Provide an appropriate response.What is the largest interval over which f(x) = <img src="https://sciemce.com/files/4/ppg__ttttt0528191001__f1q189g1.jpg" style="vertical-align: -21.0px;" /> increases?
In a certain village, the height of men in inches follows the Normal (69, 2.5) distribution. Find the probability that a randomly selected man from the village is between 67 in. and 71in. tall.
Use mathematical induction to solve for all positive integers n.
<img src="https://sciemce.com/files/2/ppg__cognero__Section_11.4_Mathematical_Induction__media__cfc06290-36d1-41cd-b112-1d09e4277386.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_85ae1992e06445499c31f0582" />
Solve the problem.Determinants are used to show that three points lie on the same line (are collinear). If <img src="https://sciemce.com/files/4/ppg__tttt0529191404__f1q106g1.jpg" style="vertical-align: -27.0px;" /> = 0,then the points (x1, y1), (x2, y2), and (x3, y3) are collinear. If the determinant does not equal 0, then the points are not collinear. Are the points <img src="https://sciemce.com/files/4/ppg__tttt0529191404__f1q106g2.jpg" alt="" style="vertical-align: -4.0px;" />, <img src="https://sciemce.com/files/4/ppg__tttt0529191404__f1q106g3.jpg" alt="" style="vertical-align: -4.0px;" />, and <img src="https://sciemce.com/files/4/ppg__tttt0529191404__f1q106g4.jpg" alt="" style="vertical-align: -4.0px;" /> collinear?
Use the figure to find the exact value of the trigonometric function.
cot 2θ
<img alt="" src="https://sciemce.com/files/2/ppg__cognero__Section_7.5_Multiple_Angle_and_Product_to_Sum_Formulas__media__04765ab2-390d-4384-9ffd-3613a0f059d7.PNG" style="vertical-align:0px;width:166px;height:79px;top:68px;" width="130px" height="54px" />
a = 1, b = 6
Find the limit of the sequence or determine that the limit does not exist.an = <img src="https://sciemce.com/files/4/ppg__tttt0612191518__f1q142g1.jpg" alt="" style="vertical-align: -17.0px;" />n
Find an equation for the graph.<img src="https://sciemce.com/files/4/ppg__tttt0529191033__f1q77g1.jpg" alt="" style="vertical-align: 0.0px;" height="170" width="239" />
Provide an appropriate response.If <img src="https://sciemce.com/files/4/ppg__ewadas0609191750__f1q172g1.jpg" style="vertical-align: -12.0px;" /> converges, what can be said about <img src="https://sciemce.com/files/4/ppg__ewadas0609191750__f1q172g2.jpg" style="vertical-align: -12.0px;" />?
List the first n terms of the geometric sequence satisfying the given conditions.a1 = <img src="https://sciemce.com/files/4/ppg__tttt0604191018__f1q216g1.jpg" style="vertical-align: -17.0px;" />, r = -9, n = 4
Find (by inspection) the expected value and standard deviation of the random variable with the following density function: <img src="https://sciemce.com/files/4/ppg__wdrsad0602192025__f1q22g1.jpg" alt="" style="vertical-align: -19.0px;" />Enter your answer as just two numbers (a real number to one decimal place followed by a reduced fraction) separated by a comma, the first representing E(X) and the second representing <img src="https://sciemce.com/files/4/ppg__wdrsad0602192025__f1q22g2.jpg" style="vertical-align: -4.0px;" />.
Draw the following angle in standard position; find the sine, the cosine, and the tangent of the angle below.
<img src="https://sciemce.com/files/3/ppg__cognero__Section_1.3_Definition_I_Trigonometric_Functions__media__05b8796d-cbbf-4f71-bfba-dda20011eeef.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_ad1e1442c0e6440cb9ffb1726" />
Estimate the volume of the solid that lies above the square R = [0, 4] and below the elliptic paraboloid f(x, y) = 68 - x² -y². Divide into four equal squares and use the Midpoint rule.
Provide an appropriate response.Evaluate <img src="https://sciemce.com/files/4/ppg__tttt0604191435__f1q31g1.jpg" style="vertical-align: -21.0px;" /><img src="https://sciemce.com/files/4/ppg__tttt0604191435__f1q31g2.jpg" style="vertical-align: -17.0px;" /> = by first converting it to a derivative at a particular x-value.
Solve the problem.Find the average distance from a point <img src="https://sciemce.com/files/4/ppg__10611192124__f1q251g1.jpg" alt="" style="vertical-align: -4.0px;" /> in the first two quadrants of the disk <img src="https://sciemce.com/files/4/ppg__10611192124__f1q251g2.jpg" alt="" style="vertical-align: -4.0px;" /> to the origin.
Use the information given about the angle θ, 0 ≤ θ ≤ 2π, to find the exact value of the indicated trigonometric function.tan θ = <img src="https://sciemce.com/files/4/ppg__qas0526191658__f1q177g1.jpg" style="vertical-align: -17.0px;" />, π < θ < <img src="https://sciemce.com/files/4/ppg__qas0526191658__f1q177g2.jpg" style="vertical-align: -17.0px;" />Find sin (2θ).
Identify the equation as a circle, a parabola, an ellipse, or a hyperbola.
<img src="https://sciemce.com/files/3/ppg__cognero__Section_10.4_Hyperbolas__media__d7d1d80b-2134-4916-a2f0-e996b57ca138.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_f1168152d8344f41b01c5bec5" />
Solve the problem.If a graph is symmetric with respect to the y-axis and it contains the point (5, -6), which of the following points is also on the graph?
Solve the problem.A group of college students had LDL cholesterol readings that ranged from 127.8 to 161.2 inclusive. Let x represent the value of the LDL cholesterol readings. Use inequalities to describe this range of values and graph the corresponding interval on a number line.<img src="https://sciemce.com/files/4/ppg__tttt0525191426__f1q143g1.jpg" alt="" style="vertical-align: 0.0px;" height="40" width="320" />
Identify the open intervals where the function is changing as requested.Increasing<img src="https://sciemce.com/files/4/ppg__dsd0601191704__f1q141g1.jpg" alt="" style="vertical-align: 0.0px;" height="225" width="225" />
Solve the problem.A bird flies from its nest 3 km in the direction 3° north of east, where it stops to rest on a tree. It then flies 6 km in the direction 4° south of west and lands atop a telephone pole. With an xy-coordinate system where the origin is the bird's nest, the x-axis points east, and the y-axis points north, at what point is the telephone pole located?
Provide an appropriate response.Find the direction in which the function is increasing most rapidly at the point P0.f(x, y, z) = xy - ln(z), P0(2, -2, 2)
Well whether the function <img src="https://sciemce.com/files/3/ppg__cognero__Section_2.2_Polynomial_Functions_of_Higher_Degree__media__2146e230-cd81-4fcb-9c43-efd9476638f5.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_b9b7e0ebfc02456196f4d2526" /> is even or odd. If it is neither, so indicate.
For the given demand function, find the value(s) of x for which total revenue is a maximum.x = D(x) = <img src="https://sciemce.com/files/4/ppg__sdgfdf0530191628__f1q66g1.jpg" style="vertical-align: -21.0px;" />
Write an equivalent double integral with the order of integration reversed.<img src="https://sciemce.com/files/4/ppg__as0610191830__f1q213g1.jpg" style="vertical-align: -25.0px;" />
Solve the problem. Round your answer, if appropriate.The volume of a sphere is increasing at a rate of 6 cm3/sec. Find the rate of change of its surface area when its volume is <img src="https://sciemce.com/files/4/ppg__tttt0615190901__f1q90g1.jpg" style="vertical-align: -17.0px;" /> cm3. (Do not round your answer.)
Decide whether or not the functions are inverses of each other.f(x) = (x - 4)2, x ≥ 4; g(x) = <img src="https://sciemce.com/files/4/ppg__tttt0527191010__f1q199g1.jpg" style="vertical-align: -4.0px;" />
Solve the problem.Show that the midpoint of the hypotenuse of a right triangle is equidistant from all three vertices. [Hint: See the figure below. Show that <img src="https://sciemce.com/files/4/ppg__ttt0613191016__f1q138g1.jpg" alt="" style="vertical-align: -17.0px;" /> = <img src="https://sciemce.com/files/4/ppg__ttt0613191016__f1q138g2.jpg" alt="" style="vertical-align: -17.0px;" />.] <img src="https://sciemce.com/files/4/ppg__ttt0613191016__f1q138g3.jpg" alt="" style="vertical-align: 0.0px;" height="169" width="221" />
Solve the problem.At time t, the position of a body moving along the s-axis is <img src="https://sciemce.com/files/4/ppg__tttt0615190841__f1q219g1.jpg" alt="" style="vertical-align: -4.0px;" /> Find the total distance traveled by the body from <img src="https://sciemce.com/files/4/ppg__tttt0615190841__f1q219g2.jpg" alt="" style="vertical-align: -4.0px;" /> to <img src="https://sciemce.com/files/4/ppg__tttt0615190841__f1q219g3.jpg" alt="" style="vertical-align: -4.0px;" />
Use Simpson's Rule with n = 4 steps to estimate the integral.<img src="https://sciemce.com/files/4/ppg__tttt0612191457__f1q78g1.jpg" style="vertical-align: -23.0px;" />
Solve the problem.Find the average distance from a point <img src="https://sciemce.com/files/4/ppg__10612191744__f1q185g1.jpg" alt="" style="vertical-align: -4.0px;" /> in the region bounded by <img src="https://sciemce.com/files/4/ppg__10612191744__f1q185g2.jpg" alt="" style="vertical-align: -4.0px;" /> to the origin.