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fomenos
3 years ago
9

Find r if (r, 6) and (5, -4) are two points on a line with a slope of 5/7 (Hint: use the slope formula)

Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
4 0

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

We have

(r,\ 6),\ (5,\ -4)\\\\m=\dfrac{5}{7}

Substitute

\dfrac{-4-6}{5-r}=\dfrac{5}{7}\\\\\dfrac{-10}{5-r}=\dfrac{5}{7}\qquad|\text{cross multiply}\\\\5(5-r)=(-10)(7)\qquad|\text{use distributive property}\\\\25-5r=-70\qquad|-25\\\\-5r=-95\qquad|:(-5)\\\\\boxed{r=19}

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Ex 2.8<br> 3. find the maximum value of y for the curve y=x^5 -3 for -2≤x≤1
harkovskaia [24]
y=x^5-3\\ y'=5x^4\\\\ 5x^4=0\\ x=0\\ 0\in [-2,1]\\\\ y''=20x^3\\\\&#10;y''(0)=20\cdot0^3=0

The value of the second derivative for x=0 is neither positive nor negative, so you can't tell whether this point is a minimum or a maximum. You need to check the values of the first derivative around the point.
But the value of 5x^4 is always positive for x\in\mathbb{R}\setminus \{0\}. That means at x=0 there's neither minimum nor maximum.
The maximum must be then at either of the endpoints of the interval [-2,1].
The function y is increasing in its entire domain, so the maximum value is at the right endpoint of the interval.

y_{max}=y(1)=1^5-3=-2
4 0
3 years ago
Write an inequality for the sentence: The total t is less than sixteen.
RoseWind [281]
T<16 is your inequality.
7 0
3 years ago
Find the distance and the midpoint of the line segment with endpoints (-1,4) and (-5,3)
Marina CMI [18]

Answer:

see explanation

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1,4) and (x₂, y₂ ) = (- 5, 3)

d = \sqrt{(-5+1)^2+(3-4)^2}

  = \sqrt{(-4)^2+(-1)^2}

  = \sqrt{16+1} = \sqrt{17} ≈4.12 ( to 2 dec. places )

To find the midpoint use the midpoint formula

[0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]

Using the same points as above then

midpoint = [0.5(- 1- 5), 0.5(4 + 3 ) ] = [0.5(- 6), 0.5(7) ] = (- 3, 3.5 )

4 0
3 years ago
Chistopher is 20 years younger than ishaan. Ishaan and chistopher first met two years ago. Fourteen years ago, ishaan was 3 time
lisabon 2012 [21]

Answer:

Ishaan is 49 years old.

Step-by-step explanation:

Let the present age of Christopher be 'C'.

Let the present age of Ishaan be 'I'.

From the given data, we can form equations which will help us solve the problem.

Christopher is 20 years younger than Ishaan. This means:

C = I - 20                  . . . (1)

Fourteen years ago, Ishaan would have been (I -14) years old and Christopher (C - 14) years old.

From the data, I - 14 = 3(C - 14)         . . . (2)

Substituting the value of C in Equation 2, we get:

I - 14 = 3(I - 20 - 14)

⇒ I - 14 = 3(I - 34)

⇒ I - 14 = 3I - 112

⇒ 2I = 112 + 14 = 98

⇒ I = 49

So, Ishaan is 49 years old.

4 0
3 years ago
A trampoline has an area of 49pi square feet what's the diameter of the trampoline
Anna007 [38]
Area of a circle is π*r²
sub what we're given 
49π= πr²
49π= π*r²
r²= 49π/π
r²=49
r=7
The diameter is twice the radius therefore the diameter is 14 units
7 0
3 years ago
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