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3 years ago

X and y vary inversely, and x=50 when y=5. find y when x=10. what is k?

1 answer:

n200080 [17]3 years ago

7 0

Y varies inversely with x.
⇒ y = k/x

When y = 5, x = 50
5 = k/50
k = 50 x 5 = 250

Equation: y = 250/x

When x = 10
y = 250/10 = 25

Answer: k = 250, y = 25 when x = 10

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PLEASE HELP!!!!! DUE TODAY!!!!!

prisoha [69]

Answer:

12.4 cm³

Step-by-step explanation:

From the picture attached,

Radius of the circular top of the cone = $\frac{\text{Diameter}}{2}$ = $\frac{2}{2}=1$

Height of the cone = h

Lateral height of the cone = h

By applying Pythagoras theorem in the right triangle of the cone,

l² = r² + h²

6² = 1² + h²

h = $\sqrt{36-1}$

h = $\sqrt{35}$

Ice cream needed to fill one cone = Volume of the cone

Since, formula for the volume of the cone V = $\frac{1}{3} \pi r^{2} h$

V = $\frac{1}{3}\pi (1)^2(\sqrt{35})$

= 6.195

≈ 6.20 cm³

Ice cream needed to fill the two cones = 2 × 6.20

= 12.4 cm³

Therefore, ice cream needed to fill the two cone = 12.4 cm³

4 0

3 years ago

Suppose that theta is an angle in standard position whose terminal side Intersects the unit circle at (-11/61, -60/61)

Blizzard [7]

Answer:

The exact values of the tangent, secant and cosine of angle theta are, respectively:

$\cos \theta = -\frac{11}{61}$

$\tan \theta = \frac{-\frac{60}{61} }{-\frac{11}{61} } = \frac{60}{11}$

$\sec \theta = \frac{1}{-\frac{11}{61} } = -\frac{61}{11}$

Step-by-step explanation:

The components of the unit vector are $x = -\frac{11}{61}$ and $y = -\frac{60}{61}$ . Since $r = 1$ , then $x = \cos \theta$ and $y = \sin \theta$ . By Trigonometry, tangent and secant can be calculated by the following expressions:

$\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x}$

$\sec \theta = \frac{1}{\cos \theta} = \frac{1}{x}$

Now, the exact values of the tangent, secant and cosine of angle theta are, respectively:

$\cos \theta = -\frac{11}{61}$

$\tan \theta = \frac{-\frac{60}{61} }{-\frac{11}{61} } = \frac{60}{11}$

$\sec \theta = \frac{1}{-\frac{11}{61} } = -\frac{61}{11}$

3 0

3 years ago

If you change the y-intercept in the equation y = -2x + 5 to y = -2x + 1, how will its graph change? A. It will increase at a fa

FinnZ [79.3K]

The starting value will decrease.

6 0

3 years ago

A gardener wants to create a rectangular vegetable garden in a backyard. She wants it to have a total area of 120 square feet, a

erastova [34]

Comment
This is an area problem. The key words are 120 square feet and 12 feet longer.
And of course width is a key word when you are reading this.

Formula
Area = L * W

Givens
W = W
L = W + 12

Substitute and Solve
Area = L* W
120 = W*(W + 12)
W^2 + 12W = 120 square feet
w^2 + 12w - 120 = 0

This does not factor easily. I would have thought that a graph might help but not if the dimension has to be to the nearest 1/100 of a foot. The only thing we can do is use the quadratic formula.

a = 1
b = 12
c = - 120

w = [ -b +/- sqrt(b^2 - 4ac) ]/(2a)
w = [-12 +/- sqrt(12^2 - 4*(1)(-120)] / 2*1
w = [-12 +/- sqrt(144 - (-480)]/2
w = [-12 +/- sqrt(624)] / 2
w = [- 12 +/- 24.979992] / 2 The minus root has no meaning whatever.
w = (12.979992) / 2
w = 6.489995 I'll round all this when I get done

L = w + 12
L = 6.489995 + 12
L = 18.489995

check
Area = L * W
Area = 6.489995*18.489995
Area = 119.999935 The difference is a rounding error

Answer
L = 18.489995 = 18.49 feet
W = 6.489995 = 6.49 feet

Note: in the check if you round first to the answer, LW = 120.0001 when you find the area for the check. Kind of strange how that nearest 1/100th makes a difference.

5 0

3 years ago

A 6-ft ladder is placed against a wall with its base 2 ft from the wall. How high above the ground is the top of the ladder

Zarrin [17]

Use pythagorean theorem - a^2+ b^2 = c^2
a = 2ft, b = ?, c = 6ft
2 x 2 + b^2 = 6 x 6
4 + b^2 = 36
b^2 = 36 - 4 = 32
b = square root of 32
= 5.66ft

4 0

4 years ago