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3 years ago

find three consecutive even intergers such that the sum of twice the smallest and 4 times the largest is 304. Please help

1 answer:

8 0

The smallest integer is represented by x. The largest is represented by x+4.

2x+4(x+4)=304
2x+4x+16=304
6x+16=304
6x=288
x=48

Final answer: 48, 50, 52

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Find the vectors T, N, and B at the given point. r(t) = < t^2, 2/3t^3, t >, (1, 2/3 ,1)

maxonik [38]

Answer with Step-by-step explanation:

We are given that

$r(t)=< t^2,\frac{2}{3}t^3,t >$

We have to find T,N and B at the given point t > (1, $2/3$ ,1)

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$\mid r'(t) \mid=\sqrt{(2t)^2+(2t^2)^2+1}=\sqrt{(2t^2+1)^2}=2t^2+1$

$T(t)=\frac{r'(t)}{\mid r'(t)\mid}=\frac{}{2t^2+1}$

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$N(1)=\frac{T'(1)}{\mid T'(1)\mid}$

$N(1)=\frac{}{\frac{2}{3}}=$

$N(1)=$

$B(1)=T(1)\times N(1)$

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$B(1)=i(\frac{-4}{9}-\frac{2}{9})-j(\frac{-4}{9}+\frac{1}{3})+k(\frac{4}{9}+\frac{2}{9})$

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3 years ago

Find the equation of a line that has a slope of 2 and passes through the point. point (-7, 5)

sashaice [31]

Answer:

$\large\boxed{y-5=2(x+7)\leftarrow\text{point-slope form}}\\\boxed{y=2x+19\leftarrow\text{slope-intercept form}}$

Step-by-step explanation:

The point-slope form of an equation of a line:

$y-y_1=m(x-x_1)$

m - slope

(x₁, y₁) - point

We have the slope m = 2 and the point (-7, 5) → x₁ = -7, y₁ = 5.

Substitute:

$y-5=2(x-(-7))\\\\y-5=2(x+7)$

Convert to the slope-intercept form (y = mx + b):

$y-5=2(x+7)$ use distributive property

$y-5=2x+14$ add 5 to both sides

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3 years ago

I need this answer step by step but if you can't that's fine too!

Naily [24]

Since the scale factor is 0.5, it means that you have to divide in half each side.
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4 years ago