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valentinak56 [21]
3 years ago
5

Use the arc length formula to find the length of the curve y = 4x − 5, −1 ≤ x ≤ 3. Check your answer by noting that the curve is

a line segment and calculating its length by the distance formula.
Mathematics
1 answer:
Reptile [31]3 years ago
5 0

Answer:

4\sqrt{17}

Step-by-step explanation:

Let's find the answer by using the arc length formula which is:

\int\limits^a_b {\sqrt{1+(\frac{dy}{dx})^{2} } } \, dx

First, let's find dy/dx which is:

y=4x-5

y'=4*(1)-0

y'=4, now let's use the formula:

\int\limits^3_{-1} {\sqrt{1+4^{2}} } \, dx=\sqrt{17} *(3-(-1))=4\sqrt{17}

Now, using the distance formula we have:

d=\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }

y(-1)=4*(-1)-5=-9 \\y(3)=4*(3)-5=7

So we have two points (-1, -9) and (3, 7) so:

d=\sqrt{(3-(-1))^{2} +(7-(-9))^{2} }=4\sqrt{17}

Notice both equations gave the same length 4\sqrt{17}.

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yulyashka [42]

{\qquad\qquad\huge\underline{{\sf Answer}}}

Here we go ~

As we can see in the figure, lines m and n are parallel to each other. so we can apply Angle pair properties ~

So,

\qquad \sf  \dashrightarrow \:  \angle1  \cong \angle2

[ they form corresponding angle pair ]

and it's given that :

\qquad \sf  \dashrightarrow \:  \angle2 \cong\angle 3

therefore, by using above information. we can conclude that :

\qquad \sf  \dashrightarrow \:  \angle1 \cong \angle3

7 0
2 years ago
What is the value of the expression “three less than the quotient of ten and a number, increased by six” when n = 2?
alisha [4.7K]

Answer:

8

Step-by-step explanation:

The given expression is "three less than the quotient of ten and a number, increased by six”

The quotient of ten and a number increased by six is translated into mathematical expression as:

\frac{10}{n}+6

Three less than the quotient of ten and a number, increased by six is

(\frac{10}{n}+6)-3

When we substitute n=2, we get:

(\frac{10}{2}+6)-3

Divide to get:

(5+6)-3

Add to get:

11-3

Subtract

8

4 0
3 years ago
Find the area.<br> 2 ft.<br> 19 ft<br> 4f<br> 5 ft.<br> 7
ch4aika [34]

Answer: 20 ft squared

Step-by-step explanation:

separate the figures

4 0
3 years ago
Convert 4 5/7 to an improper fraction
Musya8 [376]

Answer:

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Step-by-step explanation:

8 0
3 years ago
Evaluate the expression and write your answer in the form a + bi. 1) (2-6i)+(4+2i)2) (6+5i)(9-2i)3) 2/(3-9i)4) (3 − 5i)(7 − 2i)
laiz [17]

Answer:

Step-by-step explanation:

Given the following complex numbers, we are to expressed them in the form of a+bi where a is the real part and b is the imaginary part of the complex number.

1) (2-6i)+(4+2i)

open the parenthesis

= 2-6i+4+2i

collect like terms

= 2+4-6i+2i

= 6-4i

2)  (6+5i)(9-2i)

= 6(9)-6(2i)+9(5i)-5i(2i)

= 54-12i+45i-10i²

= 54+33i-10i²

In complex number i² = -1

= 54+33i-10(-1)

= 54+33i+10

= 54+10+33i

= 64+33i

3) For the complex number 2/(3-9i), we will rationalize by multiplying by the conjugate of the denominator i.e 3+9i

= 2/3-9i*3+9i/3+9i

=2(3+9i)/(3-9i)(3+9i)

= 6+18i/9-27i+27i-81i²

= 6+18i/9-81(-1)

= 6+18i/9+81

= 6+18i/90

= 6/90 + 18i/90

= 1/15+1/5 i

4) For (3 − 5i)(7 − 2i)

open the parenthesis

= 3(7)-3(2i)-7(5i)-5i(-2i)

= 21-6i-35i+10i²

= 21-6i-35i+10(-1)

= 21-41i-10

= 11-41i

4 0
3 years ago
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