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Alex17521 [72]
3 years ago
5

Please help me!!! will give brainlists!

Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
5 0
You have a rectangular prism on your hands. The formula for the volume of a rectangular prism is

(B/2) • l

Where B is the area of the base, and l is the length.

If you notice, you do NOT have the height of the triangle. However, you know that it is an equilateral triangle. So, you may split the triangle into two. Once you do, you can see that it is a right triangle. It’s hypotenuse is 3. If you know your triangles, you will realize that this is a 30 60 90 triangle. Therefore, the height will be 1.5 * sqrt(3)

So, to get B...

3 * 1.5sqrt(3)
4.5sqrt(3)
(Divide by 2)
2.25sqrt(3)
O
(9sqrt(3))/4
Multiply by the length of the prism, 6

This is your final answer in fraction form

27
— 2^rt(3)
2
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Let T be the plane-2x-2y+z =-13. Find the shortest distance d from the point Po=(-5,-5,-3) to T, and the point Q in T that is cl
GaryK [48]

Answer:

d=10u

Q(5/3,5/3,-19/3)

Step-by-step explanation:

The shortest distance between the plane and Po is also the distance between Po and Q. To find that distance and the point Q you need the perpendicular line x to the plane that intersects Po, this line will have the direction of the normal of the plane n=(-2,-2,1), then r will have the next parametric equations:

x=-5-2\lambda\\y=-5-2\lambda\\z=-3+\lambda

To find Q, the intersection between r and the plane T, substitute the parametric equations of r in T

-2x-2y+z =-13\\-2(-5-2\lambda)-2(-5-2\lambda)+(-3+\lambda) =-13\\10+4\lambda+10+4\lambda-3+\lambda=-13\\9\lambda+17=-13\\9\lambda=-13-17\\\lambda=-30/9=-10/3

Substitute the value of \lambda in the parametric equations:

x=-5-2(-10/3)=-5+20/3=5/3\\y=-5-2(-10/3)=5/3\\z=-3+(-10/3)=-19/3\\

Those values are the coordinates of Q

Q(5/3,5/3,-19/3)

The distance from Po to the plane

d=\left| {\to} \atop {PoQ}} \right|=\sqrt{(\frac{5}{3}-(-5))^2+(\frac{5}{3}-(-5))^2+(\frac{-19}{3}-(-3))^2} \\d=\sqrt{(\frac{5}{3}+5))^2+(\frac{5}{3}+5)^2+(\frac{-19}{3}+3)^2} \\d=\sqrt{(\frac{20}{3})^2+(\frac{20}{3})^2+(\frac{-10}{3})^2}\\d=\sqrt{\frac{400}{9}+\frac{400}{9}+\frac{100}{9}}\\d=\sqrt{\frac{900}{9}}=\sqrt{100}\\d=10u

7 0
3 years ago
Dairy farmers are aware there is often a linear relationship between the age, in years, of a dairy cow and the amount of milk pr
Jobisdone [24]

Answer:

B. A cow of 5 years is predicted to produce 5.5 more gallons per week.

Step-by-step explanation:

Let M(a) = 40.8-1.1\cdot a, where a is the age of the dairy cow, measured in years, and M(a) is the predicted milk production, measured in gallons per week.

Besides, we consider a_{1} and a_{2}, such that a_{1}\ne a_{2}, we define the difference between predicted milk productions (\Delta M) below:

\Delta M = -1.1\cdot (a_{2}-a_{1}) (1)

If we know that a_{1} = 5\,yr and a_{2} = 10\,yr, then the difference between predicted milk productions is:

\Delta M = -1.1\cdot (10-5)

\Delta M = -5.5\,\frac{gal}{week}

That is, a cow of 5 years is predicted to produce 5.5 more gallons per week than a cow of 10 years. Hence, the right answer is B.

6 0
2 years ago
Can 12(x^3+y^2)+6(y^2+1) be the factored form of 12x^3+18y^2+6?
Misha Larkins [42]

Answer:

YES

Step-by-step explanation:

So how you can figure this out is you do the Distributive Property.

So it will be 12x^3+12y^2+6y^2+6.

The next thing you have to do is add together the ones that are similar which is 12y^2+6y^2 to get 18y^2.

Your answer is 12x^3+18y^2+6. So YES it can be factored into that form.

4 0
3 years ago
Read 2 more answers
Karen works at a toy story. She has 2 7/8 of marbles . She is making 1/16 pound packages . How many packages will she make?
MArishka [77]

Answer:

46 packages

Step-by-step explanation:

2 7/8= 23/8= 46/16...THUS SINCE SHE IS MAKING 1/16 POUND PACKAGES, SHE CAN MAKE 46 PACKAGES

5 0
3 years ago
at the dog show there are 4 times as many boxers as spaniel if there is a total of 30 dogs. how many dogs are spaniel
alexgriva [62]

4x+x = 30

5x = 30

x = 30/5 =6

 6*4 = 24 boxers

 and 6 spaniels

5 0
3 years ago
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