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3 years ago

A chain fits tightly around two gears as shown. What is the radius of the smaller gear? Round your answer to the nearest tenth.

Mathematics

2 answers:

GrogVix [38]3 years ago

7 0

Using the Pythagorean theorem we can solve for the radius

see attached picture:

nika2105 [10]3 years ago

7 0

Answer:

The correct option is 3.

Step-by-step explanation:

From the given figure it is noticed that the radius of a circle is 11 inches and the centers of two circles are 20 inches apart. The length of the direct common tangent between both circles is 19 inches.

If the centers of two circles of radius r₁ and r₂ are d units apart, then the length of the direct common tangent between them is

$l=\sqrt{d^{2}-(r_{1}-r_{2})^{2}}$

$19=\sqrt{20^{2}-(11-r_{2})^{2}}$

Square both sides.

$361=400-(11-r_{2})^{2}$

$(11-r_{2})^{2}=400-361$

$(11-r_{2})^{2}=39$

Tnking square root both sides.

$11-r=\sqrt{39}$

$11-6.245=r$

$4.775=r$

$r\approx 4.8$

Therefore the radius of second circle is 4.8 inches and option 3 is correct.

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[need math help] Study buddies part #2

rosijanka [135]

Answer:

Part A) The distance between Whitney's house and Anh's house is 6.5 miles.

Part B) The total distance traveled by Whitney during the trip was 9.5 miles.

Step-by-step explanation:

Part A)

Notice that during Whitney's journey to Anh's house, her velocity was negative for some time. So, Whitney was travelling backwards. Hence, the total distance Whitney traveled will be greater than the actual distance from Whitney's house to Anh's.

So, instead, we can calculate Whitney's total displacement. Total displacement is given by:

$\displaystyle \text{Displacement}=\int_a^bv(t)\, dt$

Where v(t) is the velocity function.

So, the displacement of Whitney when she traveled from her house to Anh's house will be:

$\displaystyle \text{Displacement}=\int_0^{24}v(t)\, dt$

To calculate the integral, we can split it off at t = 11, t = 16, and t = 24.

The three regions represent three geometric figures, which we can use to calculate the area and then find the integral. Rewriting:

$\displaystyle \text{Displacement}=\int_0^{11}v(t)\, dt+\int_{11}^{16}v(t)\, dt+\int_{16}^{24}v(t)\, dt$

Now, we can calculate the area of each figure.

The first figure is a trapezoid with a height of 0.8 and two bases of 11 and 3. So, its area is:

$\displaystyle A_1=\frac{1}{2}(0.8)(11+3)=5.6\text{ miles}$

The second figure is a triangle with a height of 0.6 and a base of 5. So, its area is:

$\displaystyle A_2=\frac{1}{2}(0.6)(5)=1.5\text{ miles}$

Lastly, the third figure is another triangle will a height of 0.6 and a base of 8. So, its area is:

$\displaystyle A_3=\frac{1}{2}(0.6)(8)=2.4\text{ miles}$

However, notice that the second figure is below the x-axis. During that interval, Whitney was traveling backwards. Hence, we will subtract the second area from the rest of the areas.

Then the displacement will be:

$\displaystyle \text{Displacement}=5.6-1.5+2.4=6.5\text{ miles}$

So, the distance between Whitney's house and Anh's house is 6.5 miles.

Part B)

The total distance differs from displacement in that it includes all the distances in both directions. It is given by:

$\displaystyle \text{Distance}=\int_a^b|v(t)|\, dt$

In other words, all of our values are now positive. We will utilize the same strategy:

$\displaystyle \text{Distance}=\int_0^{11}|v(t)|\, dt+\int_{11}^{16}|v(t)|\, dt+\int_{16}^{24}|v(t)|\, dt$

Substitute. The only difference is that we will add 1.5 instead of subtracting it. So:

$\displaystyle \text{Distance} =5.6+1.5+2.4=9.5$

Therefore, in this instance, Whitney traveled a total of 9.5 miles to get to Anh's house.

6 0

3 years ago

When Janelle woke up, it was –3 degrees Fahrenheit outside. As the morning progressed, the temperature rose 2 degrees every hour

m_a_m_a [10]

Answer: g(x)

Step-by-step explanation:

7 0

4 years ago

Read 2 more answers

Solve the equation for x.

ivann1987 [24]

Answer:

x = 44

Step-by-step explanation:

sqrt(x+5) -3 =4

Add 3 to each side

sqrt(x+5) -3+3 =4+3

sqrt(x+5) =7

Square each side

(sqrt(x+5))^2 =7^2

x+5 = 49

Subtract 5 from each side

x+5-5 = 49-5

x=44

3 0

3 years ago

Read 2 more answers

Determine whether the improper integral converges or diverges, and find the value of each that converges.

Temka [501]

Answer:

It diverges.

Step-by-step explanation:

We are given the inetegral: $\int\limits^{\infty}_2 \frac{1}{x} (\ln x)^2 dx$

$\int\limits^{\infty}_2 \frac{1}{x} (\ln x)^2 dx=\int\limits^{\infty}_2 (\ln x)^2 d(\ln x)=\\\\=\lim_{t \to \infty} \int\limits^t_2 (\ln x)^2d(\ln x)=\lim_{t \to \infty} \frac{(\ln t)^3}{3} |^t_2=\infty-\frac{(\ln 2)^3}{3} =\infty$

So it is divergent.

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4 years ago

Mr. Evans is paid $9.20 per hour for the first 40 hours he works in a week.He is paid 1.5 that rate for each hour after that . l

stiks02 [169]

No, Mr.Evans will make under $400. His base pay, 9.20 times the hours he worked at regular pay(40) would equal $368. Now, take those extra 2.25 hours he worked at 1.5 times his base pay of 9.20, which would give you $13.80. Now, multiply 13.80 and 2.25, and you get 31.05. These two amount added, would equal $399.05, leaving Mr. Evans at just under $400 earned that week.

3 0

4 years ago