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3 years ago

HELP ASAP PLEASE!!!!

Mathematics

1 answer:

DENIUS [597]3 years ago

6 0

Answer:

q=(1,5) t=(-2,3)r=(3,-1)s=(0,0)

Step-by-step explanation:

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Part B: If a cross section of the rectangular pyramid is cut perpendicular to the base, passing through the top vertex, what wou

Katyanochek1 [597]

Answer:

A triangle.

Step-by-step explanation:

The plane would pass through opposite sloping faces of the pyramid and through the base; the shape formed is a triangle.

6 0

3 years ago

A firework is launched at the rate of 10 feet per second from a point on the ground 50 feet from an observer. to 2 decimal place

Kazeer [188]

The rate of change of the angle of elevation when the firework is 40 feet above the ground is 0.12 radians/second.

First we will draw a right angle triangle ΔABC, where ∠B = 90°

Lets, assume the height(AB) = h and base(BC)= x

If the angle of elevation, ∠ACB = α, then

tan(α) = $\frac{AB}{BC} = \frac{h}{x}$

Taking inverse trigonometric function, α = tan⁻¹ ( $\frac{h}{x}$ ) .............(1)

As we need to find the rate of change of the angle of elevation, so we will differentiate both sides of equation (1) with respect to time (t) :

$\frac{d\alpha}{dt}=[\frac{1}{1+ \frac{h^2}{x^2}}]*(\frac{1}{x})\frac{dh}{dt}$

Here, the firework is launched from point B at the rate of 10 feet/second and when it is 40 feet above the ground it reaches point A,

that means h = 40 feet and $\frac{dh}{dt}$ = 10 feet/second.

C is the observer's position which is 50 feet away from the point B, so x = 50 feet.

$\frac{d\alpha}{dt}= [\frac{1}{1+ \frac{40^2}{50^2}}] *\frac{1}{50} *10\\ \\ \frac{d\alpha}{dt} = [\frac{1}{1+\frac{16}{25}}] *\frac{1}{5}\\ \\ \frac{d\alpha}{dt} = [\frac{25}{41}] *\frac{1}{5}\\ \\ \frac{d\alpha}{dt}= \frac{5}{41} =0.1219512$

= 0.12 (Rounding up to two decimal places)

So, the rate of change of the angle of elevation is 0.12 radians/second.

5 0

3 years ago

If you were to pull colored marbles out of the bag (one at a time, and putting the marble back each time) for 500 tries, approxi

shepuryov [24]

Answer:

We need to know the other marbles in the bag and how many there are of each.

5 0

2 years ago

The sum of two numbers is 35.

LUCKY_DIMON [66]

Answer:

Larger number(x)=20

Step-by-step explanation:

They're saying that the larger number 3 times is EQUAL(the same) to 4 times the smaller number.

The smallest number=35-x.

The larger number= x.

3 times the larger number=3x

4 times the smaller number=4(35-x)

Now, input it into an equation and solve:

3x=4(35-x) Distribute by multiplying 4 with 35 and x.

3x+4x=140-4x+4x Get 140 by itself by adding 4x.

7x/7=140/7 Divide.

x=20

Since x= the larger number, x=20.

8 0

3 years ago

Suppose a triangle has two sides of length 32 and 35, and that the angle

pantera1 [17]

Answer:

The third side is around 58.043

Step-by-step explanation:

Use the law of cosines: $c^2=a^2+b^2-2abcos(C)$

Plug in the two sides we know (into a and b) and the angle we know (into angle C).

Thus:

$c^2=32^2+35^2-2(32)(35)cos(120)$

Use a calculator:

$c^2=3369\\$

$c=58.043087...$

(Note: Make sure you're in Degrees mode.)

3 0

2 years ago