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3 years ago

NEEEEEEEEDDDDDDDDS HELLLPLLPP

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

3 0

We know that angle2+angle3+90=180 (since we see the right angle in the corner and all internal angles add up to 180) so

angle3=40
subsitute
angle2+40+90=180
angle2+130=180
subtract 130
angle2=50
answer is 50 degrees

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Maurice walked 6 miles in 132 minutes. Monica walked 4.5 miles in 90 minutes. is the ratio of miles walked to minutes the same f

expeople1 [14]

No its not the same.
Maurice walked 1 mile in 22 mins
Monica walked 1 mile in 20 mins

3 0

3 years ago

Luis was in charge of collecting money for a group of charities. He collected

babymother [125]

Answer:

$89 hope it helps.

Step-by-step explanation:

6 0

3 years ago

A company wishes to manufacture some boxes out of card. The boxes will have 6 sides (i.e. they covered at the top). They wish th

Serhud [2]

Answer:

The dimensions are, base $b=\sqrt[3]{200}$ , depth $d=\sqrt[3]{200}$ and height $h=\sqrt[3]{200}$ .

Step-by-step explanation:

First we have to understand the problem, we have a box of unknown dimensions (base $b$ , depth $d$ and height $h$ ), and we want to optimize the used material in the box. We know the volume $V$ we want, how we want to optimize the card used in the box we need to minimize the Area $A$ of the box.

The equations are then, for Volume

$V=200cm^3 = b.h.d$

For Area

$A=2.b.h+2.d.h+2.b.d$

From the Volume equation we clear the variable $b$ to get,

$b=\frac{200}{d.h}$

And we replace this value into the Area equation to get,

$A=2.(\frac{200}{d.h} ).h+2.d.h+2.(\frac{200}{d.h} ).d$

$A=2.(\frac{200}{d} )+2.d.h+2.(\frac{200}{h} )$

So, we have our function $f(x,y)=A(d,h)$ , which we have to minimize. We apply the first partial derivative and equalize to zero to know the optimum point of the function, getting

$\frac{\partial A}{\partial d} =-\frac{400}{d^2}+2h=0$

$\frac{\partial A}{\partial h} =-\frac{400}{h^2}+2d=0$

After solving the system of equations, we get that the optimum point value is $d=\sqrt[3]{200}$ and $h=\sqrt[3]{200}$ , replacing this values into the equation of variable $b$ we get $b=\sqrt[3]{200}$ .

Now, we have to check with the hessian matrix if the value is a minimum,

The hessian matrix is defined as,

$H=\left[\begin{array}{ccc}\frac{\partial^2 A}{\partial d^2} &\frac{\partial^2 A}{\partial d \partial h}\\\frac{\partial^2 A}{\partial h \partial d}&\frac{\partial^2 A}{\partial p^2}\end{array}\right]$

we know that,

$\frac{\partial^2 A}{\partial d^2}=\frac{\partial}{\partial d}(-\frac{400}{d^2}+2h )=\frac{800}{d^3}$

$\frac{\partial^2 A}{\partial h^2}=\frac{\partial}{\partial h}(-\frac{400}{h^2}+2d )=\frac{800}{h^3}$

$\frac{\partial^2 A}{\partial d \partial h}=\frac{\partial^2 A}{\partial h \partial d}=\frac{\partial}{\partial h}(-\frac{400}{d^2}+2h )=2$

Then, our matrix is

$H=\left[\begin{array}{ccc}4&2\\2&4\end{array}\right]$

Now, we found the eigenvalues of the matrix as follow

$det(H-\lambda I)=det(\left[\begin{array}{ccc}4-\lambda&2\\2&4-\lambda\end{array}\right] )=(4-\lambda)^2-4=0$

Solving for $\lambda$ , we get that the eigenvalues are: $\lambda_1=2$ and $\lambda_2=6$ , how both are positive the Hessian matrix is positive definite which means that the function $A(d,h)$ is minimum at that point.

4 0

3 years ago

Raul simplified the expression, as shown below.

Softa [21]

Answer:

Raul's errors are in the application of the distributive property(he applied it wrongly), in not respecting the precedence of operations, and in the multiplication of two terms with the same base(we add the exponent).

Step-by-step explanation:

Distributive property:

The distributive property of multiplication is:

a*(b + c) = a*b + a*c

Precedence of operations:

First multiplication, then addition.

Multiplication of terms with the same base:

The multiplication of h*h = h², which Raul missed.

The correct simplification is given by:

$-[3h + 7h(2-h)] = -[3h + 14h - 7h^2] = -[17h - 7h^2]=7h^2 - 17h$

4 0

3 years ago

Read 2 more answers

If speed varies inversely as the time it takes to drive and Kris takes 5 hours driving at 55 mph, what speed will Martin need to

Fudgin [204]

Answer:

<em>55mph . None of the options are correct </em>

Step-by-step explanation:

If the speed varies inversely as the time it takes to drive, then v ∝ 1/t. where;

v is the speed

t is the time taken

Hence;

v = k/t with k being the constant of proportionality.

Since it takes Kris 5 hours when driving at 55 mph, we will substitute v = 55mph and t = 5 hours. into the equation above to get the value of k as shown:

55 = k/5

Cross multiply

k = 55*5

k = 275

Hence, to calculate the speed it will Martin to drive for 5 hours, we will substitute k = 275 and t = 5 into the original equation v = k/t as shownl

v = 275/5

v = 55 mph

<em>Hence, we can conclude that Martin will also need to drive at a speed of 55mph if he wants to take 5hours.</em>

3 0

3 years ago