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Delicious77 [7]
3 years ago
13

a counter top is in the shape of a trapezoid. The lengths of the bases are 70 1/2 and 65 1/2 inches long. The area of the counte

r top is 1,224 square inches. Find the height of the counter top
Mathematics
1 answer:
nekit [7.7K]3 years ago
7 0
For the trapezoid, the equation used to solve for the area is,
                           A = (0.5)(b₁ + b₂)(h)
where b₁ and b₂ are the measure of the bases and h is the height. Substituting the known values above,
                          1224 = (0.5)(70.5 + 65.5)(h)
                                     h = 18
Thus, the height of the counter top is 18 inches. 
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Mr johnson sells erasers for 3 dollars each he sold 96 last week and sold 204 erasers this week about how much morr mone did he
Alecsey [184]
Last Week's Earning = 96 x $3 = $288

This Week's Earning = 204 x $3 = $612

Difference = $612 - $288 = $324

---------------------------------------------------------------------------------
Answer: He makes $324 more this week than last week.
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7 0
3 years ago
The length and width of a rectangle are in a 3:5 ratio. The perimeter of the rectangle is 64. What are the length and width of t
Levart [38]

Hey there! I'm happy to help!

We know that the perimeter is 2L+2W. Le'ts plug in the values 3 and 5 from our ratio and see what our perimeter would be with that.

2(3)+2(5)

6+10

16

How can we get this 16 to 64?

64/16=4

So, we need to multiply this length and width by four to get 64 as our perimeter!

3*4=12

5*4=20

We can plug this into our perimeter equation

2(12)+2(20)

24+40

64

Therefore, our length is 12 and our width is 20.

Have a wonderful day! :D

5 0
3 years ago
SOLUTION We observe that f '(x) = -1 / (1 + x2) and find the required series by integrating the power series for -1 / (1 + x2).
Ann [662]

Answer:

Required series is:

\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....

Step-by-step explanation:

Given that

                           f'(x) = -\frac{1}{1 + x^{2}} ---(1)

We know that:

                  \frac{d}{dx}(tan^{-1}x)=\frac{1}{1+x^{2}} ---(2)

Comparing (1) and (2)

                           f'(x)=-(tan^{-1}x) ---- (3)

Using power series expansion for tan^{-1}x

f'(x)=-tan^{-1}x=-\int {\frac{1}{1+x^{2}} \, dx

= -\int{ \sum\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx

= -\sum{ \int\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx

=-[c+\sum\limits^{ \infty}_{n=0} (-1)^{n}\frac{x^{2n+1}}{2n+1}]

=C+\sum\limits^{ \infty}_{n=0} (-1)^{n+1}\frac{x^{2n+1}}{2n+1}

=C-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....

as

                 tan^{-1}(0)=0 \implies C=0

Hence,

\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....

7 0
3 years ago
What does x=?........................
Bas_tet [7]

Answer:

x = -25 / 3

Step-by-step explanation:

10 / 3 = x / (-5/2)

10 / 3 * (-5 / 2) = x

x = -50 / 6

x = -25 / 3

5 0
3 years ago
Read 2 more answers
A cube has a surface area of 294 square cm. Find the length of one side.
DerKrebs [107]
Since a cube has 6 sides, we can divide 294 by 6, so we have the area of one side. Since it is a cube, we can just square root that, and you get 7 cm.
6 0
3 years ago
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