Answer:
Therefore the equation of the line through ( 4 , -8 ) and ( 8 , 5 ) is
13x - 4y = 84.
Step-by-step explanation:
Given:
Let,
point A( x₁ , y₁) ≡ ( 4 ,-8)
point B( x₂ , y₂) ≡ (8 , 5)
To Find:
Equation of Line AB =?
Solution:
Equation of a line passing through Two points A( x₁ , y₁) and B( x₂ , y₂)is given by the formula
Substituting the given values in a above equation we get
Therefore the equation of the line through ( 4 , -8 ) and ( 8 , 5 ) is
13x - 4y = 84.
The lowest possible fraction is 3/4 because 0.75=75/100 then you divide both terms by 25 and get 3/4
Answer:
x=4 Inch
Step-by-step explanation:
Length of the Square = 24 Inches
If a Square of Length x cm is cut out from each corner
Length of the Box = 24-x-x=(24-2x) Inches
Width of the Box =24-x-x=(24-2x) Inches
Height of the box = x inches
Volume of a Cuboid = Length X Width X Height
V(x)= x(24-2x)(24-2x)
Simplifying
V(x)=4x(12-x)(12-x)
To determine the value of x at which V is largest, we take the derivative of V(x) and solve for the critical points.
V(x)=4x(12-x)(12-x)
Set the derivative equal to zero to obtain the critical points
x cannot be equal to 12 as it divides the length of the square cardboard into exactly two equal parts.
When x=4
V(4)=4*4(12-4)(12-4)=16*8*8=1024 Cubic Inches
When x=4 Inch, the volume, V of the open box is largest.
Answer: The answer to this question is 15.53lt/sec.
Step-by-step explanation: 1 liter is equal to 0.264gallons
1 minutes is equal to 60 seconds.
To convert we have to multiply 246gal/min by 1min/60sec then by 1lt/0.264gal to get the answer in lt/s
Where the answer is 15.53lt/s
Okay, so your first one, number six. You have two shapes there, a cone and a circle. Now you have a full cone and a half of a circle. Let's start with the cone. The formula for the volume of a cone is πr²h/3. You have your height, that is 12, so get your paper out and plug that in. H = 12. Now, your radius is where it gets a bit tricky. Have you ever heard of the Pythagorean theorem? It's a²+b²=c². Look at the cone, but look at it like it's a two-dimensional shape. You see the triangle in the middle, ignore the rest and pretend it's only that triangle. You now have a right triangle, You know your height is 12, and by looking at the triangle adjacent to it, and know it's equal, you know that your hypotenuse (the longest side of your triangle) is 15. So plug that into the Pythagorean theorem. Now you have 12²+b²=15². Use algebra to work that out, and you're left with 9. So your radius is 9. Now plug that into your volume of a cone equation. The volume of the cone is about 1017.88. Now find the circle or sphere. The formula is 4/3πr³. Just plug in your radius and get your answer, which is 3053.63. Now cut that in half, as you've only got half a circle. Now you've got 1526.82. Now add that to the volume of your cone, and you've got your final answer. 2544.7, or about that. I used π on a calc, and not 3.14, so it might be a little different.
Do you think you can do the next one? Just look at your triangle in there. You've already got one side and a hypotenuse, so plug it into the Pythagorean theorem and get your last side. Then look at the little marks on there and you can see if places are the same. If you need help with it don't hesitate to ask. I'm staying up all night anyway. Homeschooled and behind, so I'm not going anywhere.
