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2 years ago

A 28 foot ladder is propped against a wall. The base of the ladder is 19 ft from the wall how far up the wall does the ladder go

Mathematics

1 answer:

docker41 [41]2 years ago

8 0

Answer:

20.6

Step-by-step explanation:

The problem can be solved by applyPythagoreanean theory

a^2+b^2= c^2

19^2 + b^2= 28^2

361 + b^2= 784

b^2= 784-361

= 423

b= √423

= 20.6

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The perimeter of a triangle garden is 54 feet. Find the length of the three sides if the middle length side is 4 feet greater th

jeka94

9514 1404 393

Answer:

9 ft, 22 ft, 23 ft

Step-by-step explanation:

Let s represent the length of the shortest side. Then the middle length side is (2s+4) and the longest side is (3s-4). The perimeter is the sum of the side lengths:

54 = s +(2s +4) +(3s -4)

54 = 6s . . . . . . . . . . . . . . collect terms

9 = s . . . . . . . . . . divide by 6

2s+4 = 2·9 +4 = 22

3s -4 = 3·9 -4 = 23

The lengths of the three sides are 9 feet, 22 feet, and 23 feet.

6 0

2 years ago

Fifteen equals s over thirteen

zimovet [89]

Can you restate the question please

6 0

3 years ago

Find the length of the curve. R(t) = cos(8t) i + sin(8t) j + 8 ln cos t k, 0 ≤ t ≤ π/4

arsen [322]

we are given

$R(t)=cos(8t)i+sin(8t)j+8ln(cos(t))k$

now, we can find x , y and z components

$x=cos(8t),y=sin(8t),z=8ln(cos(t))$

Arc length calculation:

we can use formula

$L=\int\limits^a_b {\sqrt{(x')^2+(y')^2+(z')^2} } \, dt$

$x'=-8sin(8t),y=8cos(8t),z=-8tan(t)$

now, we can plug these values

$L=\int _0^{\frac{\pi }{4}}\sqrt{(-8sin(8t))^2+(8cos(8t))^2+(-8tan(t))^2} dt$

now, we can simplify it

$L=\int _0^{\frac{\pi }{4}}\sqrt{64+64tan^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8\sqrt{1+tan^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8\sqrt{sec^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8sec(t) dt$

now, we can solve integral

$\int \:8\sec \left(t\right)dt$

$=8\ln \left|\tan \left(t\right)+\sec \left(t\right)\right|$

now, we can plug bounds

and we get

$=8\ln \left(\sqrt{2}+1\right)-0$

so,

$L=8\ln \left(1+\sqrt{2}\right)$ ..............Answer

5 0

2 years ago

How to find slope? I'm confused on using y=mx+b

Mumz [18]

Slope is mx is that makes sense

4 0

3 years ago

Read 2 more answers

Find the sum and simplify 2_1/3 + 1_3/ 4

Anna35 [415]

Answer:

49/12=4 1/12

Step-by-step explanation:

7/3+7/3=28/12+21/12=49/12=4 1/12

7 0

2 years ago