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2 years ago

PLS ANSWER THIS I NEED HELP

Mathematics

1 answer:

saw5 [17]2 years ago

3 0

Answer:

Here is your answer

Hope it helps

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A curve is given by y=(x-a)√(x-b) for x≥b, where a and b are constants, cuts the x axis at A where x=b+1. Show that the gradient

ankoles [38]

Answer:

A curve is given by y=(x-a)√(x-b) for x≥b. The gradient of the curve at A is 1.

Solution:

We need to show that the gradient of the curve at A is 1

Here given that ,

$y=(x-a) \sqrt{(x-b)}$ --- equation 1

Also, according to question at point A (b+1,0)

So curve at point A will, put the value of x and y

$0=(b+1-a) \sqrt{(b+1-b)}$

0=b+1-c --- equation 2

According to multiple rule of Differentiation,

$y^{\prime}=u^{\prime} y+y^{\prime} u$

so, we get

${u}^{\prime}=1$

$v^{\prime}=\frac{1}{2} \sqrt{(x-b)}$

$y^{\prime}=1 \times \sqrt{(x-b)}+(x-a) \times \frac{1}{2} \sqrt{(x-b)}$

By putting value of point A and putting value of eq 2 we get

$y^{\prime}=\sqrt{(b+1-b)}+(b+1-a) \times \frac{1}{2} \sqrt{(b+1-b)}$

$y^{\prime}=\frac{d y}{d x}=1$

Hence proved that the gradient of the curve at A is 1.

7 0

2 years ago

Beth filled 32 jars with paint. If each jar holds 1 pint of paint how many gallons of paint did Beth use

Sloan [31]

If there are 8 pints in a gallon there are 4 gallons 32(pints) divided by 8 is 4

3 0

3 years ago

Quadrilateral ABCD has vertices A(1,0) B(5,0) C (7,2) D(3,2). Use slope to prove that ABCD is a parallelogram.

Galina-37 [17]

Answer:

$AD \parallel BC$

$AB \parallel CD$

Step-by-step explanation:

The vertices of quadrilateral ABCD are A(1,0) B(5,0) C (7,2) D(3,2).

The slope of side AB is

$M_{AB}=\frac{0-0}{5-1} =\frac{0}{4}=0$

The slope of side BC is

$M_{BC}=\frac{2-0}{7-5} =\frac{2}{2}=1$

The slope of side CD is

$M_{CD}=\frac{2-2}{3-7} =\frac{0}{-4}=0$

The slope of AD is

$M_{AD}=\frac{2-0}{3-1} =\frac{2}{2}=1$

$AD \parallel BC$

$AB \parallel CD$

We see that the opposite sides of the quadrilateral ABCD are equal.

Hence the quadrilateral is a parallelogram

4 0

2 years ago

The sum of two consecutive intergers is no more than 209 . Whatbis the large of two integers

soldi70 [24.7K]

104 and 105 are consecutive numbers that add up to 209. Maybe this answers your question? Let me know otherwise.

8 0

3 years ago

A B C D need this to be right!!!!!

dezoksy [38]

The correct answer is C!!

Hope this helped!!!

7 0

3 years ago

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