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2 years ago

Find the indicated side of the triangle.

Mathematics

1 answer:

Damm [24]2 years ago

3 0

Answer:

$\huge \orange{b = \boxed{ 6} \sqrt{ \boxed{3}} }$

Step-by-step explanation:

$a = 12 \sin 30 \degree \\ \\ \implies \: a = 12 \times \frac{1}{2} \\ \\ \implies \: \huge \red{ a = 6} \\ \\ b = 12 \cos 30 \degree \\ \\ \implies \: b = 12 \times \frac{ \sqrt{3} }{2} \\ \\ \implies \: b = 6 \times \sqrt{3} \\ \\ \implies \: \huge \orange{b = \boxed{ 6} \sqrt{ \boxed{3}} }$

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Is x^2y^5 simplified?

Marizza181 [45]

Yes it is indeed nothing else can be done to this problem

6 0

3 years ago

Z varies jointly as x and y. z=60 when x=5 and y=6. find z when x = 7 and y=3

Aneli [31]

Answer:

z = 42

Step-by-step explanation:

The question can be answered in 2 steps as follows:

Step 1: Calculation of the constant of the variation

The equation for the joint variation can be given as follows:

z = cxy ................... (1)

Where;

z = 60

c = constant = ?

x = 5

y = 6

Substituting the values into equation (1) and solve c, we have:

60 = c * 5 * 6

60 = c * 30

c = 60 / 30

c = 2

Step 2: find z when x = 7 and y = 3

Since from Step 1 c = 2, we now use equation (1) and substitute the values into it to find z as follows:

z = 2 * 7 * 3

z = 42

4 0

3 years ago

An object dropped from a height of 600 feet has a height, h(t), in feet after t seconds have elapsed, such that h(t)=600 - 16t^2

gulaghasi [49]

Answer:

t as a function of height h is t = √600 - h/16

The time to reach a height of 50 feet is 5.86 minutes

Step-by-step explanation:

Function for height is h(t) = 600 - 16t²

where t = time lapsed in seconds after an object is dropped from height of 600 feet

t as a function of height h

replacing the function with variable h

h = 600 - 16t²

Solving for t

Subtracting 600 from both side

h - 600 = -16t²

Divide through by -16

600 - h/ 16 = t²

Take square root of both sides

√600 - h/16 = t

Therefore, t = √600 - h/16

Time to reach height 50 feet

t = √600 - h/16

substituting h = 50 in the equation

t = √600 - 50/16

t = √550/16

t= 34.375

t = 5.86 minutes

7 0

3 years ago

2 ft

sdas [7]

Answer:

88/7 ft = 12.6 ft (nearest tenth)

Step-by-step explanation:

Circumference of a circle = 2 $\pi$ r

Radius of inner circle

Given:

circumference of inner circle = 22ft
$\pi$ = 22/7

⇒ 22 = 2 x (22/7) x r

⇒ r = 3.5

So the radius of the inner circle is 3.5 ft

Radius of outer circle

If the distance between the inner circle and the outer circle is 2 ft, then the radius of the outer circle = 3.5 + 2 = 5.5

Circumference of outer circle

Therefore, circumference of outer circle:

= 2 x (22/7) x 5.5

= 242/7 ft

Difference between circumferences

Difference = outer circle circumference - inner circle circumference

= 242/7 - 22

= 88/7 ft

= 12.6 ft (nearest tenth)

4 0

2 years ago

If (x+yi)(1-3i)=10 Then x+y=

Naily [24]

Answer:

x + y = 4

Step-by-step explanation:

Given that, (x + iy)(1 - 3i) = 10, then we have to calculate x + y.

Now, (x + iy)(1 - 3i) = 10

⇒ x(1 - 3i) + iy(1 - 3i) = 10

⇒ x - 3xi + iy - 3yi² = 10

⇒ (x + 3y) + i(y - 3x) = 10

Now, comparing the real and imaginary part of both sides we get,

(x + 3y) = 10 ............. (1) and

y - 3x = 0

⇒ y = 3x ............... (2)

Solving equations (1) and (2) we get

x + 3(3x) = 10

⇒ x = 1

So, y = 3x = 3

Therefore, x + y = 1 + 3 = 4 (Answer)

7 0

3 years ago