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2 years ago

I need this asap pls (will give brainliest)

Mathematics

1 answer:

sesenic [268]2 years ago

3 0

Step-by-step explanation:

I am thinking the X axis. if wrong, sorry. but I am really thinking that is the answer

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Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

$y=6x^2+14x$

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

$\frac{dy}{dx}=12x+14$

We know that length of curve

$s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx$

We have a=-2 and b=1

Using the formula

Length of curve= $s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx$

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

$dt=12dx$

$dx=\frac{1}{12}dt$

Length of curve= $s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt$

We know that

$\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C$

By using the formula

Length of curve= $s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})$

Length of curve= $s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})$

Length of curve= $s=32.66$

5 0

3 years ago

A girl is on the beach and the angle of elevation from her feet to the top of a lighthouse is 62' If the lighthouse is 30ft tall

soldi70 [24.7K]

Answer:

15.95 feets

Step-by-step explanation:

Given that:

Angle of elevation = 62°

Using trigonometric relation :

Tanθ = opposite / Adjacent

From the drawing attached :

Opposite = 30 feets

Distance between girl and lighthouse = d

Tan 62 = 30 / d

1.8807264 * d = 30

d = 30 / 1.8807264

d = 15.951283

d = 15.95 feets

3 0

3 years ago

What is the volume of the rectangular prism?

lara31 [8.8K]

1/2^3=1/8
we have 30 of them so
30.1/8=30/8 => 3 and 6/8 or 3 and 3/4 if simplified

6 0

2 years ago

An elementary school teacher wants to know if the words in a book are too difficult for her students. She reads the first senten

raketka [301]

Answer:

d.every word in the first sentence of the first page of every chapter.

Step-by-step explanation

the sample space means the set of total possible outcomes or ALL possible outcomes.

so here, the situation is about the teacher reading a sentence.

the favorable outcome is the set which has all the words that the students would not know from all the words read by the teacher or simply from the sample space.

since the teacher reads the first sentence on the first page in every chapter , all the words in that sentence will be sample in this situation.

7 0

3 years ago

Why is a the y-intercept of the graph of the function y=ab^x

8090 [49]

The y-intercept occurs on a graph when x = 0. Therefore on a graph of y= ab^x when x = 0, y = ab^0 = 1. Therefore the y-intercept is at the point (0,1).
Hope this helps!

3 0

3 years ago