a boy flies a kite with a 100 foot long string. the angle of elevation of the string is 48 degrees. how high is the kite from the ground?

Answers

Answer 1

Answer: we know that
in a right triangle
sin ∅=opposite side angle ∅/hypotenuse
opposite side angle ∅=hypotenuse*sin ∅

in this problem
angle ∅=48°
hypotenuse=100 ft
opposite side angle ∅=?----> height of the kite from the ground

opposite side angle ∅=100*sin 48°------> 74.31 ft

the answer is
74.31 ft

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Solve for x. 7(x - 3) = 4(x + 5)
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9^x=27^(x+2)how do I do that? I don't get how to do it with different bases
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Can you please explain how you write 0.5 in words?

Answers

50 tenths??>? I think thats right maybe

Corey collection 4pound of newspaper on day 1after day one he collected 4 times the amount on which day did he first collect over a 1000 pounds of new paper

Answers

Answer:

Fifth Day (1024 pounds)

Step-by-step explanation:

For every subsequent day, he collected 4 times the previous day.

This increase is a ratio/product, therefore the sequence is a geometric sequence.

The nth term of a geometric sequence, $U_n=ar^(n-1)$

Where:

a=first term

r=common ratio

n=number of terms

Corey collected 4 pounds of newspaper on day 1., a=4

After day one he collected 4 times the amount and for every subsequent day, he collected 4 times the previous day. r=4

We want to determine on which day he will first collect over a 1000 pounds of new paper.

$U_n=1000\n4 X 4^(n-1) =1000\n4^(n-1)=250$

In order to apply law of indices, we look for the next term greater than 250 which is an index of 4.

$4^(n-1)>256>250\n4^(n-1)>4^4\nn-1>4\nn>4+1\nn>5$

Therefore on the fifth day, he will collect an amount over 1000 pounds, precisely 1024 pounds.

If the point ((4,-2) what is included in a direct viration relationship which point also belongs and variation

Answers

Answer:

The answer is "This direct variant (-4,2) is part of it".

Step-by-step explanation:

The equation expresses its direct variation relation

$y = mx ........ (1)$

Where x and y vary directly, and k vary continuously.

Now so the point (4,-2) is in the direct relation of variation, so from equation (1) we are given, $-2 = 4m$

$\to m=-(1)/(2)$

The equation (1) is therefore converted into

$\to y=-(1)/(2)x \n\n\to x + 2y = 0 ......... (2)$

Then only the point (-4,2) satisfies the connection with the four possibilities (2). Therefore (-4,2) is a direct variant of this.

Victor borrowed money at 5.25 percent simple annual interest. At the end of the year, the interest on the loan is $255.94. What was the amount of the loan?

Answers

You can write it as an algebraic equation:

p x 5.25% x 1 = 255.94
p x 0.0525 x 1 = 255.94
p x 0.0525 = 255.94
p x 0.0525/0.0525 = 255.94/0.0525
p = 4875.04

Two bicyclists leave the center of town at the same time. One heads due north and the other heads due west. Later, the two cyclists are exactly 25 mi apart. The cyclist headed north has traveled 5 mi farther than the cyclist going west.How far has the cyclist going west traveled?

Answers

Answer:

Distance traveled by bicyclist traveling west = 15 miles

Step-by-step explanation:

These two cyclists travel at angle 90°

Relative displacement can be calculated using Pythagoras theorem.

Let d be the distance traveled by bicyclist traveling west

Distance traveled by bicyclist traveling north = d + 5

$25^2=d^2+(d+5)^2\n\nd^2+d^2+10d+25=625\n\n2d^2+5d-600=0\n\nd^2+5d-300=0\n\nd=(-5\pm √(5^2-4* 1* (-300)))/(2* 1)\n\nd=(-5\pm √(25+1200))/(2)\n\nd=(-5\pm √(1225))/(2)\n\nd=(-5\pm 35)/(2)\n\nd=15miles\texttt{ or }d=-20miles$

Negative displacement is not possible.

Hence d = 15 miles

Distance traveled by bicyclist traveling west = d = 15 miles

This situation is represented in annex.
From Pythagorean theorem you've got equation:
$x^2+(x+5)^2=25 \n \n \hbox{From formula} \ \ \ (a+b)^2 = a^2+2ab+b^2: \n \n x^2+x^2+10x+25=25 \n 2x^2+10x=0 \n \n \hbox{Factor out} \ \ 2x: \n 2x(x+5)=0 \n \n \hbox{So you've got:} \n \n x_1=0 \n x_2=-5$

There isn't any solutions where x>0, so this situation is IMPOSSIBLE.

Did you write correctly this question....?

In gym class, you run 3/5 mile. Your coach runs 10 times that distance each day, How far does your coach run each day?

Answers

first you have to get 3/5 to a decimal to make it easier to multiply. so you would do 5 times 20 and that would make your denominator 100.

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100

if you times the denominator by 20, you have to do the same thing to the numerator so 3 times 20 is 60 so that's 60/100 which is 0.60 and that's equivalent to 3/5 and 6/10 and all that.so 0.60 times 10 is 6, so your coach runs 6 miles everyday. or you could do 10/1 times 3/5. hope that helped.

Answer:

6 miles

Step-by-step explanation:

3/5 multiplied by 10

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