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Svetradugi [14.3K]
3 years ago
10

PLZZZ DO THE PROBLEM THAT HAS THE ORANGE RECTANGLE PLZZZZZZZZZZZ!!!!!!

Mathematics
2 answers:
Ksivusya [100]3 years ago
8 0

Answer:

8 units = L

Step-by-step explanation:

The area of a rectangle is the product of length and width.

A = L*W

If A = 56 units^2 and W = 7 units, then L = (56 units^2) / (7 units) = 8 units = L

ehidna [41]3 years ago
8 0
56= l * w

56= l* 7

8= l



The length is 8 and we can check this doing 8*7 which is 56.
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For what values of θ on the polar curve r=θ, with 0≤θ≤2π , are the tangent lines horizontal? Vertical?
Bond [772]
Given that r=\theta, then r'=1

The slope of a tangent line in the polar coordinate is given by:

m= \frac{r'\sin\theta+r\cos\theta}{r'\cos\theta-r\sin\theta}

Thus, we have:

m= \frac{\sin\theta+\theta\cos\theta}{\cos\theta-\theta\sin\theta}



Part A:

For horizontal tangent lines, m = 0.

Thus, we have:

\sin\theta+\theta\cos\theta=0 \\  \\ \theta\cos\theta=-\sin\theta \\  \\ \theta=- \frac{\sin\theta}{\cos\theta} =-\tan\theta

Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:

</span><span>θ = 0

</span>θ = <span>2.02875783811043
</span>
θ = <span>4.91318043943488



Part B:

For vertical tangent lines, \frac{1}{m} =0

Thus, we have:

\cos\theta-\theta\sin\theta=0 \\  \\ \Rightarrow\theta\sin\theta=\cos\theta \\  \\ \Rightarrow\theta= \frac{\cos\theta}{\sin\theta} =\sec\theta

</span>Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:

</span>θ = <span>4.91718592528713</span>
3 0
3 years ago
A gift box has a surface area of 6.25 square feet. What is the surface area of the box in square inches?
guapka [62]

The surface area of the box in square inches will be 39.0625 inches².

<h3>How to calculate the area?</h3>

From the information, the gift box has a surface area of 6.25 square feet.

Therefore, the surface area of the box in square inches will be:

= Side × Side

= 6.25 × 6.25

= 39.0625 inches²

Therefore, the surface area of the box will be 39.0625 inches².

Learn more about area on:

brainly.com/question/25292087

#SPJ1

4 0
1 year ago
Larry Thomas's charge account statement shows an unpaid balance of $800. The monthly finance charge is 1.5% of the unpaid balanc
lilavasa [31]

Answer:

The new account balance is <u>$812</u>.

Step-by-step explanation:

Given:

Larry Thomas's charge account statement shows an unpaid balance of $800.

The monthly finance charge is 1.5% of the unpaid balance.

Now, to find the new account balance.

Unpaid balance = $800.

Monthly finance charge of the unpaid balance = 1.5%.

Now, to get the new account balance:

$800 + 1.5% of $800.

=800+\frac{1.5}{100} \times 800.

=800+0.015\times 800.

=800+12.

=\$812.

Therefore, the new account balance is $812.

5 0
3 years ago
Renna pushes the elevator button, but the elevator does not move. The mass limit for the elevator is 450 kg, but Renna and her l
pychu [463]

Answer:

620-37.4p\leq 450

Step-by-step explanation:

Let p be the number of identical packages.

We have been given that each package has a mass of 37.4 kg, so weight of p packages will be 37.4p.

The total mass of Renna and her load of identical packages is 620 kg.

We have been given that the mass limit for the elevator is 450 kg. This means that Renna can remove p packages from 620 kg such that 620 minus weight of p packages will be less than or equal to 450 kg.

We can represent this information in an inequality as:

620-37.4p\leq 450

Therefore, the inequality 620-37.4p\leq 450 can be used to determine the number of packages, p, Renna could remove from the elevator to meet the mass requirement.

3 0
3 years ago
Read 2 more answers
John is buying food for his cat, Fluffy. Fluffy LOVES a fancy wet food which costs $1.50 per day. Fluffy will also tolerate dry
Vedmedyk [2.9K]

Answer:

The answer is below

Step-by-step explanation:

Let x represent the number of days that fluffy eats wet food in a week and y represents the number of days that fluffy eats dry food in a week.

Hence:

x + y = 7                    (1)

Also, John wants to spend at most $9.00 on cat food each week. Hence:

1.5x + 0.75y ≤ 9       (2)

The list of possible points after solving graphically are:

(0,7), (6,0), (0,12) and (5, 2). If x,y > 0, then the point that satisfies the inequality is:

(5, 2) i.e. 5 wet food and 2 dry food

5 0
3 years ago
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