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3 years ago

But for real, quick question for fifty points.

Mathematics

2 answers:

yanalaym [24]3 years ago

8 0

Answer:

D)16

Step-by-step explanation

we are given a 30-60-90 triangle and the longer side of the triangle

remember the properties of 30-60-90 triangle

the hypotenuse is twice as much as the shorter leg
the longer leg is the square root of 3 times shorter leg

as we are given the longer leg we'll use the second property

let the shorter leg be x

so our equation is

$\displaystyle x\sqrt{3}=16\sqrt{3}$

divide both sides by √3:

$\displaystyle \frac{x\sqrt{3}}{\sqrt{3}}=\frac{16\sqrt{3}}{\sqrt{3}}$

$\displaystyle x=16$

hence,

the length of the shorter leg is 16

Ilya [14]3 years ago

4 0

Answer:

8√3

Step-by-step explanation:

adj = 16√3 ÷ 2 = 8√3

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4 years ago

Gabriel deposits $2,500 into each of two savings accounts.

charle [14.2K]

Answer:

$5,612.16

Step-by-step explanation:

Part 1) Account I earns 4% annual simple interest.

we know that

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where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

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substitute in the formula above

Part 2) Account II earns 4% interest compounded annually.

we know that

The compound interest formula is equal to

A=P(1+rt)

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

t=3 years

p=$2,500

r=4%=4/100=0.04

substitute in the formula above

A=2,500(1+0.04 * 3)

A=2,500 (1.12)

A=$2,800

Part 3) What is the sum of the balances of Account I and Account II at the end of 3 years?

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$2,800 + $2,812.16 = $5.612.16

8 0

4 years ago

a dog searching for a bone walks 3.5 m southeast, then 8.2 m at an angle 30 degrees north of east. Find the magnitude of the dog

Anton [14]

Answer:

Step 1: Firstly, we draw both of the axes.

Step 2: We then draw a vector of length 3.5 m (theoretical) along the (-x) axis.

Step 3: Next, we draw a vector of length 8.2 m from the endpoint towards to top, at an angle of 60° from that point (N.B: 90-30, since it is required to make a 30°∠ with the current vertical; eventually the triangle being formed will be 90° minus the 30°.) Most importantly, the 8.2 m vector should be drawn in such a way so that it is higher than the starting point of the 3.5 m vector. )

Step 4: Lastly, we draw a 15 m vector from the endpoint of the 8.2 m vector, running above the original vector, and to the left. This one should be drawn on the left side, and must be situated far enough.

∴ Triangle 1 () is of angles 30°, 60° and 90°;

On solving for the vertical side (the slope similar to the 3.5 vector), we get

(8.2/2) m = 4.1 m

Next, we solve for the opposite side via 4.1 × √3= 7.1 m

Moving on to Triangle 2 (),

top side = (15 - 7.1) m = 7.9 m

similarly, right side = (4.1 - 3.5) m = 0.6 m

∴ last side = resultant displacement:

⇒ + (0.6)² = 7.9 m

and, direction of displacement = arcTan(y/x)

= arcTan(0.6/7.9)

= 4.3° north of west

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4 years ago

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3 years ago

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Gelneren [198K]

The answer to this function is M = 1/9 (The slope is "M").

8 0

4 years ago