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3 years ago

If y varies jointly with x and z and y=90 when x=2 and z=9, find x when y=105 and z=3

Mathematics

1 answer:

Inessa05 [86]3 years ago

3 0

Answer:

Step-by-step explanation:

y & xz

y = kxz

k = y/xz

When y = 90, x = 2 and z = 9

k = 90/(2×9) = 10/2

k = 5

y = 5xz

When y = 105 and z = 3

105 = 5×3x

105 = 15x

x = 105/15

x = 7

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Ted says that 3 tenths multiplied by 100 equals 300 thousands.is he correct? Use. Place value chart to explain your anwer

abruzzese [7]

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2 years ago

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Assuming that a soap bubble is a perfect sphere, what is the diameter of a bubble containing 1,000 cm^3 of air? Round to the nea

jenyasd209 [6]

Answer:

A is correct

Step-by-step explanation:

In this question, we are concerned with. calculating the diameter of a bubble given the volume of the bubble.

Since we have assumed the bubble to be a perfect sphere, it’s volume V = 4/3 * pi * r^3

Plugging the value of V = 1000cm^3 , we have

1000 = 4/3 * pi * r^3

3000/4pi = r^3

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This is same as 6.2cm

5 0

2 years ago

09:57:09

Sveta_85 [38]

8 cm and 9 cm is the correct answer

8 0

2 years ago

Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total

Katarina [22]

Answer:

t-shirts: 2790

profit: $12209

Step-by-step explanation:

Given the function:

p(x) = -x³ + 4x² + x

we want to maximize it.

The following criteria must be satisfied at the maximum:

dp/dx = 0

d²p/dx² < 0

dp/dx = -3x² + 8x + 1 = 0

Using quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 -4(a)(c)}}{2(a)}$

$x = \frac{-8 \pm \sqrt{8^2 -4(-3)(1)}}{2(-3)}$

$x = \frac{-8 \pm 8.72}{-6}$

$x_1 = \frac{-8 + 8.72}{-6}$

$x_1 = -0.12$

$x_2 = \frac{-8 - 8.72}{-6}$

$x_2 = 2.79$

d²p/dx² = -6x + 8

d²p/dx² at x = -0.12: -6(-0.12) + 8 = 8.72 > 0

d²p/dx² at x = 2.79: -6(2.79) + 8 = -8.74 < 0

Then, he should prints 2.79 thousands, that is, 2790 t-shirts to make maximum profits.

Replacing into profit equation:

p(x) = -(2.79)³ + 4(2.79)² + 2.79 = 12.209

that is, $12209

3 0

3 years ago