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Find equations of tangent lines using limits

88A) REGULARITY Determine whether △DEF≅△PQR \triangle D E F \cong \triangle P Q R .\newlineD(−6,1),E(1,2),F(−1,−4),P(0,5),Q(7,6),R(5,0) D(-6,1), E(1,2), F(-1,-4), P(0,5), Q(7,6), R(5,0) \newlineFind the side lengths of each triangle.\newlineDE=52,PQ=52,EF=10,QR=10,DF=52,PR=52 D E=5 \sqrt{2}, P Q=5 \sqrt{2}, E F=\sqrt{10}, Q R=\sqrt{10}, D F=5 \sqrt{2}, P R=5 \sqrt{2} \newlineDE=2,PQ=2,EF=10,QR=10,DF=2,PR=2 D E=\sqrt{2}, P Q=\sqrt{2}, E F=\sqrt{10}, Q R=\sqrt{10}, D F=\sqrt{2}, P R=\sqrt{2} \newlineDE=52,PQ=52,EF=210,QR=210,DF=52,PR=52 D E=5 \sqrt{2}, P Q=5 \sqrt{2}, E F=2 \sqrt{10}, Q R=2 \sqrt{10}, D F=5 \sqrt{2}, P R=5 \sqrt{2} \newlineDE=52,PQ=510,EF=210,QR=210,DF=510,PR=52 D E=5 \sqrt{2}, P Q=5 \sqrt{10}, E F=2 \sqrt{10}, Q R=2 \sqrt{10}, D F=5 \sqrt{10}, P R=5 \sqrt{2} \newline88B) Fill in the blanks using the available answer choices.\newlineIs \qquad DEF≅△PQR D E F \cong \triangle P Q R ? Explain.\newline△ \triangle \newlineDEF D E F \qquad to \qquad DE=52,PQ=52,EF=10,QR=10,DF=52,PR=52 D E=5 \sqrt{2}, P Q=5 \sqrt{2}, E F=\sqrt{10}, Q R=\sqrt{10}, D F=5 \sqrt{2}, P R=5 \sqrt{2} 11 by DE=52,PQ=52,EF=10,QR=10,DF=52,PR=52 D E=5 \sqrt{2}, P Q=5 \sqrt{2}, E F=\sqrt{10}, Q R=\sqrt{10}, D F=5 \sqrt{2}, P R=5 \sqrt{2} 22 because corresponding sides have \qquad and are \qquad (Blank I)\newline(Blank 22)\newline(Blank: 33)\newlineBlank 11 options\newlineBlank 22 options\newlineBlank 33 options\newline- is congruent\newline- the same measure\newline- is not congruent\newline- different measures\newline- congruent\newline- not congruent
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Let f f be the function given by f(x)=4x2−x3 f(x)=4 x^{2}-x^{3} , and let t t be the line y=18−3x y=18-3 x , where ℓ \ell is tangent to the graph ∝+f \propto+f . Let R R be the region bounded by the graph of f f and the x x -axis, and let S S be the region bounded by the graph of f f , the line ℓ \ell , and the x x -axis, as shown.\newline(a) Show that ℓ \ell is tangent to the graph of f(x)=4x2−x3 f(x)=4 x^{2}-x^{3} 44 at the point f(x)=4x2−x3 f(x)=4 x^{2}-x^{3} 55.\newline(b) Find the area of S S .\newline(c) Find the volume of the solid generated when R R is revolved about the x x -axis.
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22. Given the likelihood function;\newline Lf =1σn(2xˉ)nexp⁡(−−1/2∑(Yi−β1−β2x2i)2σ2) \text { Lf }=\frac{1}{\sigma^{n}(\sqrt{2} \bar{x})^{n}} \exp \left(-\frac{-1 / 2 \sum\left(Y_{i}-\beta_{1}-\beta_{2} x_{2 i}\right)^{2}}{\sigma^{2}}\right) \newline(a) Derive the log likelihood function as a function of β1,β2 \beta_{1}, \beta_{2} , and σ2 \sigma^{2} .\newlineScanned with CamScanner\newline(b) Choose. β1,β2 \beta_{1}, \beta_{2} , and σ2 \sigma^{2} to maximize the log likefihood function.\newline(c) Dexive the maximum liketihood enor variance. Is it the same as the ceast equare minimization error variance? If nit, state the condition under which the two error vasiances will be the same.
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Evaluate the integral, where E E is enclosed by the parabolold z=9+x2+y2 z=9+x^{2}+y^{2} , the cyllinder x2+y2=5 x^{2}+y^{2}=5 , and the xy x y -plane. Use cylindrical coordinates.\newline∭Ee2dv \iiint_{E} e^{2} d v \newlineStep 11\newlineIn cylindrical coordinates, the parabolold z=9+x2+y2 z=9+x^{2}+y^{2} has the equation z=9+r2,9+r2 z=9+r^{2}, 9+r^{2} and the cylinder x2+y2=5 x^{2}+y^{2}=5 has the equation r=5 r=\sqrt{5} \newlineSim⁡2 \operatorname{Sim} 2 \newlineTherefore, the reglon E E enclosed by the parabolold, the cylinder, and the xy x y -plane is described by\newlineE={(r,θ,z)∣0≤z≤□□.0≤r≤5,0≤θ≤2π E=\left\{(r, \theta, z) \mid 0 \leq z \leq \square \square^{.0 \leq r \leq \sqrt{5}}, \quad 0 \leq \theta \leq 2 \pi\right.
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Which of the following is an equation of the line in the xy x y -plane that passes through the point (1,1) (1,1) and is parallel to the line with equation y=−3x−1 y=-3 x-1 ?\newlineChoose 11 answer:\newline(A) y=13x+4 y=\frac{1}{3} x+4 \newline(B) y=13x+1 y=\frac{1}{3} x+1 \newline(C) y=−3x+4 y=-3 x+4 \newline(D) y=−3x+1 y=-3 x+1
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