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3 years ago

How do I do question 9 & 11? Please help thank you!

Mathematics

1 answer:

Novay_Z [31]3 years ago

5 0

<h2>9.</h2><h3>Given</h3>

sphere with radius 15 cm

linear approximation to the volume when the radius increases 0.4 cm

<h3>Solution</h3>

The equation for volume of a sphere is

... V = (4/3)π·r³

Differentiating gives

... dV = 4π·r²·dr

Filling in the given numbers gives

... change in volume ≈ 4π·(15 cm)²·(0.4 cm)

... = 360π cm³ ≈ 1130.97 cm³ . . . . . . volume of layer 4mm thick

<h2>11.</h2><h3>Given</h3>

an x by x by 2x cuboid with surface area 129.6 cm²
rate of change of x is 0.01 cm/s

rate of change of volume

<h3>Solution</h3>

The area is that of two cubes of dimension x joined together. The area of each such cube is 6x², but the two joined faces don't count in the external surface area. Thus the area of the cuboid is 10x².

The volume of the cuboid is that of two cubes joined, so is 2x³. Then the rate of change of volume is

... dV/dt = (d/dt)(2x³) = 6x²·dx/dt

We know x² = A/10, where A is the area of the cuboid, so the rate of change of volume is ...

... dV/dt = (6/10)A·dx/dt = 0.6·(129.6 cm²)(0.01 cm/s)

... dV/dt = 0.7776 cm³/s

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I need help on this one

umka2103 [35]

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Hope this helped.

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2 years ago

How is multiplying exponents (x² ⋅ x⁴) different from raising a power to a power ((x²)⁴)?

goblinko [34]

Answer:

When you are "multiplying" exponents, you're really just adding them together. So in the case of (x² ⋅ x⁴), you add the exponents:

2 + 4 = 6

$x^{6}$ would be the answer.

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$x^{8}$ would be the answer.

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2 years ago

You pick a card at random .without putting the first card back you pick a second card at random what is the probability of picki

garik1379 [7]

Answer:

For on it depends on how many cards you have and how many 4's there are

Step-by-step explanation:

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3 years ago

Given: an=3+an−1 and a1=5<br><br> What is the explicit rule for the arithmetic sequence?

Flura [38]

The explicit rule for the arithmetic sequence for the sequence is a(n) = 3n + 2.

<h3>What is a sequence?</h3>

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have given:

$\rm a_n=3+a_n_-_1$ and

$\rm a_1=5$

$\rm a_n-a_n_-_1= 3$

The above expression represents the common ratio:

d = 3

First term:

a = 5

The explicit rule for the arithmetic sequence:

a(n) = 5 + (n - 1)3

a(n) = 3n + 2

Thus, the explicit rule for the arithmetic sequence for the sequence is a(n) = 3n + 2.

Learn more about the sequence here:

brainly.com/question/21961097

#SPJ1

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1 year ago

J.c. Penny sells a timed watch for $139.99 that cost$89.97. J.C. Penny’s percent of markup based on the selling price is:

vodka [1.7K]

So it cost them 89.97 and they're selling it for 139.99, the difference is 50.02.

so, the markup is 50.02, if we take 89.97 to be the 100%, how much is 50.02 off of that in percentage?

$\bf \begin{array}{ccll}
amount&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
89.97&100\\
50.02&p
\end{array}\implies\cfrac{89.97}{50.02}=\cfrac{100}{p}\implies p=\cfrac{50.02\cdot 100}{89.97}$

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3 years ago