Help me please thanks

If AD = 6, DC = 14, and BE = 4.75, calculate EC. Image not set to scale.

MAXImum [283]

Answer:

$\Large \boxed{11.08}$

Step-by-step explanation:

The triangles are congruent, we can use ratios to solve.

AD/DC = BE/EC

Let the length of EC be x.

6/14 = 4.75/x

Solve for x.

Cross multiply.

6 × x = 14 × 4.75

6x = 66.5

Divide both sides by 6.

(6x)/6 = (66.5)/6

x = 11.083333...

8 0

3 years ago

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How do I use substitution to integrate x*sqrt 3x^2+4?

katrin2010 [14]

Finding the indefinite integral by substitution:

$\large\begin{array}{l} \mathsf{\displaystyle\int x\sqrt{3x^2+4}\,dx}\\\\ =\mathsf{\displaystyle\int \frac{1}{6}\cdot 6x\sqrt{3x^2+4}\,dx}\\\\ =\mathsf{\displaystyle \frac{1}{6}\int\sqrt{3x^2+4}\cdot 6x\,dx\qquad\quad(i)} \end{array}$

$\large\begin{array}{l} \textsf{Substitute}\\\\ \mathsf{3x^2+4=u~~\Rightarrow~~6x\,dx=du}\\\\\\ \textsf{then (i) becomes}\\\\ =\mathsf{\displaystyle \frac{1}{6}\int\sqrt{u}\,du}\\\\ =\mathsf{\displaystyle \frac{1}{6}\int u^\frac{1}{2}\,du}\\\\ =\mathsf{\dfrac{1}{6}\cdot \dfrac{u^{\frac{1}{2}+1}}{\frac{1}{2}+1}+C} \end{array}$

$\large\begin{array}{l} =\mathsf{\dfrac{1}{6}\cdot \dfrac{~u^{\frac{3}{2}}~}{\frac{3}{2}}+C}\\\\ =\mathsf{\dfrac{1}{6}\cdot \dfrac{2}{3}\,u^{\frac{3}{2}}+C}\\\\ =\mathsf{\dfrac{1\cdot 2}{6\cdot 3}\,u^{\frac{3}{2}}+C}\\\\ =\mathsf{\dfrac{1\cdot \diagup\!\!\!\! 2}{\diagup\!\!\!\! 2\cdot 3\cdot 3}\,u^{\frac{3}{2}}+C}\\\\ =\mathsf{\dfrac{1}{9}\,u^{\frac{3}{2}}+C} \end{array}$

$\large\begin{array}{l} \textsf{Substitute back for }\mathsf{u=3x^2+4:}\\\\ =\mathsf{\dfrac{1}{9}\,(3x^2+4)^{\frac{3}{2}}+C}\\\\\\ \therefore~~\boxed{\begin{array}{c} \mathsf{\displaystyle\int x\sqrt{3x^2+4}\,dx=\frac{1}{9}\,(3x^2+4)^{\frac{3}{2}}+C} \end{array}}\qquad\checkmark \end{array}$

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$\large\textsf{I hope it helps.}$

Tags: definite integral integrate limits function irrational square root sqrt composite substitution integral calculus

3 0

3 years ago

A school district has two high schools. The district could only afford to hire 13 guidance counselors. Determine how many counse

Olegator [25]

Answer:

a)

Lowell: 4 counselors

Fairview: 9 counselors

b)

2 new counselors

Step-by-step explanation:

How many counselors should be assigned to each school using Hamilton's method?

Number of students

Lowell: 3584

Fairview: 6816

Total number of students: 10400

Divisor D = (Total number of students)/(number of counselors)= 10400/13 = 800

Temporal assignment

3584/800 = 4 + 0.48 ==> 4 counselors for Lowell

6816/800 = 8 + 0.52 ==> 8 counselors for Fairview

There is one counselor left. According to Hamilton's method she should be assigned to the school with the largest remainder, that is Fairview.

Final assignment

Lowell: 4 counselors

Fairview: 9 counselors

The next year, a new school is opened, with 1824 students. Using the divisor from above, determine how many additional counselors should be hired for the new school

1824/800 = 2 + 0.28

Two new counselors should be hired.

3 0

3 years ago

Two trains, train a and train , weigh a total of 466 tons. Train A is heavier than train b. The difference of there weights is 3

AlexFokin [52]

Answer: A = 396 tons

B = 70 tons

Step-by-step explanation:

From the question,

Weight of A + Weight of B = 466

Weight of A - Weight of B = 326

A + B = 466 ......... i

A - B = 326 ..........ii

Subtract equation ii from I

2B = 140

B = 140/2

B = 70 tons

A = 466 - 70

A = 396 tons

5 0

3 years ago

For health reasons Sarah needs to limit her fat intake to 25% of the total calories consumed in a day if the fat intake is 550 c

juin [17]

25% of x calories is 550 calories.

25% * x = 550

0.25x = 550

Divide both sides by 0.25

x = 2200

Answer: 2200 calories

4 0

3 years ago

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