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Tpy6a [65]
2 years ago
9

A small plane flew 808 miles in 4 hours with the wind. Then on the return trip flying against the wind it travels only 488 miles

in 4 hours. What were the wind velocity and speed of the plane?
Mathematics
1 answer:
Blababa [14]2 years ago
8 0

Answer:

Step-by-step explanation:

let wind velocity=x

speed of plane=y

(x+y)*4=808

x+y=808/4=202   ...(1)

(y-x)*4=488

y-x=122 ...(2)

add (1) and (2)

2y=202+122=324

y=324/2=162

from (1)

x+162=202

x=202-162=40

wind velocity=40 m/hr

speed of plane=162 m/hr

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In ΔXYZ, ∠Y=90° and ∠X=73°. ∠ZWY=80° and XW=80. Find the length of ZY to the nearest 100th.
lawyer [7]

Answer:

Solution given:

Y=90°

∠X=73°.

∠ZWY=80°

and XW=80.

ZY=?

We know that

In right angled triangle ∆ XYZ

Tan 73=\frac{p}{h}

3.27=\frac{yz}{xy}

3.27×[xy]=yz

xw+wy=\frac{yz}{3.27}

wy=\frac{yz}{3.27}-80...........(1)

again

In right angled triangle WYZ

Tan 80=\frac{yz}{wy}

5.67×wy=yz

wy=\frac{yz}{5.67}

yz=5.67×wy............................................(2)

E<u>q</u><u>u</u><u>a</u><u>t</u><u>i</u><u>n</u><u>g</u><u> </u><u>equation</u><u> </u><u>1</u><u>&</u><u>2</u>

\frac{yz}{5.67}=\frac{yz}{3.27}-80

\frac{yz}{3.27}-\frac{yz}{5.67}=80

5.67yz-3.27yz=80*5.67*3.27

2.4yz =1483.272

yz=\frac{1483.272}{2.4}

yz=618.03

:.y=618.03unit.<u>the length of ZY to the nearest 100</u><u>th</u><u> </u><u>is</u><u> </u><u>6</u><u>1</u><u>8</u><u>.</u>

8 0
3 years ago
1000 was invested at 5.5% interest, compounded annually. After sometime the amount had grown to 1550. How long was the money inv
scZoUnD [109]

compound interest equation for annually compounded

A=P(1+r)^t

A=final amount

P=principal

r=rate in decimal

t=time in years


given that

A=1550

P=1000

r=5.5%=0.055

find t


1550=1000(1+0.055)^t

divide both sides by 1000

1.55=1.055^t

take ln of both sides

ln(1.55)=ln(1.055^t)

use ln rule ln(a^b)=b(ln(a))

ln(1.55)=t(ln(1.055))

divide both sides by ln(1.055)

\frac{ln(1.55)}{ln(1.055)}=t

using a calculator, we get that t=8.18544 yrs

so about 8.2yrs

4 0
3 years ago
The difference between a and b is 10. The number a is 4 more than 3 times the number b. Which of the following pairs of equation
k0ka [10]

Answer:

D. a−b=10 a=3b+4

Step-by-step explanation:

Difference between a and b means to subtract b from a

We have,

a-b=10

a is 4 more than 3 times b

4 more than means to add 4

3 times b means to multiply b by 3

Therefore, a=3 times b + 4

a=3b+4

a - b=10; a=3b+4

4 0
3 years ago
A company that manufactures cars for freight trains manufactured 393 cars in the month of​ August, out of which 168 were boxcars
mr Goodwill [35]
393/393 - 168/393 = 225/393

Simplify 225/393 by 3 because that is is the fractions GCF

75/131

4 0
3 years ago
Suppose that a butterfly can fly 82 feet in 4 seconds. A dragonfly can fly 50 feet in 2 seconds. Which can fly faster and by how
Lady bird [3.3K]

A butterfly can fly 82 feet in 4 seconds.

Distance traveled by butterfly = 82 feet.

Time taken by butterfly =4 seconds

Speed = distance /time

Speed of butterfly = 82/4 = 20.5 feet/second

A dragonfly can fly 50 feet in 2 seconds.

Distance traveled by dragonfly =50 feet.

Time taken by dragonfly =2 seconds.

Speed of dragonfly = 50/2 = 25 feet/second

So dragonfly can fly faster than the butterfly.

Difference in speed = speed of dragonfly - speed of butterfly = 25-20.5 = 4.5

So The dragonfly is 4.5 feet per second faster than butterfly.

Answer: B) The dragonfly is 4.5 feet per second faster.  


5 0
3 years ago
Read 2 more answers
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