28 deliveries in 4 hours = ____ deliveries per hour

Helen gathered 37 mushrooms in three hours. How many mushrooms did she gather every hour, if she gathered 7 more mushrooms in th

mihalych1998 [28]

Answer:

On the first hour she gathered 8 mushroons, on the second 15 mushroons and on the third she gathered 14 mushroons.

Step-by-step explanation:

Helen gathred a total of 37 mushroons in three hours. On the first hour she gathered "x" mushroons, on the second hour she gathered "x + 7" mushroons and on the third hour she gathered "x + 6". Therefore the sum of mushrrons she gathered on each hour should be equal to the total she gathered as shown below:

37 = x + (x+ 7) + (x + 6)

37 = 3*x + 13

3*x + 13 = 37

3*x = 37 - 13

3*x = 24

x = 24 / 3

x = 8

On the first hour she gathered 8 mushroons, on the second 15 mushroons and on the third she gathered 14 mushroons.

8 0

1 year ago

Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).

Elan Coil [88]

Answer: $\int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV$ = 1087.5

Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.

An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.

Given the points, determine the vectors:

P = (5,0,0); Q = (0,9,0); R = (0,0,4)

vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)

vector QR = (0,9,0) - (0,0,4) = (0,9,-4)

Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:

n = PQ × QR = $\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right]$ $\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right]$

n = 36i + 0j + 45k - (0k + 0i - 20j)

n = 36i + 20j + 45k

Equation of a plane is generally given by:

$a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0$

Then, replacing with point P and normal vector n:

$36(x-5) + 20(y-0) + 45(z-0) = 0$

The equation is: 36x + 20y + 45z - 180 = 0

Second, in evaluating the triple integral, set limits:

In terms of z:

$z = \frac{180-36x-20y}{45}$

When z = 0:

$y = 9 + \frac{-9x}{5}$

When z=0 and y=0:

x = 5

Then, triple integral is:

$\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx$

Calculating:

$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$

$\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )} \, dy } \, dx$

$\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}} \, dy } \, dx$

$\frac{1}{45} \int\limits^5_0 {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx$

$\frac{1}{45} \int\limits^5_0 {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4} } \, dx$

$\frac{1}{45} [30375-60750+118462.5-39150]$

$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$ = 1087.5

The volume of the tetrahedon is 1087.5 cubic units.

3 0

2 years ago

Rory is staying in a cabin on a hill 300 feet above sea level. She walks down the hill to the water’s edge. The equation of her

Anastasy [175]

For this problem, we plug in the numbers for t and the appropriate letters for e to the equation e = 300 - 10t.

a) a = 300 - 10(-2)

simplify: a = 300 + 20

simplify: a = 320 ft.

But, this is not a viable point because when t≤0, she doesn't move anywhere, thus, should consistently be 300 ft.

b) b = 300 - 10(3.5)

simplify: b = 300 - 35

simplify: b = 265 ft.

c) c = 300 - 10(30)

simplify: c = 300 - 300

simplify: c = 0 ft.

8 0

2 years ago

Read 2 more answers

Which model represents the factors of 4x2 – 9? An algebra tile configuration. 5 tiles are in the Factor 1 spot: 2 +x , 3 negativ

Arturiano [62]

Answer:

Step-by-step explanation:

4x² - 9

(2x)² - 3²

(2x + 3)(2x - 3)

Factor 1 spot:

2 tiles of x

3 tiles of positive 1

Factor 2 spot:

2 tiles of x

3 tiles of negative 1

5 0

2 years ago

Read 2 more answers

A shoe manufacture reported earnings of -$453,000 for 2012. In 2013 the company reported earnings of $813,000, and in 2014 the c

vitfil [10]

D $837,000 because your dealing with a negative number. -$453 - 384 = 744 because your still going down in the negatives.

5 0

2 years ago

Read 2 more answers