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3 years ago

14

A wire attached to the top of a pole reaches a stake in the ground 20 feet from the foot of the pole and makes an angle of 58° w

ith the ground. Find the length of the wire.

1 answer:

Finger [1]3 years ago

6 0

It is a right triangle
cos 58 = 20/length of rope
length of rope = 20/cos 58 degrees
= 37.74 feet

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There are 42 students on a large bus and the rest are on a smaller bus. If 40% of the students are on the smaller bus how many t

Liono4ka [1.6K]

Answer:

<u>There are 70 students on the two buses, 42 on the large and 28 on the smaller.</u>

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Number of students on the large bus = 42

Number of students on the small bus = 40% of the students

2. How many total students are on the two buses?

For answering the question, we will use the Rule of Three Simple, this way:

42 students are 60% of total students, how much students are the 100%?

Total students = 42 * 100/60

Total students = 4,200/60 = 70

<u>There are 70 students on the two buses, 42 on the large and 28 on the smaller.</u>

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3 years ago

Use the arc length formula to find the length of the curve y = 4x − 5, −1 ≤ x ≤ 2. check your answer by noting that the curve is

professor190 [17]

Ok, here we go. Pay attention. The formula for the arc length is $AL= \int\limits^b_a { \sqrt{1+( \frac{dy}{dx})^2 } } \, dx$ . That means that to use that formula we have to find the derivative of the function and square it. Our function is y = 4x-5, so y'=4. Our formula now, filled in accordingly, is $AL= \int\limits^2_1 { \sqrt{1+4^2} } \, dx$ (that 1 is supposed to be negative; not sure if it is til I post the final answer). After the simplification we have the integral from -1 to 2 of $\sqrt{17}$ . Integrating that we have $AL= \sqrt{17}x$ from -1 to 2. $2 \sqrt{17}-(-1 \sqrt{17} )$ gives us $3 \sqrt{17}$ . Now we need to do the distance formula with this. But we need 2 coordinates for that. Our bounds are x=-1 and x=2. We will fill those x values in to the function and solve for y. When x = -1, y=4(-1)-5 and y = -9. So the point is (-1, -9). Doing the same with x = 2, y=4(2)-5 and y = 3. So the point is (2, 3). Use those in the distance formula accordingly: $d= \sqrt{(2-(-1))^2+(3-(-9))^2}$ which simplifies to $d= \sqrt{9+144}= \sqrt{153}$ . The square root of 153 can be simplified into the square root of 9*17. Pulling out the perfect square of 9 as a 3 leaves us with $3 \sqrt{17}$ . And there you go!

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2 years ago

Determine all possibilities for the solution set of a system of 2 equations in 2 unknowns. I. No solutions whatsoever. II. One a

Minchanka [31]

Answer:

II. One and only one solution

Step-by-step explanation:

Determine all possibilities for the solution set of a system of 2 equations in 2 unknowns. I. No solutions whatsoever. II. One and only one solution. III. Many solutions.

Let assume the equation is given as;

x + 3y = 11 .... 1

x - y = -1 ....2

Using elimination method

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(x-x) + 3y-y = 11-(-1)

0+2y = 11+1

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y = 12/2

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x-y = -1

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<em>Hence we can say the equation has One and only one solution since we have just a value for x and y</em>

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3 years ago

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Answer:

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3 years ago

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Before we get started, it is good to remember PEMDAS - the acronym that tells you the order to carry out equations.

P = parentheses
E = exponents
M = multiplication
D = division
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Knowing this, we should start by doing the equations <em>within </em>each parentheses.

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So we did the addition and subtraction pieces within each group leaving us with the above equation. Now let's multiply:

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20 is the answer.

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3 years ago