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3 years ago

The length of a string between a kite and a point on the ground is 90 m. If

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

8 0

Answer:

79.4 m

Step-by-step explanation:

In this problem we deal with a right triangle with hypotenuse 90 m. We are told that tan Ф = 15/8; 15 represents the vertical distance of the kite off the ground and 8 represents the horizontal distance from the kite flyer to the kite. This is sufficient info from which to determine the angle of elevation from kite flyer to kite: tan Ф = 15/8 yields Ф = 1.08 radians.

Using this same angle Ф = 1.08 radians, sin Ф = (vertical distance) / hypotenuse = sin 1.08 rad = 0.882.

Then the vertical distance (height of the kite) is

(90 m)(0.882) = 79.4 m

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What valur of x makes the equation below true? 9^5 * 9^7=9^x

klasskru [66]

Answer:

x=12

Step-by-step explanation:

(9^5)(9^7)=9^x

282429536481=9^x

<em>Step 1: Flip the equation.</em>

9^x=282429536481

<em>Step 2: Solve Exponent.</em>

9^x=282429536481

log(9^x)=log(282429536481)(Take log of both sides)

x*(log(9))=log(282429536481)

x=log(282429536481)/log(9)

x=12

8 0

2 years ago

Write 2.3181818... as a mixed number

JulsSmile [24]

Let x= 2.3181818...

then

10x=23.181818... and

1,000x=2,318.1818...

1,000x-10x=2,318.1818...-23.181818...

990x = 2,318 - 23
990x = 2295

x=2295/990

dividing by 5 both numerator and denominator:

x= 459/198

now, x= 198 + 198+ 63

so $x= 2\frac{63}{198}$

Answer: $x= 2\frac{63}{198}$

7 0

3 years ago

A math teacher instructed students to graph the following equations on a coordinate plane. y=2.5x+2 and y=2x+4. If graphed corre

algol [13]

Both the graphical lines will intersect at (4,12)

Step-by-step explanation:

Step 1; We must find the point in the graph where the lines of y=2.5x+2 and y=2x+4 intersect. To find out the intersecting point we must substitute values of x in both equations and see in which co-ordinate they are the same.

Step 2; We plot various values of x on the line governed by the equation y=2.5x+2

For a value of x=1 , y=2.5(1) + 2 = 4.5

For a value of x=2 , y=2.5(2) + 2 = 7

For a value of x= 3, y=2.5(3) + 2 = 9.5

For a value of x= 4, y=2.5(4) + 2 = 12

For a value of x= 5, y=2.5(5) + 2 = 14.5

Step 3; Now we also plot the values of x on the other line governed by y=2x+4

For a value of x= 1, y=2(1) + 4 = 6

For a value of x= 2, y=2(2) + 4 = 8

For a value of x= 3, y=2(3) + 4 = 10

For a value of x= 4, y=2(4) + 4 = 12

For a value of x= 5, y=2(5) + 4 = 14

Step 4; For both lines we must see if any of the values repeat at a particular point. In this case at the point (4,12) repeats for both so that becomes the point of intersection.

8 0

3 years ago

Rewrite the following equation in exponential form.

ira [324]

Answer:

5² = 25

Step-by-step explanation:

log5 25 = 2

log(b) (x) = (y)

make b^(y) = (x)

5² = 25

I hope this helps!

5 0

2 years ago

|6m|=42 please help me with absolute value

ANTONII [103]

Since there is nothing on the left side of the equation besides the absolute value, you have to take 6m out of the absolute value and create 2 separate equations. These 2 equation will be 6m = 42 and 6m = -42.

You solve the equations normally:
6m = 42 6m = -42 (inverse to get m by itself, do on both sides)
/6 /6 /6 /6

m = 7 m = -7

The answer is a solution set:
[7, -7]

3 0

3 years ago