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Liono4ka [1.6K]

3 years ago

9

Can there be a negative change in length? i.e. a negative ΔL ?

1 answer:

Ratling [72]3 years ago

5 0

Answer:

$length \: cant \: be \: negative \: but \\ change \: can \: negative \\ if \: length \: decreases \: then \: \\ change = final \: - initial \: will \: be \: negative \\ thank \: you$

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the gas tank in mr.makies car hold 15 1/5 gallongs of gas .how many gallongs are in the tank when its 1/4 full

Wittaler [7]

Answer:

3.8 Gallongs

Step-by-step explanation:

15.2/4

6 0

3 years ago

Circle Y is shown. Line segments X Y and Z Y are radii. The length of X Y is 16. Sector X Y Z of the minor angle is shaded.

GrogVix [38]

Answer:

96pi units²

Step-by-step explanation:

Area of sector = ½ × r² × theta

½ × 16² × (3pi/4)

96pi units²

3 0

3 years ago

Read 2 more answers

Differentiate with respect to x and simplify your answer. Show all the appropriate steps? 1.e^-2xlog(ln x)^3 2.e^-2x(log(ln x))^

serious [3.7K]

(1) I assume "log" on its own refers to the base-10 logarithm.

$\left(e^{-2x}\log(\ln x)^3\right)'=\left(e^{-2x}\right)'\log(\ln x)^3+e^{-2x}\left(\log(\ln x)^3\right)'$

$=-2e^{-2x}\log(\ln x)^3+\dfrac{e^{-2x}}{\ln10(\ln x)^3}\left((\ln x)^3\right)'$

$=-2e^{-2x}\log(\ln x)^3+\dfrac{3e^{-2x}(\ln x)^2}{\ln10(\ln x)^3}\left(\ln x\right)'$

$=-2e^{-2x}\log(\ln x)^3+\dfrac{3e^{-2x}(\ln x)^2}{\ln10\,x(\ln x)^3}$

$=-2e^{-2x}\log(\ln x)^3+\dfrac{3e^{-2x}}{\ln10\,x\ln x}$

Note that writing $\log(\ln x)^3=3\log(\ln x)$ is one way to avoid using the power rule.

(2)

$\left(e^{-2x}(\log(\ln x))^3\right)'=(e^{-2x})'(\log(\ln x))^3+e^{-2x}\left(\log(\ln x))^3\right)'$

$=-2e^{-2x}(\log(\ln x))^3+3e^{-2x}(\log(\ln x))^2(\log(\ln x))'$

$=-2e^{-2x}(\log(\ln x))^3+3e^{-2x}(\log(\ln x))^2\dfrac{(\ln x)'}{\ln10\,\ln x}$

$=-2e^{-2x}(\log(\ln x))^3+\dfrac{3e^{-2x}(\log(\ln x))^2}{\ln10\,x\ln x}$

(3)

$\left(\sin(xe^x)^3\right)'=\left(\sin(x^3e^{3x})\right)'=\cos(x^3e^{3x}(x^3e^{3x})'$

$=\cos(x^3e^{3x})((x^3)'e^{3x}+x^3(e^{3x})')$

$=\cos(x^3e^{3x})(3x^2e^{3x}+3x^3e^{3x})$

$=3x^2e^{3x}(1+x)\cos(x^3e^{3x})$

(4)

$\left(\sin^3(xe^x)\right)'=3\sin^2(xe^x)\left(\sin(xe^x)\right)'$

$=3\sin^2(xe^x)\cos(xe^x)(xe^x)'$

$=3\sin^2(xe^x)\cos(xe^x)(x'e^x+x(e^x)')$

$=3\sin^2(xe^x)\cos(xe^x)(e^x+xe^x)$

$=3e^x(1+x)\sin^2(xe^x)\cos(xe^x)$

(5) Use implicit differentiation here.

$(\ln(xy))'=(e^{2y})'$

$\dfrac{(xy)'}{xy}=2e^{2y}y'$

$\dfrac{x'y+xy'}{xy}=2e^{2y}y'$

$y+xy'=2xye^{2y}y'$

$y=(2xye^{2y}-x)y'$

$y'=\dfrac y{2xye^{2y}-x}$

8 0

3 years ago

What are some important features of a prism? In other words, what makes a prism a prism?

Flauer [41]

Answer:

A solid figure whose bases or ends have the same size and shape and are parallel to one another, and each of whose sides is a parallelogram.

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Use the scale factor to determine the height of the real house. Round you answer to the nearest whole number.

Elanso [62]

Answer:

21.25ft?

Step-by-step explanation:

Make the ratio equal to 1

so 2÷2 = 1

and 5÷2 = 2.5

so the ratio is 1in :2.5 ft

so if the drawing is 8.5 in

then in (ft) it is 8.5×2.5=21.25ft

7 0

3 years ago