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4 years ago

Given: ∆AKL, AK = 9, m∠K = 90°, m∠A = 60°. Find: The perimeter of ∆AKL, The area of ∆AKL.

1 answer:

5 0

Perimeter = 27 + 9*sqrt(3), Approximately 42.58845727
Area = 40.5*sqrt(3). Approximately 70.14805771
Since all triangles have a total of 180 degrees and we've been given 2 of those angles, the remaining angle is 180 - 90 - 60 = 30 degrees. So we have a 30,60,90 degree right triangle. Drawing the triangle and assigning the proper angle to each vertex shows that AK is the short leg of the triangle. And since it's a 30,60,90 triangle, the hypotenuse is AL and it will be twice the length of AK, so it's 18. And finally, we can use the Pythagorean theorem to calculate the length of KL. So
KL = sqrt(18^2 - 9^2) = sqrt(324 - 81) = sqrt(243) = sqrt(81*3) = 9*sqrt(3)
So the perimeter is
P = 9 + 18 + 9*sqrt(3) = 27 + 9*sqrt(3). Which is approximately 42.58845727
The area is base times height divided by 2. And we have a base of 9 and a height of 9*sqrt(3). So
A = 9 * 9*sqrt(3)/2 = 81*sqrt(3)/2 = 40.5*sqrt(3). Which is approximately 70.14805771

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Find the surface area of each figure (spheres and hemispheres)

xenn [34]

Answer:

7. 1520.53 cm²

8. 232.35 ft²

9. 706.86 m²

10. 4,156.32 mm²

11. 780.46 m²

12. 1,847.25 mi²

Step-by-step explanation:

Recall:

Surface area of sphere = 4πr²

Surface area of hemisphere = 2πr² + πr²

7. r = 11 cm

Plug in the value into the appropriate formula

Surface area of the sphere = 4*π*11² = 1520.53 cm² (nearest tenth)

8. r = ½(8.6) = 4.3 ft

Plug in the value into the appropriate formula

Surface area of the sphere = 4*π*4.3² = 232.35 ft² (nearest tenth)

9. r = ½(15) = 7.5 m

Surface area of the sphere = 4*π*7.5² = 706.86 m² (nearest tenth)

10. r = ½(42) = 21 mm

Plug in the value into the formula

Surface area of hemisphere = 2*π*21² + π*21² = 2,770.88 + 1,385.44

= 4,156.32 mm²

11. r = 9.1 m

Plug in the value into the formula

Surface area of hemisphere = 2*π*9.1² + π*9.1² = 520.31 + 260.15

= 780.46 m²

12. r = 14 mi

Plug in the value into the formula

Surface area of hemisphere = 2*π*14² + π*14² = 1,231.50 + 615.75

= 1,847.25 mi²

8 0

3 years ago

Use a inequality symbol to compare -3x+7 -10-2

abruzzese [7]

Hey there,

Let's remember that a (inequality symbol) is things like (<), (>), (≤),(≥), (≠).

So, I believe that (-3x+7) and (-10-2) are separate. So we will find that out :)

Let's first do (-3x+7). As simplifying this expression here, we take that "x" of for a while and just stick to (-3+7).

-3
+ 7
______
4

Let's bring that "x" back, and the answer would be 4x for a while.

So far, 4x is the answer.
_____________________________________________________________

Now, Let's work on the other side.

We are talking about (<span>-10-2)

-10
- 2
_______
</span> -12

So, by solving the answer to (-10-2), we got -12.

So, let's determine what is greater . . . . .

$What \ is \ greater?$

-12 or 4.

-12 is on the negative side, and the number 4 is positive. This would conclude that 4 is great than -12.

Your correct answer would look like . . .

<span>(-3x+7) > (-10-2)
</span>
I really hope this helps you alot.

~Jurgen

8 0

3 years ago

Read 2 more answers

Naz is swimming the English Channel from France to England. A few minutes ago, she was swimming in calm waters at a velocity (sp

Jlenok [28]

Answer:

is this right

Step-by-step explanation:

This is a list of notable successful swims across the English Channel,[1] a straight-line distance of about 21 miles (34 km).[2]

3 0

3 years ago

Which is more, 2 fluid ounces or 1 pint