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4 years ago

The perimeter of a rectangle is 98 centimeters. The width is 19 centimeters. Find the length. Show work.

Mathematics

1 answer:

Komok [63]4 years ago

8 0

Answer:

length=30

Step-by-step explanation:

P=2l+2w

98=2l+2(19)

98-2(19)=2l

98-38=2l

60=2l

30=l

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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)

$r'(t)=$

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

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

Now, substitute t=1

$T(1)=\frac{}{2+1}=\frac{1}{3}$

$T'(t)=\frac{-4t}{(2t^2+1)^2} +\frac{1}{2t^2+1}$

$T'(1)=-\frac{4}{9}+\frac{1}{3}$

$T'(1)=\frac{1}{9}=$

$\mid T'(1)\mid=\sqrt{(\frac{-2}{9})^2+(\frac{4}{9})^2+(\frac{-4}{9})^2}=\sqrt{\frac{36}{81}}=\frac{2}{3}$

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

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

$N(1)=$

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

$B(1)=\begin{vmatrix}i&j&k\\\frac{2}{3}&\frac{2}{3}&\frac{1}{3}\\\frac{-1}{3}&\frac{2}{3}&\frac{-2}{3}\end{vmatrix}$

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

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

$B(1)=\frac{1}{3}$

5 0

3 years ago

Which one is the unit of force<br> A.Joules<br> B. Newton<br> C. Celsius<br> D. Kelvin

Snezhnost [94]

Answer:

Newtons

Step-by-step explanation:

Joules measure electrical power and celcius and Kelvin measures temperature.

7 0

4 years ago

Read 2 more answers

SOMEONE HELP ME PLEASE

Nikolay [14]

Answer:

<h3>Angle 6 = 101°</h3><h3>Angle 5 = 79°</h3><h3>Angle 7 = 79</h3>

Step-by-step explanation:

Angle 6 will 101°

This is because we can see that Angle 4 is alternate interior angle to Angle 6 and alternate interior angles are always equal.

<h2>So angle 6 will be 101°</h2>

Angle 7 = 79°

Here we can see that Angle 6 and angle 7 are supplementary which means it has a measure of 180°

So the value of Angle 7 will be

$180 - 101 = 79$

<h2>Hence the measure of angle 7 will be 79°</h2>

Angle 5 = 79°

Angle 7 and Angle 5 is vertically opposite to each other and we know that vertically opposite angles are always equal so the measure will be 79°

<h3>Hence the measure of Angle 5 will be 79°</h3>

3 0

3 years ago

A person wants to create a vegetable garden and keeps the rabbits out by enclosing it with 100 feet of fencing. The area of the

alekssr [168]

Answer:

The garden can not have area of 700ft^2

Step-by-step explanation:

We are given equation for area as

$A(w)=w\times (50-w)$

where

w is the width (in feet) of the garden

now, we are given area =700 ft^2

so, we can set area =700

and then we can solve for w

$w\times (50-w)=700$

$50w-w^2=700$

$-w^2+50w-700=0$

now, we can use quadratic formula

$ax^2+bx+c=0$

$w=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

we can compare and find a,b, and c

a=-1 , b=50 , c=-700

now, we can plug values

$w=\frac{-50\pm \sqrt{50^2-4\left(-1\right)\left(-700\right)}}{2\left(-1\right)}$

$w=25-5\sqrt{3}i,\:w=25+5\sqrt{3}i$

We can see that values of w is not real

so, w does not exists when area =700

so, The garden can not have area of 700ft^2

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3 years ago

A linear regression is done on data the line of best fit is y= 1.25x-6.25. What is the residual for the point (1,1)?

Damm [24]

Answer:

Step-by-step explanation:

Find the predicted y value when x=1:

$\hat{y}=1.25x-6.25\\\hat{y}=1.25(1)-6.25\\\hat{y}=1.25-6.25\\\hat{y}=-5$

Find the residual:

$\text{Residual}=\text{Actual Value}-\text{Predicted Value}\\\text{Residual}=y-\hat{y}\\\text{Residual}=1-(-5)\\\text{Residual}=1+5\\\text{Residual}=6$

Because our residual is positive, this is an indicator that our predicted y value is too low.

6 0

3 years ago