Explanation:
The correct answer of 9°43´39.28” can be explained by using the concept of trigonometry. The problem provides the horizontal distance (35 cm) and the vertical distance (6 cm) of the brick from a point. By using the tangent function, we can calculate the angle of inclination. The tangent of an angle is equal to the ratio of the opposite side (vertical distance) to the adjacent side (horizontal distance). In this case, the tangent of the angle is 6 cm / 35 cm. By taking the inverse tangent (arctan) of this ratio, we can find the angle of inclination, which is approximately 9°43´39.28”.
Explanation:
The correct answer is $5034.04. To determine the amount of money in the money market account, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the given values, we have A = 2500(1 + 0.07/365)^(365*10) = $5034.04.
Explanation:
The correct answer is "". This is the component form of a vector with a magnitude of 10 and a direction of 150 degrees. The first component, -5√3, represents the horizontal displacement of the vector, and the second component, -5, represents the vertical displacement.
Explanation:
The missing number in the sequence is 12. The given sequence follows a pattern of adding 3 to each number. Starting with 3, we add 3 to get 6, then add 3 again to get 9. Following the same pattern, we add 3 to 9 to get 12, and then add 3 again to get 15. Therefore, the missing number is 12.
Explanation:
Given that the shadow cast by the flagpole is 11.6m and the elevation angle of the sun is 35° 40', we can use trigonometry to find the length of the rope. The shadow cast by the flagpole represents the adjacent side of a right triangle, while the height of the flagpole represents the opposite side. We can use the tangent function to find the length of the rope, which is the hypotenuse of the triangle. By using the formula tan(angle) = opposite/adjacent, we can calculate the length of the rope to be approximately 16.65m.
Explanation:
The correct answer is dy/dx = 7 /(7x+2). This is the correct differentiation of the given function y= ln(7x+2). The derivative of ln(u) with respect to x is du/dx divided by u. In this case, u = 7x+2, so du/dx = 7. Therefore, the derivative of ln(7x+2) with respect to x is 7/(7x+2).
Explanation:
The angle of the tube for the gamma rays to affect the tumor can be calculated using trigonometry. Since the tumor is located 5.7 cm under the skin and the technician moves the tube 8.3 cm to one side, we can consider a right triangle with the hypotenuse being the distance from the tube to the tumor (8.3 cm) and the opposite side is the depth of the tumor (5.7 cm). The angle can be found using the inverse tangent function, which gives us an angle of 34°28’45”.
Explanation:
The logarithm of a number represents the exponent to which a base must be raised to obtain that number. In this case, we are given that log 5 = 0.6990. To evaluate log 5000, we need to find the exponent to which the base 5 must be raised to obtain 5000. Since 5^4 = 625, and 5^5 = 3125, we can conclude that 5000 is between these two values. Therefore, the exponent must be between 4 and 5. Since the answer choices are in the form of 0.6990, we can deduce that the correct answer is 3.6990, as it falls between 3 and 4.
Explanation:
The magnitude of a vector is calculated by taking the square root of the sum of the squares of its components. In this case, the vector has a magnitude of √(2^2 + (-3)^2) = √(4 + 9) = √13. Therefore, the correct answer is √13.
Explanation:
The turtle moves from coordinate P = (3,2) to Q = (5,6). To find the vector that models the turtle's motion, we need to find the difference between the coordinates of Q and P. The x-coordinate of Q is 5 and the x-coordinate of P is 3, so the x-component of the vector is 5 - 3 = 2. Similarly, the y-coordinate of Q is 6 and the y-coordinate of P is 2, so the y-component of the vector is 6 - 2 = 4.
Explanation:
If v = 〈a,b〉, then a is the horizontal component of v. This is because, in a two-dimensional Cartesian coordinate system, the x-axis represents the horizontal direction. The vector v = 〈a,b〉 represents a displacement in the x-axis (horizontal direction) of units and in the y-axis (vertical direction) of b units. Therefore, a represents the displacement in the horizontal direction, making it the horizontal component of v.
