An open box with a square base should be constructed. the bottom, should be constructed from a heavy duty cardboard that cost $3 per square inches and the sides from a medium duty cardboard that cost $2 per square inches. if the volume of the box must be 120 cubic inches, what should be the dimensions of the box in order to minimize the cost for the material?

To eliminate the parameter t in the parametric equations x = 6 cos t and y = 3 sin t, we can use the trigonometric identity

cos⁡²t + sin⁡²t = 1cos²t + sin²t = 1.

Starting with x=6 cos t, we can rewrite it as cos t=x6​ and from y=3 sin t, we can rewrite it as sin t = (y/3)​.

Now, we square both equations:

(cos t)² = (x/6​)²

(sin t)² = (y/3​)²

As soon as we multiply both sides by 36, we arrive at:

x² + 4y² = 36

Therefore, the equation x² + 4y² = 36 is the Cartesian equation that eliminates the parameter t from the given parametric equations.

To eliminate the parameter t in the parametric equations x=6 cos t and y=3 sin t, we use trigonometric identities.

From x=6 cost, we get cos t = x//6​, and from y = 3 sin t, we get sin t = (y/3).

Squaring both equations and using the identity cos2t+sin2t=1 we obtain (x/6​)² + (y/3​)² = 1. Simplifying, we get (x²/36) + (y²/9) = 1 which, after multiplying by 36, becomes x² + 4y² = 36. Thus x² + 4y² = 36 is the Cartesian equation eliminating the parameter t.

Complete Question:

Eliminate the parameter, t, in the parametric equation, x=6 cos t, and y =3 sin t.

Answer:

\text{If QR is tangent to circle then m}\angle PQR=90^o

\text{We can use the converse of Pythagorean theorem}

8\ and\ 4\sqrt3\\\\check:\ 4^2+(4\sqrt3)^2=8^2\\16+16\cdot3=64\\16+48=64\\64=64\ -O.K.\\\\2\ and\ 4\sqrt2\\\\check:\ 4^2+2^2=(4\sqrt2)^2\\16+4=16\cdot2\\20=32\ -FALSE\\\\3\ and\ 5\\\\check:\ 3^2+4^2=5^2\\9+16=25\\25=25\ -O.K.\\\\2\ and\ 2\sqrt5\\\\check:\ 4^2+2^2=(2\sqrt5)^2\\16+4=4\cdot5\\20=20\ -O.K.\\\\6\ and\ 10\\check:\ 4^2+6^2=10^2\\16+36=100\\52=100\ -FALSE

\text{Answer:}\boxed{8\ and\ 4\sqrt3;\ 3\ and\ 5;\ 2\ and\ 2\sqrt5}

10.

\text{Look at the pictures}

\text{Therefore}\\\\C=2\cdot8+2\cdot16+2\cdot9+2\cdot6=16+32+18+12=78cm

Other\ method:\\C=2\cdot(8+16+6+9)=2\cdot39=78cm

Step-by-step explanation:

t will represent temperature  

t > -15°

We have been given that the cost to start the sandwich stand is $230.

Now, the cost of one sandwich is given by $4.25

Also, it has been given that total 75 sandwiches sold.

Thus, the cost of 75 sandwiches is given by

[tex]75 \times 4.25\\ \$ 318.75[/tex]

Now, the sandwich stand cost $230 and the earning in selling of 75 sandwiches is $ 318.75.

Therefore, the profit is given by

[tex]318.75-230 =\$88.75[/tex]

Hence, I can make $88.75 on selling of 75 sandwiches.

Answer:

one triangle

Step-by-step explanation:

Answer - C

Add 4530 + 540 + 400 = 5470

Answer:

[tex]x=41^o[/tex]

Step-by-step explanation:

We have been given an equation [tex]sin(49^o)=cos(x)[/tex] and we are asked to find the value of x.

Since we know that trigonometric ratios are applied to right triangles and we also know that [tex]sin(a)=cos(b)[/tex], where a and b are the angles other than 90 degree angle.

As one angle of our triangle is given 49 degrees, so to find the value of angle x we need to subtract 49 degrees from 90 degree angle as 49 degree angle and x will be equal to 90 degrees.

[tex]x=90^o-49^o[/tex]

[tex]x=41^o[/tex]

Therefore, the value of x is 41 degrees.

Secrecy (also called clandestinity or furtiveness) is the practice of hiding information from certain individuals or groups who do not have the "need to know", perhaps while sharing it with other individuals. That which is kept hidden is known as the secret.

Answer:

review and revisions

Step-by-step explanation:

Answer:

Step-by-step explanation:

Alright, lets get started.

The most precise measurement is,  the one which has most numbers after the decimal.

The number round off to hundred decimal place is more precise than the number round off to tenth decimal place.

There are 4 different numbers in which two numbers are complete number 7 and 19.

20.1 is rounded off to nearest tenth.

15.98 is rounded off to nearest hundred.

So, 15.98 yards is the most precise.   :   Option C

Hope it will help :)

Answer:

15.98 yards

Step-by-step explanation:

The mean or the average of a number is calculated by adding the frequencies of the given data and then dividing by the total frequency. It is represented by the formula mentioned under -

Mean = [tex] \frac{Sum of all the frequencies}{Number of frequencies} [/tex]

Similarly, here, we need to find the mean of their time spent in brushing.

It will be calculated as -

For Fiona

Mean of time spent in brushing = [tex] \frac{Sum of the total time spent in 10 days}{10 days} [/tex]

Similarly, for Gary

Mean of time spent in brushing = [tex] \frac{Sum of the total time spent in 10 days}{10 days} [/tex]

Final answer:

To estimate the number of successful raptors in 2015, we can use the success rate provided by the website. If we assume a success rate of 35 percent, approximately 82 raptors were successful that year.

Explanation:

To estimate the number of successful raptors in 2015, we can use the success rate provided by the website. The success rate is between 35 and 40 percent. So, if we assume a success rate of 35 percent, we can calculate the number of successful raptors as follows:

Number of successful raptors = 35% of 234 raptors

Number of successful raptors = 0.35 * 234

Number of successful raptors = 81.9

Rounding to the nearest whole number, approximately 82 raptors were successful in 2015.