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4 years ago

If x^3=64, what is the value of x?

Mathematics

1 answer:

pickupchik [31]4 years ago

6 0

Answer:

x=4

Step-by-step explanation:

all you need to do is the 3rd root of 64

which is 4.

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A peach orchard owner wants to maximize the amount of peaches produced by her orchard.

qaws [65]

Answer:

a) Y(x) = {900, x≤30; 900-40(x-30), x>30}

b) T(x) = {900x, x≤30; 2100x-40x², x>30}

c) dT/dx = {900, x≤30; 2100-80x, x>30}

Step-by-step explanation:

a) The problem statement gives the function for x ≤ 30, and gives an example of evaluating the function for x = 35. So, replacing 35 in the example with x gives the function definition for x > 30.

$\displaystyle Y(x)=\left\{\begin{array}{lcl}900&\text{for}&x\le 30\\900-40(x-30)&\text{for}&x>30\end{array}\right.$

b) The yield per acre is the product of the number of trees and the yield per tree:

T(x) = x·Y(x)

$\displaystyle T(x)=\left \{\begin{array}{lcl}900x&\text{for}&x\le 30\\2100x-40x^2& \text{for}&x>30\end{array}\right.$

c) The derivative is ...

$\displaystyle\frac{dT}{dx}=\left \{\begin{array}{lcl}900&\text{for}&x\le 30\\2100-80x& \text{for}&x>30\end{array}\right.$

_____

The attached graph shows the yield per acre (purple, overlaid by red for x<30), the total yield (black), and the derivative of the total yield (red). You will note the discontinuity in the derivative at x=30, where adding one more tree per acre suddenly makes the rate of change of yield be negative.

6 0

3 years ago

The area of the small shape is 35 square feet. The big shape is larger by a scale factor of 4/3. Find the area of the large shap

sdas [7]

Answer:

Option a) 62.2 square feet

Step-by-step explanation:

we know that

The dilation is a non-rigid transformation that produces similar figures

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x ----> the area of the large shape

y ----> the area of the small shape

$z^{2}=\frac{x}{y}$

we have

$z=\frac{4}{3}$

$y=35\ ft^2$

substitute

$(\frac{4}{3})^{2}=\frac{x}{35}$

$\frac{16}{9}=\frac{x}{35}$

solve for x

$x=\frac{16}{9}(35)=62.2\ ft^2$

4 0

3 years ago

8. Find the value of x in the isosceles triangle.

yan [13]

X is 15 inches long.
Work is shown in the picture

4 0

3 years ago

The combination for a lock is a 3-digit number. The digits are the prime factors of 42 listed from least to greatest. What is th

Dvinal [7]

Answer:

2, 3, 7

Step-by-step explanation:

Since you know your multiplication tables, you know that ...

42 = 6 × 7

and

6 = 2 × 3

The numbers 2, 3, and 7 are prime numbers (not further divisible). This list is in order least to greatest, so is the combination of the lock.

3 0

4 years ago

Find the volume of the sphere. Either enter an exact answer in terms N(Pi) Or ya 3.14 for N(pi)

xz_007 [3.2K]

Full Question:

Find the volume of the sphere. Either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the nearest hundredth. with a radius of 10 cm

Answer:

The volume of the sphere is ⅓(4,000π) cm³ or 4186.67cm³

Step-by-step explanation:

Given

Solid Shape: Sphere

Radius = 10 cm

Required

Find the volume of the sphere

To calculate the volume of a sphere, the following formula is used.

V = ⅓(4πr³)

Where V represents the volume and r represents the radius of the sphere.

Given that r = 10cm,.all we need to do is substitute the value of r in the above formula.

V = ⅓(4πr³) becomes

V = ⅓(4π * 10³)

V = ⅓(4π * 10 * 10 * 10)

V = ⅓(4π * 1,000)

V = ⅓(4,000π)

The above is the value of volume of the sphere in terms of π.

Solving further to get the exact value of volume.

We have to substitute 3.14 for π.

This gives us

V = ⅓(4,000 * 3.14)

V = ⅓(12,560)

V = 4186.666667

V = 4186.67 ---- Approximated

Hence, the volume of the sphere is ⅓(4,000π) cm³ or 4186.67cm³

4 0

4 years ago