Which of the following is an appropriate question to ask

Can anyone help me solve these math problems?

Veseljchak [2.6K]

Answer:

x = 2
r = 48
3536 ft
√10
10°

Step-by-step explanation:

1. The Pythagorean theorem applies, so the sum of the squares of the legs is equal to the square of the hypotenuse.

x² + (x+3)² = (√29)²

2x² +6x +9 = 29 . . . . . . eliminate parentheses, collect terms

2x² +6x -20 = 0 . . . . . . subtract 29

x² +3x -10 = 0 . . . . . . . . divide by 2

(x +5)(x -2) = 0 . . . . . . . . factor

x = -5 or +2 . . . . . . . . . . . . values that make the factors zero (-5 is extraneous)

The value of x is 2.

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2. Even though the figure is drawn incorrectly the Pythagorean theorem still applies. (The second attachment shows the circle in the right place. The figure is not to scale.)

14² + r² = (r+2)²

196 + r² = r² +4r +4 . . . . eliminate parentheses

192 = 4r . . . . . . . . . . . . . .subtract r²+4 from both sides

48 = r . . . . . . . . . . . . . . . . divide by 4

The value of r is 48.

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3. You will recognize that the triangle involving the distance above the ground, the distance along the ground, and the straight-line bullet path is an isosceles right triangle. So, the hypotenuse is √2 times the length of either leg. The path length of the bullet is ...

(2500 ft)√2 ≈ 3536 ft

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4. see below for the diagram

The length to the terminal point is found using the Pythagorean theorem:

d = √(3² +(-1)²) = √10

The distance from the origin to the terminal point is √10 ≈ 3.16.

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5. Angles "a" and "8a" total 90°, so we have ...

a + 8a = 90°

9a = 90° . . . . . . . . collect terms

a = 10° . . . . . . . . . . divide by 9

The value of a is 10°.

8 0

3 years ago

Express the set W = { x∣x < 4 or x > 7 } using interval notation. Use "U" for or .

mixer [17]

Answer:

[1,∞)

Step-by-step explanation:

5 0

1 year ago

What is the coefficient of the expression −x/3+7 ?

Eddi Din [679]

3 hope this helped :)

3 0

3 years ago

Consider the initial value function y given by

Nuetrik [128]

Answer:

y(s) = $\frac{5s-53}{s^{2} - 10s + 26}$

we will compare the denominator to the form $(s-a)^{2} +\beta ^{2}$

$s^{2} -10s+26 = (s-a)^{2} +\beta ^{2} = s^{2} -2as +a^{2} +\beta ^{2}$

comparing coefficients of terms in s

$s^{2} :$ 1

s: -2a = -10

a = -2/-10

a = 1/5

constant: $a^{2}+\beta ^{2} = 26$

$(\frac{1}{5} )^{2} + \beta ^{2} = 26\\\\\beta^{2} = 26 - \frac{1}{10} \\\\\beta =\sqrt{26 - \frac{1}{10}} =5.09$

hence the first answers are:

a = 1/5 = 0.2

β = 5.09

Given that y(s) = $A(s-a)+B((s-a)^{2} +\beta ^{2} )$

we insert the values of a and β

$\\5s-53$ = $A(s-0.2)+B((s-0.2)^{2} + 5.09^{2} )$

to obtain the constants A and B we equate the numerators and we substituting s = 0.2 on both side to eliminate A

5(0.2)-53 = A(0.2-0.2) + B((0.2-0.2)²+5.09²)

-52 = B(26)

B = -52/26 = -2

to get A lets substitute s=0.4

5(0.4)-53 = A(0.4-0.2) + (-2)((0.4 - 0.2)²+5.09²)

-51 = 0.2A - 52.08

0.2A = -51 + 52.08

A = -1.08/0.2 = 5.4

the constants are

a = 0.2

β = 5.09

A = 5.4

B = -2

Step-by-step explanation:

since the denominator has a complex root we compare with the standard form $s^{2} -10s+26 = (s-a)^{2} +\beta ^{2} = s^{2} -2as +a^{2} +\beta ^{2}$
Expand and compare coefficients to obtain the values of a and β as shown above
substitute the values gotten into the function
Now assume any value for 's' but the assumption should be guided to eliminate an unknown, just as we've use s=0.2 above to eliminate A
after obtaining the first constant, substitute the value back into the function and obtain the second just as we've shown clearly above

Thanks...

3 0

2 years ago

20 is what percent of 160

stira [4]

In this problem WP means what percent

20 = WP X 160

solve for WP, by dividing both sides by 160

and you get:

0.125 = WP

Change your decimal into a percent by multiplying by 100%

12.5% is your result.

7 0

3 years ago