dt} =4.9761  ft/sec

So the rate from which man and woman moving apart is 4.9761 ft/sec.

3 0
3 years ago
The volume of a cube, in cubic centimeters, is given by the function V(x) = x3, where x is the side length of the cube in centim
Sav [38]

I think we can all agree that 1 centimeter=10millimeters.

And if x is the side in centimeters then 10x will be the side in millimeters.

We just need to rewrite x^3 into (10x)^3.

Because you need to do the exponent to all part of the ( )...

(10x)^3=1000x^3

V(x)=1000x^3 cubic millimeters is the answer

5 0
3 years ago
This is a timed test so I need help fast
FinnZ [79.3K]

Answer:

1st option

Step-by-step explanation:

(x²+x-6)/(x-7)≤0

x≤-3

2≤x≤7

These are the solutions you'll find solving the inequation

Answered by GAUTHMATH

3 0
3 years ago
If K is the midpoint of JL, JK = 8x+11 and KL = 14x-1, find JL.
gladu [14]

Step-by-step explanation:

Since, K is the midpoint of JL.

\therefore \: JK = KL \\ 8x + 11 = 14x - 1 \\ 11 + 1 = 14x - 8x \\ 12 = 6x \\  \frac{12}{6}  = x \\ 2 = x \\  \\  \because \: JL = JK + KL \\   \therefore \: JL = 8x + 11 + 14x - 1 \\ \therefore \: JL = 8x + 14x + 11 - 1 \\ \therefore \: JL = 22x + 10\\  \therefore \: JL = 22 \times 2 + 10..(plug \: x = 2) \\  \therefore \:JL = 44 + 10 \\  \huge \red{ \boxed{\therefore \:JL = 54}}

7 0
3 years ago
Read 2 more answers
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