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VikaD [51]
2 years ago
13

A rectangular lot whose perimeter is 350 ft is fenced along three slides. An expensive fencing along the lots length cost 18$ pe

r foot. An inexpensive fencing along the two side widths costs only 3$ per foot. The total cost of the fencing along the three sides come to $2430. What are the lots dimensions?
Need help asap
Mathematics
1 answer:
antoniya [11.8K]2 years ago
6 0

Answer:

The sum of the first twenty terms of an arithmetic progression is 45, and the sum of the first fourty term is 290, find the first terms and the Common difference.

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What is the area of this composite figure?
Mkey [24]

We have two congruent trapezoids.

The formula of an area of a trapezoid:

A=\dfrac{base_1+base_2}{2}\cdot\ height

We have:

base_1=210\ mm\\\\base_2=150\ mm\\\\height=55\ mm

Substitute:

A=\dfrac{210+150}{2}\cdot55=\dfrac{360}{2}\cdot55=180\cdot55=9,900\ mm^2

Answer:

2A=2\cdot9,900\ mm^2=19,800\ mm^2

6 0
3 years ago
Greetings. As a beginner, I'm struggling a bit to learn calculus. May I know what is the derivative of x to the power 4 step by
elena-14-01-66 [18.8K]

If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate x^4.

We have

\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h

Expand the numerator using the binomial theorem, then simplify and compute the limit.

\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}

In general, the derivative of a power function f(x) = x^n is \frac{df}{dx} = nx^{n-1}. (This is the aptly-named "power rule" for differentiation.)

3 0
2 years ago
If p = -2 and q = 5, is the value of p/q equivalent to 2/5?
grandymaker [24]

Answer:

No.

Step-by-step explanation:

1. Subsutute p/q with the numbers given, p = -2 and q = 5.

-2 / 5.

2. Divide 2/5 and -2/5 and compare.

2 / 5 = 0.40

-2 / 5 = -0.40

-0.40 < 0.40

If they are not =, then they are <u>NOT</u> equivalent.

Which means, they are Not equivalent.

5 0
3 years ago
In order to have 290,000 in 10 yrs you should deposit how much each month​
never [62]

Answer:2416{APPROX}

Step-by-step explanation:

AMOUNT=290000

NO OF YEARS=10

NO OF MONTHS IN 10 YEARS=120 MONTHS.

SO AMOUNT TO DEPOSIT PER MONTH=290000/120=2416(APPROX)

7 0
3 years ago
Help me with this one
Artist 52 [7]

9514 1404 393

Answer:

  "complete the square" to put in vertex form

Step-by-step explanation:

It may be helpful to consider the square of a binomial:

  (x +a)² = x² +2ax +a²

The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...

  2a = 1

  a = 1/2

That means we can write ...

  (x +1/2)² = x² +x +1/4

But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:

  x^2+x+1\\\\=(x^2+x+\frac{1}{4})+\frac{3}{4}\\\\=(x+\frac{1}{2})^2+\frac{3}{4}

_____

Another way to consider this is ...

  x² +bx +c

  = x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*

  = (x +b/2)² +(c -(b/2)²)

for b=1, c=1, this becomes ...

  x² +x +1 = (x +1/2)² +(1 -(1/2)²)

  = (x +1/2)² +3/4

_____

* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).

5 0
2 years ago
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