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A top is formed by fusing two identical right circular cones by their bases as shown. The height of the top, h h , which is the distance between the two cone points, is 6 6 centimeters (cm \text{cm} ). The diameter of the circular cone bases, d d , is also 6 6 cm. What is the volume of the entire object, in cubic centimeters?

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Volume of cubes and rectangular prisms: word problemsright chevron icon

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Chinedu was given this problem:\newlineA person stands at a distance of 1818 meters east of an intersection and watches a car driving away from the intersection to the north at 33 meters per second. The function y(t) y(t) gives the car's distance, in meters, north of the intersection at time t t . At a certain instant t0 t_{0} , the angle θ(t0) \theta\left(t_{0}\right) between the line of sight from the person to the car and the line of sight from the person to the intersection is 00.77 radians. What is the rate of change of the angle θ(t) \theta(t) at that instant?\newlineWhich equation should Chinedu use to solve the problem?\newlineChoose 11 answer:\newline(A) tan⁡[θ(t)]=y(t)18 \tan [\theta(t)]=\frac{y(t)}{18} \newline(B) θ(t)=18⋅y(t)2 \theta(t)=\frac{18 \cdot y(t)}{2} \newline(C) θ(t)+18+y(t)=180 \theta(t)+18+y(t)=180 \newline(D) [θ(t)]2=182+[y(t)]2 [\theta(t)]^{2}=18^{2}+[y(t)]^{2}
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Posted 9 months ago

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Steve was given this problem:\newlineThe radius r(t) r(t) of a circle is increasing at a rate of 33 centimeters per second. At a certain instant t0 t_{0} , the radius is 88 centimeters. What is the rate of change of the area A(t) A(t) of the circle at that instant?\newlineWhich equation should Steve use to solve the problem?\newlineChoose 11 answer:\newline(A) A(t)=2π⋅r(t) A(t)=2 \pi \cdot r(t) \newline(B) A(t)=π[r(t)]2 A(t)=\pi[r(t)]^{2} \newline(C) A(t)=4π[r(t)]2 A(t)=4 \pi[r(t)]^{2} \newline(D) A(t)=43π[r(t)]3 A(t)=\frac{4}{3} \pi[r(t)]^{3}
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Posted 9 months ago

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Benjamin invests $400 \$ 400 in a savings account that earns 5% 5 \% interest each year.\newlineWhich expression gives the balance in the account after 33 years?\newlineChoose 11 answer:\newline(A) 400⋅0.05⋅0.05⋅0.05 400 \cdot 0.05 \cdot 0.05 \cdot 0.05 \newline(B) 400+(1+0.05)(1+0.05)(1+0.05) 400+(1+0.05)(1+0.05)(1+0.05) \newline(C) 400+0.05⋅0.05⋅0.05 400+0.05 \cdot 0.05 \cdot 0.05 \newline(D) 400(1+0.05)(1+0.05)(1+0.05) 400(1+0.05)(1+0.05)(1+0.05)
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Posted 9 months ago

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Let f(x)=x+1xex+ex f(x)=\frac{x+1}{xe^{x}+e^{x}} when x≠−1 x\neq-1 .\newlinef f is continuous for all real numbers.\newlineFind f(−1) f(-1) .\newlineChoose 11 answer:\newline(A) 1 1 \newline(B) e e \newline(C) 2 2
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Posted 8 months ago

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v=3RTM v=\sqrt{\frac{3 R T}{M}} \newlineThe root-mean-square speed is the measure of the speed of particles in a gas. Root-mean-square speed, v v , can be calculated using the equation shown, where M M is the molar mass of a gas, R R is the molar gas constant, and T T is the temperature. Which of the following equations correctly expresses the molar mass of a gas in terms of root-mean-square speed, temperature, and the molar gas constant?\newlineChoose 11 answer:\newline(A) M=(3RTv)2 M=\left(\frac{3 R T}{v}\right)^{2} \newline(B) M=3RT(v)2 M=\frac{3 R T}{(v)^{2}} \newline(C) M=(v)23RT M=\frac{(v)^{2}}{3 R T} \newline(D) M=3RTv M=\frac{\sqrt{3 R T}}{v}
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Posted 7 months ago

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f=3π(d2)2h f=3 \pi\left(\frac{d}{2}\right)^{2} h \newlineA board foot is a 11 foot by 11 foot by 11 inch thick volume. The formula estimates the board feet, f f , available in a tree with a diameter of d d inches and a height of h h feet. Which of the following equations correctly gives the diameter in terms of the board feet and the height of the tree?\newlineChoose 11 answer:\newline(A) d=2f3πh d=\sqrt{\frac{2 f}{3 \pi h}} \newline(B) d=2f3πh d=2 \sqrt{\frac{f}{3 \pi h}} \newline(C) d=2f23πh d=\frac{2 f^{2}}{3 \pi h} \newline(D) d=f223πh d=\frac{f^{2} \sqrt{2}}{3 \pi h}
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Posted 7 months ago

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The surface area of a cylinder is increasing at a rate of 9π 9 \pi square meters per hour.\newlineThe height of the cylinder is fixed at 33 meters.\newlineAt a certain instant, the surface area is 36π 36 \pi square meters.\newlineWhat is the rate of change of the volume of the cylinder at that instant (in cubic meters per hour)?\newlineChoose 11 answer:\newline(A) 9π 9 \pi \newline(B) 27π 27 \pi \newline(C) π3 \frac{\pi}{3} \newline(D) 12 \frac{1}{2} \newlineThe surface area of a cylinder with base radius r r and height h h is 2πr2+2πrh 2 \pi r^{2}+2 \pi r h .\newlineThe volume of a cylinder with base radius r r and height h h is πr2h \pi r^{2} h .
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Posted 7 months ago

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The radius of the base of a cone is increasing at a rate of 1010 meters per second.\newlineThe height of the cone is fixed at 66 meters.\newlineAt a certain instant, the radius is 11 meter.\newlineWhat is the rate of change of the volume of the cone at that instant (in cubic meters per second)?\newlineChoose 11 answer:\newline(A) 20π 20 \pi \newline(B) 40π 40 \pi \newline(C) 400π 400 \pi \newline(D) 200π 200 \pi \newlineThe volume of a cone with radius r r and height h h is πr2h3 \pi r^{2} \frac{h}{3} .
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Posted 7 months ago

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The side of the base of a square prism is increasing at a rate of 55 meters per second and the height of the prism is decreasing at a rate of 22 meters per second.\newlineAt a certain instant, the base's side is 66 meters and the height is 77 meters.\newlineWhat is the rate of change of the volume of the prism at that instant (in cubic meters per second)?\newlineChoose 11 answer:\newline(A) 492492\newline(B) −492-492\newline(C) −348-348\newline(D) 348348\newlineThe volume of a square prism with base side s s and height h h is s2h s^{2} h .
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Posted 7 months ago

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The side of the base of a square pyramid is increasing at a rate of 66 meters per minute and the height of the pyramid is decreasing at a rate of 11 meter per minute.\newlineAt a certain instant, the base's side is 33 meters and the height is 99 meters.\newlineWhat is the rate of change of the volume of the pyramid at that instant (in cubic meters per minute)?\newlineChoose 11 answer:\newline(A) −111-111\newline(B) 111 \mathbf{1 1 1} \newline(C) −105-105\newline(D) 105105\newlineThe volume of a square pyramid with base side s s and height h h is 13s2h \frac{1}{3} s^{2} h .
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Posted 7 months ago

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