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Ivenika [448]
3 years ago
12

Dustins tea cup weighs 100g and holds 160cm3 He fills it with water what will it weigh in grams?

Mathematics
1 answer:
maw [93]3 years ago
6 0

Answer:

Assuming he fills the entire tea cup (160 cm^3), it will weigh 260g.

Step-by-step explanation:

1 cm^3 of water weighs 1g, thus 160 cm^3 of water would weigh 160g.

100g + 160g = 260g

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For each value of x, determine whether it is a solution to x&gt; 8.<br> Is it a solution?
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Find the equation of the tangent line to the curve (a lemniscate)
olya-2409 [2.1K]

Answer:

m=\frac{9}{13} and b=\frac{40}{13}

Step-by-step explanation:

The equation of curve is

2(x^2+y^2)^2=25(x^2-y^2)

We need to find the equation of the tangent line to the curve at the point (-3, 1).

Differentiate with respect to x.

2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})

4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})

The point of tangency is (-3,1). It means the slope of tangent is \frac{dy}{dx}_{(-3,1)}.

Substitute x=-3 and y=1 in the above equation.

4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})

40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})

-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}

80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240

130\frac{dy}{dx}=90

Divide both sides by 130.

\frac{dy}{dx}=\frac{9}{13}

If a line passes through a points (x_1,y_1) with slope m, then the point slope form of the line is

y-y_1=m(x-x_1)

The slope of tangent line is \frac{9}{13} and it passes through the point (-3,1). So, the equation of tangent is

y-1=\frac{9}{13}(x-(-3))

y-1=\frac{9}{13}(x)+\frac{27}{13}

Add 1 on both sides.

y=\frac{9}{13}(x)+\frac{27}{13}+1

y=\frac{9}{13}(x)+\frac{40}{13}

Therefore, m=\frac{9}{13} and b=\frac{40}{13}.

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3 years ago
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(6 + 3) + 21 = 6 + (3 + 21)

It's an ASSOCIATIVE PROPERTY
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Answer:


Step-by-step explanation:


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(10 can be divided by 5 and 2; 24 can be divided by 8, 3, 12 and 2; 38 can be divided by 19 and 2).


The others are prime numbers.

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3 years ago
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