the spoke of a wheel reaches from the center of the wheel to its rim. If the circumstances of the rim of the wheel is 42 inches, how long is each spoke?

Answers

Answer 1

Answer: The spoke of the wheel serves as the radius of the circle.
To solve for the circumference of the circle, we use this formula:

C = 2πr
42 inches = 2 * 3.14 * r
42 inches = 6.28 * r
42 inches / 6.28 = r
6.69 inches = r

The length of each spoke is 6.69 inches.

Answer with explanation:

We are given a parametric equation as:

$x=3 \sin^3 t$

and $y=3 \cos^3 t$

Hence, we can represent our equation as:

$\sin^3 t=(x)/(3)\n\n\n\sin t=((x)/(3))^{(1)/(3)}\n\n\nHence,\n\n\sin^2 t=((x)/(3))^{(2)/(3)}\n\nand\ similarly\n\n\cos^3 t=(y)/(3)\n\n\cos t=((y)/(3))^{(1)/(3)}\n\nHence,\n\n\cos^2 t=((y)/(3))^{(2)/(3)}$

As we know that:

$\cos^2 t+\sin^2 t=1$

Hence, on putting the value in the formula we get the equation in rectangular coordinates as:

$((x)/(3))^{(2)/(3)}+((y)/(3))^{(2)/(3)}=1$

Hence, this is a equation of a ASTROID.

Hello,

This is an astroïde.

(x/3)^(2/3)+(y/3)^(2/3)=1

HELPPP PLEASEEEEEEEEE

Answers

Given the equation, y - x = 3x + 7

Add x to both sides to isolate y:

y - x + x = 3x + x + 7

y = 4x + 7 (This is the linear equation in slope-intercept form, y = mx + b). The rate of change is also the slope of the line, m = 4.

Therefore, the rate of change is 4.

Please mark my answers as the Brainliest if you find my explanations helpful :)

Y=4x+7

So 4 is the rate of change because if you solve for y, x is the rate of change

Grandma Gertrude's Chocolates, a family owned business, has an opportunity to supply its product for distribution through a large coffee house chain. However, the coffee house chain has certain specifications regarding cacao content as it wishes to advertise the health benefits (antioxidants) of the chocolate products it sells. In order to determine the mean percentage of cacao in its dark chocolate products, quality inspectors sample 36 pieces. They find a sample mean of 60% with a standard deviation of 8%. What is the correct value of t to construct a 90% confidence interval for the true mean percentage of cacao? (Round to the nearest thousandth.)Select Answer:
A. (0.577, 0.623)
B. (0.539, 0.561)
C. (0.527, 0.573)
D. (0.589, 0.611)

Answers

Answer with explanation:

Given : Sample size : n = 36

Significance level for 90% confidence : $\alpha: 1-0.9=0.1$

Sample mean : $\overline{x}=0.60$

Standard deviation : $\sigma=0.08$

By using standard normal table for t-values,

Critical t-value : $t_((n-1, \alpha/2))=t_((35,\ 0.05))=1.690$

Thus, the correct value of t to construct a 90% confidence interval for the true mean percentage of cacao : $t_((35,\ 0.05))=1.690$

Confidence interval for population mean :

$\overline{x}\pm t_((n-1, \alpha/2))(\sigma)/(√(n))\n\n=0.60\pm(1.69)(0.08)/(√(36))\n\n=0.60\pm0.0225333333333\n\n\approx0.60\pm0.023\n\n=(0.60-0.023,\ 0.60+0.023)=(0.577,\ 0.623)$

Hence, A is the correct answer .

What is the answer to 1/2÷5/8?

Answers

O.8 as decimal form or 8/10 as fraction form

Hi Lurch

1/2 divide by 5/8

1/2÷5/8

1/2*8/5 (multiply numerator together and denominator together )

8/10 ( divide the numerator by 2 and same for the denominator )

4/5

I hope that's help , please if you have question(s) ask !

A box has the shape of a rectangular prism with height of 28 cm. If the height is increased by 0.2 by how much does the surface area of the box increase?

Answers

Answer:

The surface area of the box increase by 0.2P (the perimeter of the base multiplied by 0.2)

Step-by-step explanation:

we know that

The surface area of the rectangular prism is equal to

$SA=2B+Ph$

where

B is the area of the base

P is the perimeter of the base

h is the height of the prism

If the height is increased by 0.2

then

$SA=2B+P(h+0.2)$

$SA=2B+Ph+P(0.2)$

The surface area of the box increase by 0.2P (the perimeter of the base multiplied by 0.2)

Final answer:

The overall change in surface area when the height of a rectangular prism is increased by 0.2 cm can be calculated with the formula 0.4w + 0.4l.

Explanation:

In this question, we are looking at the surface area of a box that is a rectangular prism and how it will change if the height of the box is increased by 0.2 cm. The surface area of a prism is given by the formula 2lw + 2lh + 2wh, where l, w and h are the length, width and height respectively.

Now, if the height is increased by 0.2 cm, the difference in the surface area will be 2lw (because there are two ends with area lw that do not change) plus the change in the area of the sides. The sides' areas will increase by 2w x 0.2 and 2l x 0.2 respectively (since we have two opposing sides that both increase by 0.2 cm in height).

Therefore, the overall change in surface area when the height is increased by 0.2 cm is simply the sum of these two parts, which is 2w x 0.2 + 2l x 0.2. This can also be simplified to 0.4w + 0.4l.

Learn more about Surface Area of Rectangular Prism here:

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The area of the garden is 13.92 square meters. A fence is planned around the perimeter of the garden. How many meters of fencing are needed?

Answers

The meters of fencing that is needed is = 3.36m

Calculation of needed meters

The garden is designed in a trapezoid form with sides= a; 3.3m and b; 5.28m.

The area of the trapezoid garden = 13.92 m²

Therefore the meters of fencing needed which is height = ?

The formula for the area of trapezoid = A = (a+b/2)h

From the formula make h the subject of formula;

h = A *2/a+b

h = 13.92*2/3.3+5.28

h =27.84/8.28

h= 3.36m

Therefore, the meters of fencing that is needed is = 3.36m.

Learn more about trapezoid here:

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Final answer:

The amount of fencing needed is 15.96 m.

Explanation:

To find the amount of fencing needed, we need to calculate the perimeter of the garden. Since the area is given as 13.92 square meters.

The perimeter is the total length of all the sides of the garden added together.

The area of the garden is 13.92 square meters, which means that the garden is a rectangle with a length of 4 meters and a width of 3.48 meters.

Perimeter = 2 * (length + width)

Perimeter = 2 * (4 + 3.48)

Perimeter = 15.96 meters

Therefore, 15.96 meters of fencing are needed.