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Trava [24]
3 years ago
13

Are the lines x=5 and y=-9 perpendicular

Mathematics
1 answer:
Ray Of Light [21]3 years ago
7 0
Yes, they are!!!!!!!!!!!!!!!!!!!!!
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Question 2b only! Evaluate using the definition of the definite integral(that means using the limit of a Riemann sum
lara [203]

Answer:

Hello,

Step-by-step explanation:

We divide the interval [a b] in n equal parts.

\Delta x=\dfrac{b-a}{n} \\\\x_i=a+\Delta x *i \ for\ i=1\ to\ n\\\\y_i=x_i^2=(a+\Delta x *i)^2=a^2+(\Delta x *i)^2+2*a*\Delta x *i\\\\\\Area\ of\ i^{th} \ rectangle=R(x_i)=\Delta x * y_i\\

\displaystyle \sum_{i=1}^{n} R(x_i)=\dfrac{b-a}{n}*\sum_{i=1}^{n}\  (a^2 +(\dfrac{b-a}{n})^2*i^2+2*a*\dfrac{b-a}{n}*i)\\

=(b-a)^2*a^2+(\dfrac{b-a}{n})^3*\dfrac{n(n+1)(2n+1)}{6} +2*a*(\dfrac{b-a}{n})^2*\dfrac{n (n+1)} {2} \\\\\displaystyle \int\limits^a_b {x^2} \, dx = \lim_{n \to \infty} \sum_{i=1}^{n} R(x_i)\\\\=(b-a)*a^2+\dfrac{(b-a)^3 }{3} +a(b-a)^2\\\\=a^2b-a^3+\dfrac{1}{3} (b^3-3ab^2+3a^2b-a^3)+a^3+ab^2-2a^2b\\\\=\dfrac{b^3}{3}-ab^2+ab^2+a^2b+a^2b-2a^2b-\dfrac{a^3}{3}  \\\\\\\boxed{\int\limits^a_b {x^2} \, dx =\dfrac{b^3}{3} -\dfrac{a^3}{3}}\\

4 0
3 years ago
Please help! I currently have a C- in Math and I need an A before summer
san4es73 [151]
Its 12. I hope I help
6 0
3 years ago
Read 2 more answers
joe has a ring weighing 14 grams made of an alloy of 14 % silver and the rest gold. he decides to melt down the rings and add en
Nataliya [291]

With the help of the ratio method, we conclude that 72 grams of sugar should be added.

<h3>What is Ratio Method?</h3>
  • In the ratio method, we compare two quantities by equating their two ratios; this equation is also referred to as a proportion.
  • The cross-multiplication method will be used to solve it.

So, 'n=5' will be the number of rings.

  • 'w = 18 grams' will be the weight of each ring.
  • Total weight: w₀ = n × w = 5 × 18 = 90 grams

Let 's' be silver. Then,

  • New weight: wₙ = s + 90
  • Old % of gold: p₀ = 90% = 0.9
  • New % of gold: pₙ = 50% = 0.5

Now, use the ratio method as follows:

  • \frac{w_o}{w_n}=\frac{p_n}{p_o}
  • \frac{90}{s+90}=\frac{0.5}{0.9}
  • 90 × 0.9 = 0.5 × (s + 90)
  • 81 = 0.5s + 0.5 × 90
  • 81 = 0.5s + 45
  • 81 - 45 = 0.5s
  • 36 = 0.5s
  • 36/0.5 = s
  • 72 = s
  • So, s = 72

Therefore, with the help of the ratio method, we conclude that 72 grams of sugar should be added.

Know more about Ratio Method here:

brainly.com/question/26027272

#SPJ9

The correct question is given below:
A jeweler has five rings, each weighing 18 grams, made of alloys of 10% silver and 90% gold. He decides to melt down the rings and add enough silver to reduce the gold content to 50%. How much silver should he add?

3 0
2 years ago
Which are the coordinates of the transformed point (3,-2) vertical stretch of 4 a. (3,2) b.(12,-2) c.(7,-6) d. (3,-8)
denis23 [38]

The given point is (3,-2).

The transformation is a vertical stretch of 4.

Vertical stretch can be obtained when we multiply the vertical coordinate by a factor, in this case, 4.

(3,-2\cdot4)=(3,-8)<h2>Therefore, the right answer is D.</h2>
3 0
1 year ago
HELP!!<br>can someone please help me and show me how to solve this ??
boyakko [2]
Do the math. at the bottom it says 10x+4. that basicly means 10 x 4.
5 0
4 years ago
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