Which best describes the relationship between the line that passes through (7, 1) and (10, 5) and the line that

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]

<u>Answer:</u>

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

<u>Solution:</u>

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

The numbers x and y are inversely proportional. When the sum of x and y is 42, x is twice y. What is the value of y when x = -8?

dolphi86 [110]

Answer:

y= -4

Step-by-step explanation:

x+y=42. We know that x plus y equals 42.

x=2y . We also know that x equals twice y.

2y+y=42. Since we know that x=2y, we're going to replace x with 2y from the original equation, simplified would be 3y=42.

y=14. 3y=42 simplified is y=14, this is because we divided both sides by 3 (since 3 and 42 are both divisible by 3) (btw divisible by 3 simply means that it can be divided by 3)

x+14=42. Now that we know what y equals, let's replace y with 14 from the original equation.

x=28. Now that we know that x=28 and y=14, we know that y is always x/2.

When x=-8, we divide it by 2 and get, -4.

Not absolutely positive as this was all mental math, but hope this helps! :)

4 0

3 years ago

What is the area of the composite figure? ___ units^2

elena-14-01-66 [18.8K]

Answer:

34 square units

Step-by-step explanation:

The figure can be considered to be a trapezoid with a rectangle removed.

The area of the trapezoid is ...

A = (1/2)(b1 +b2)h

A = (1/2)(10 +6)(5) = 40

The area of the rectangle is ...

A = LW

A = (3)(2) = 6

Then the area of the shaded portion of the figure is ...

shaded area = trapezoid area - rectangle area

= 40 - 6 = 34 . . . square units

7 0

2 years ago

1. We can use division to solve real life problems, such as:

iren2701 [21]

Well, let's look at the answer choices.
A) If you want to fond the total cost of two sweaters you would add, not divide. So this isn't it.
B) To find out how much older someone is you would subtract. So this isn't it either.
C) To find out how many desks are needed you would multiply, since you know you need 3 rows of desks with 7 students each (3 x 7). Again, not it.
D) To find out how many pencils each student would get, you'd divide. You would divide 56 by 9. So your answer is D.

4 0

3 years ago

Read 2 more answers

Eli had 20 lemons. He used an equal number in each of 3 pitchers of lemonade. He has 2 lemons left. How many lemons did Eli use

Sidana [21]

Answer: he used 6 lemons for each pitcher so answer is =6

3 0

3 years ago