Matt says he can find the sum of 45+50 without rewriting it. Explain how you can solve this problem using mental math.

QUESTION POSTED AT 14/02/2020 - 04:41 PM

Answered by admin AT 14/02/2020 - 04:41 PM

You could add 4+5 and then 5+0 and boom there's your answer!! Hope this helped
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Can anyone help me with the process of substitution in Algebra I? It's much appreciated! Here's an example problem

Ok what you have to do is get one variable in the two equations equal but opposite to each other. You already have that in y in the first one and -y in the second. Sometimes you would have to do some manipulation to get there.

Next, add the two together:

4x+y=-5
+ 2x-y=-1
---—--------
6x=-6
x-1

Now plug in the -1 for x in one of the formulas above:
4(-1)+y=-5 solve for y
-4+y=-5
y=-5+4
y=-1

ANSWERED AT 28/02/2020 - 08:03 AM


QUESTION POSTED AT 28/02/2020 - 08:03 AM

Set up the integral needed to find the volume of the solid bounded by the hyperboloid z2 = 64 x2 y2 and by the upper nappe of the cone z2 = 2x2 2y2

\begin{cases}z^2=64+x^2+y^2\\z^2=2x^2+2y^2\end{cases}

It's clear enough that the upper half of the cone falls below the upper sheet of the paraboloid, so that \sqrt{2x^2+2y^2}\le z\le\sqrt{64+x^2+y^2}. Right away you can see that converting to cylindrical coordinates will be quite advantageous.

The intersection of the two surfaces occurs as a circle:

64+x^2+y^2=2x^2+2y^2\implies64=x^2+y^2

which is parallel to the x-y plane, has radius 8, and is centered at (0,0,8\sqrt2).

The volume of this space is given by the integral

\displaystyle\iiint_S\mathrm dV=\int_{x=-8}^{x=8}\int_{y=-\sqrt{64-x^2}}^{y=\sqrt{64-x^2}}\int_{z=\sqrt{2x^2+2y^2}}^{z=\sqrt{64+x^2+y^2}}\mathrm dz\,\mathrm dy\,\mathrm dz

where S denotes the bounded space between the surfaces. Converting to cylindrical coordinates, this can be expressed as

\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=8}\int_{z=\sqrt2r}^{z=\sqrt{64+r^2}}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta

which evaluates to \dfrac{1024\pi(\sqrt2-1)}3.

ANSWERED AT 28/02/2020 - 07:57 AM


QUESTION POSTED AT 28/02/2020 - 07:57 AM

Of all the rectangles with an area of 441 square feet, find the dimensions of the one with the smallest perimeter.

1*441 & 3*147 & 7*63 & 9*41 &21*21 are all factor pairs of 441

21&21 have the smallest sum and would make for the smallest perimeter

Answer:l=21  w=21

ANSWERED AT 28/02/2020 - 07:56 AM


QUESTION POSTED AT 28/02/2020 - 07:56 AM

Of all the rectangles with a perimeter of 100 feet, find the dimensions of the one with the largest area

P=2l+2w
100=2l+2w
divide both sides by 2
50=l+w

So what two numbers that have a sum of 50 have the largest product? 

25*25=625 which makes for a large area, the largest

answer=l=25 w=25

ANSWERED AT 28/02/2020 - 07:56 AM


QUESTION POSTED AT 28/02/2020 - 07:56 AM

If cosh x = 13 5 and x > 0, find the values of the other hyperbolic functions at x.

Recall that

\cosh^2x-\sinh^2x=1\implies \cosh x=\pm\sqrt{1+\sinh^2x}

You're given that \cosh x=\dfrac{13}5>0, so omit the negative root. Then

\dfrac{13}5=\sqrt{1+\sinh^2x}\implies\sinh^2x=\dfrac{144}{25}\implies\sinh x=\pm\dfrac{12}5

Because x>0, you have \sinh x>0 too, so omit the negative root again. Then \sinh x=\dfrac{12}5.

Now,

\mbox{sech }x=\dfrac1{\cosh x}=\dfrac5{13}
\mbox{csch }x=\dfrac1{\sinh x}=\dfrac5{12}
\tanh x=\dfrac{\sinh x}{\cosh x}=\dfrac{\frac{12}5}{\frac{13}5}=\dfrac{12}{13}
\coth x=\dfrac1{\tanh x}=\dfrac{13}{12}

ANSWERED AT 28/02/2020 - 07:54 AM


QUESTION POSTED AT 28/02/2020 - 07:54 AM

Please help with this problem!!

I believe H since those numbers are higher than all the others ones

ANSWERED AT 28/02/2020 - 07:50 AM


QUESTION POSTED AT 28/02/2020 - 07:50 AM

A hand consists of 3 cards from a well shuffled deck of 52 cards. find the number of possible 3-card poker hands

Their are 52 option for the first card, 51 for the second (because we already picked up on for the first card), and 50 for the third (because we already pickes up two cards)

52*51*50=132,600 possible hands

ANSWERED AT 28/02/2020 - 07:47 AM


QUESTION POSTED AT 28/02/2020 - 07:47 AM

I'm stuck on this problem..

Answer choice E is the correct answer.

ANSWERED AT 28/02/2020 - 07:42 AM


QUESTION POSTED AT 28/02/2020 - 07:42 AM

The daily amount of coffee, in liters, dispensed by a machine located in an airport lobby is a random variable x having a continuous uniform distribution with a = 7 and b = 10. find the probability that on a given day the amount of coffee dispensed by this machine will be more than 7.4 liters but less than 9.5 liters.

 f(x) = 1/(10-7) = 1/3, 7<x<10. 
(a) P(at most 8.8 liters) = integral(7to8.8)f(x)dx = 1.8/3 = 0.6 
(b) P(more than 7.4 liters but less than 9.5 liters) = integral(7.4 to9.5)f(x)dx = 2.1/3 = 0.7 
(c) P(at least 8.5 liters) = integral(8.5 to10)f(x)dx = 1.5/3 = 0.5

ANSWERED AT 28/02/2020 - 07:42 AM


QUESTION POSTED AT 28/02/2020 - 07:42 AM

A circle with a diameter of 2 inches and a square with 2-inch sides have the same center. Find the area of the region that is inside the square and outside the circle. Use 3.14 for p. 5.3 in.2 0.9 in.2 14.3 in.2 0.5 in.2

Area of square = 4 square inches
Area of circle = PI * radius ^2
Area of circle = 3.14 * 1^2
Area of circle = 3.14 square inches
Area inside the square and outside the circle =
4 -3.14 = .86 square inches.
answer is .9 square inches


ANSWERED AT 28/02/2020 - 07:37 AM


QUESTION POSTED AT 28/02/2020 - 07:37 AM

Find the area - 14.444 m2 - 66.4424 m2 - 4.15265 m2 - 16.61060 m2

C cause the diamiter....

ANSWERED AT 28/02/2020 - 07:36 AM


QUESTION POSTED AT 28/02/2020 - 07:36 AM

Find the general solution of x1? = x1 ? 2x2, x2? = 2x1 x2 using the eigenvalue method. do not use complex exponentials in your solution.

Guessing on how the system is expressed:

\begin{bmatrix}x_1\\x_2\end{bmatrix}'=\begin{bmatrix}1&-2\\2&1\end{bmatrix}\begin{bmatrix}x_1\\x_2\end{bmatrix}

The coefficient matrix has eigenvalues \lambda=1+2i with corresponding eigenvectors \begin{bmatrix}\pm i&1\end{bmatrix}^\top. This means the characteristic solution is

\begin{bmatrix}x_1\\x_2\end{bmatrix}=Ce^{(1+2i)t}\begin{bmatrix}i\\1\end{bmatrix}
\begin{bmatrix}x_1\\x_2\end{bmatrix}=Ce^t(\cos2t+i\sin2t)\begin{bmatrix}i\\1\end{bmatrix}
\begin{bmatrix}x_1\\x_2\end{bmatrix}=C_1\begin{bmatrix}-e^t\sin2t\\e^t\cos2t\end{bmatrix}+C_2\begin{bmatrix}e^t\cos2t\\e^t\sin2t\end{bmatrix}

ANSWERED AT 28/02/2020 - 07:36 AM


QUESTION POSTED AT 28/02/2020 - 07:36 AM

Find the average value of f(x, y = over the region, r, the triangle with vertices (0, 0, (0, 1 and (1, 1.

Can't be done without knowing what f is...

But I can tell you that the average value of f is given by

\dfrac{\displaystyle\iint_Rf(x,y)\,\mathrm dx\,\mathrm dy}{\displaystyle\iint_R\mathrm dx\,\mathrm dy}

At the very least, we can compute the denominator, which is just the area of R. You have

\displaystyle\iint_R\mathrm dx\,\mathrm dy=\int_{x=0}^{x=1}\int_{y=x}^{y=1}\mathrm dy\,\mathrm dx=\int_0^1(1-x)\,\mathrm dx=\dfrac12

so the average value will be

2\displaystyle\iint_Rf(x,y)\,\mathrm dx\,\mathrm dy

ANSWERED AT 28/02/2020 - 07:36 AM


QUESTION POSTED AT 28/02/2020 - 07:36 AM

Find the arclength of the curve \mathbf r(t = \langle 6 t^2, 2\sqrt{6} t, \ln t\rangle, 1 \le t \le 4

\mathbf r(t)=\langle6t^2,2\sqrt6 t,\ln t\rangle
\implies\dfrac{\mathrm d\mathbf r}{\mathrm dt}=\left\langle12t,2\sqrt6,\dfrac1t\right\rangle

The arc length is then given by

\displaystyle\int_1^4\sqrt{\frac{\mathrm d\mathbf r}{\mathrm dt}\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}}\,\mathrm dt
\displaystyle\int_1^4\sqrt{144t^2+24+\frac1{t^2}}\,\mathrm dt
\displaystyle\int_1^4\sqrt{\left(12t+\frac1t\right)^2}\,\mathrm dt
\displaystyle\int_1^4\left(12t+\frac1t\right)\,\mathrm dt
=90+\ln4

ANSWERED AT 28/02/2020 - 07:36 AM


QUESTION POSTED AT 28/02/2020 - 07:36 AM

Find the volume of a prism-shaped watermelon in cubic inches if it's length is 10 inches, its width is 2/3 foot and it's height is 9 inches

The volume is 60 cubic inches.

To solve, follow the formula Volume = Length · Height · Width. If you are solving without a calculator, simply multiply the length and the height first, then multiply the product of that by the width, 2 / 3.
V = 10 · 9 · 2/3
V = (10 · 9) 2/3
V = 90 · 2/3
V = 60 in.³

Hope this helps. Good luck! :)

ANSWERED AT 28/02/2020 - 07:31 AM


QUESTION POSTED AT 28/02/2020 - 07:31 AM

Find the radius or diameter of each circle with the given dimension. r=13 cm

If r=13cm, the d is double that so it is 26cm.

ANSWERED AT 28/02/2020 - 07:27 AM


QUESTION POSTED AT 28/02/2020 - 07:27 AM

7^-1+9^-1, how do you solve this exponent equation?

Raising to a negative power just makes the base value into a fraction

For example, x^-1 turns into (1/x^1)

This means that your equation goes from
7^-1+9^-1 to (1/7)+(1/9)

1/7+1/9 simplifies to 16/63 after all of the common denominator stuff

So, in short 7^-1+9^-1 = 16/63

ANSWERED AT 28/02/2020 - 07:26 AM


QUESTION POSTED AT 28/02/2020 - 07:26 AM

HELP ME!!! URGENT!!! MATH!!!!

They appear to be the same option in this picture. I would report this question to your professor. 

ANSWERED AT 28/02/2020 - 07:24 AM


QUESTION POSTED AT 28/02/2020 - 07:24 AM

Using a matrix equation solve 3x-8y=-35

You would typically be given two equations to solve for two unknowns with matrices.

ANSWERED AT 28/02/2020 - 07:24 AM


QUESTION POSTED AT 28/02/2020 - 07:24 AM

Using a matrix equation solve 3x-8y=-35

3x-8y=-35
- First thing you need move the 3x to the right hand like this one
-8y=-3x-35 ( positive move to another side change to negative )
And then you need to move -8 to the right hand to !
y=-3/-8 -35/-8 so you need to change the negative to positive y=3/8 + 35/8 ( 3/8 mean 3 over 8 )
The answer is y= 3/8 + 35/8

ANSWERED AT 28/02/2020 - 07:24 AM


QUESTION POSTED AT 28/02/2020 - 07:24 AM

Would anyone be able to help me solve this?

So because there is a graph we can pretty easily find the solution, lucky us!

So the solution is where the two paths cross or intersect.
Going off of (x,y) so the x is 3 and the y is -5

so the solution is (3,-5)

ANSWERED AT 28/02/2020 - 07:22 AM


QUESTION POSTED AT 28/02/2020 - 07:22 AM

How to solve the equation

Raise each side to the 3rd power (^3) making the equation 2x-5=125,

Then, add 5 to both sides, making the equation 2x=130

Lastly, we divide by 2, making x=65

If we substitute 65 for x, the equation is still true

3✓(2(65)-5)=5
3✓(130-5)=5
3✓(125)=5
5=5

so, X=65

ANSWERED AT 28/02/2020 - 07:22 AM


QUESTION POSTED AT 28/02/2020 - 07:22 AM

Determine if the circumference of a circle with a radius of 4 feet will be greater or less than 24 feet explain

The formula for the circumference of a circle is

C=2rπ
If r=4, then 
C=2(4)π
C=8π
Since we know that 8*3=24, and that π is greater than 3, we can reason that 8π>24ft

or we could just use a calculator and solve for 8π

C=25.12ft

Answer:The circumference is greater than 24ft


ANSWERED AT 28/02/2020 - 07:19 AM


QUESTION POSTED AT 28/02/2020 - 07:19 AM

The data are the lengths of songs (in minutes) on your new CD. Which measure of center best represents the data with and without the outlier? Explain. 2.2, 2.2, 2.4, 2.6, 2.8, 3.0, 3.2, 3.4, 14.2

The center of data would be 2.8 because it is in the middle which means it is the median

ANSWERED AT 28/02/2020 - 07:15 AM


QUESTION POSTED AT 28/02/2020 - 07:15 AM

Find the area of a circle with a radius of 1.5 cm

Area = pi * radius^2

A = 3.14 * 1.5^2

A = 7.07 square centimeters

ANSWERED AT 28/02/2020 - 07:14 AM


QUESTION POSTED AT 28/02/2020 - 07:14 AM

How to put the sum 7/10 in

That is a fraction, if you want to put it into decimal form, it would be equivalent to 0.7

ANSWERED AT 28/02/2020 - 07:13 AM


QUESTION POSTED AT 28/02/2020 - 07:13 AM

A motor has a power of 7,150 foot-pounds per second. Find the horsepower of the motor. A) 8,599,000 B) 39,325,000 C) 8 D) 13

I believe the answer is d

ANSWERED AT 28/02/2020 - 07:12 AM


QUESTION POSTED AT 28/02/2020 - 07:12 AM

What are two ways to find an equivalent ratio for 10:25?

You can find it by dividing 10 to 25 . The second way is to divided it to there common factors which in this case its 5.

ANSWERED AT 28/02/2020 - 07:12 AM


QUESTION POSTED AT 28/02/2020 - 07:12 AM