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The area of a rectangular goat pen is 54 square meters54 \, \text{square meters}. The perimeter is 30 meters30 \, \text{meters}. What are the dimensions of the pen?\newline____\_\_\_\_ meters by ____\_\_\_\_ meters

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The work done by stretching a certain spring increases by 0.13x 0.13 x joules per centimeter (where x x is the displacement, in centimeters, beyond the spring's natural length).\newlineHow much work (in Joules) must be done in order to stretch the spring from x=4 x=4 to x=10 x=10 ?\newlineChoose 11 answer:\newline(A) 55.4646\newline(B) 77.5454\newline(C) 10.92 \mathbf{1 0 . 9 2} \newline(D) 15.08 \mathbf{1 5 . 0 8}
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Ahmed is modeling the area covered by a moss using the following equation:\newlineA=t2+5.8t+9.41 A=t^{2}+5.8 t+9.41 \newlinewhere A A is the area covered in square centimeters, negative values of t t represent a number of days before noon on July 11 , 20142014 , and positive values of t t represent a number of days after noon on July 11,20142014 . Which of the following equivalent expressions contains the number of days before noon on July 11,20142014 , as a constant or coefficient, when the moss started with its smallest area of 11 square centimeter?\newlineChoose 11 answer:\newline(A) (t−(−2.9))2+1 (t-(-2.9))^{2}+1 \newline(B) (t−(−1))2+3.8t+8.41 (t-(-1))^{2}+3.8 t+8.41 \newline(C) (t−(−3.9))(t−(−1.9))+2 (t-(-3.9))(t-(-1.9))+2 \newline(D) t(t−(−5.8))+9.41 t(t-(-5.8))+9.41
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Critical Thinking \newline& Problem Solving\newlineToy rubber balls are packaged in a cylinder that holds 33 balls. The diameter of each ball is \newline5.3 cm5.3\,\text{cm}. Find the volume of the cylinder. Use 3.143.14 for \newlineπ\pi.\newlineThe volume of the cylinder is about \newline□ cm3\square\,\text{cm}^3.\newline(Round to the nearest tenth as needed.)
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The radius of a quarter circle is 1313 miles. What is the quarter circle's area?\newlineUse π≈3.14\pi \approx 3.14 and round your answer to the nearest hundredth.\newlinesquaresquare milesmiles\newlineSubmit\newlineWork it out\newlineNot feeling ready yet? These can help:\newlineArea of circles (103)(103) in
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A cone has a slant height of 8 in8\,\text{in} and the radius of the base is 3 in3\,\text{in}. What is the lateral area, in square inches? Use π=3.14\pi=3.14. Round your answer to the nearest hundredth.
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Circle FF is shown with a diameter of 1515 centimeters (extcm)( ext{cm}). Which is the area of circle FF ? Use π=3.14\pi=3.14.
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In △EFG \triangle EFG , e=47 e=47 cm, ∠E=34∘ \angle E=34^\circ and ∠F=12∘ \angle F=12^\circ . Find the area of △EFG \triangle EFG , to the nearest square centimeter.
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