Questions in mathematics

Questions in mathematics

📝 Answered - What is the value of the discriminant for the quadratic equation $-3=-x+2 x$? Discriminant $=b^2-4 a c$

📝 Answered - Graph the circle. [tex]x^2+y^2+2 x-4 y-11=0[/tex]

📝 Answered - The point $P(x, y)$ is on the terminal ray of angle $\theta$. If $\theta$ is between $\pi$ radians and $\frac{3 \pi}{2}$ radians and $\csc \theta=-\frac{5}{2}$, what are the coordinates of $P(x, y)$? A. $P(-\sqrt{21},-2)$ B. $P(\sqrt{21},-2)$ C. $P(-2, \sqrt{21})$ D. $P(-2,-\sqrt{21})$

📝 Answered - The formula [tex]$A=P+P r t$[/tex] represents the value, [tex]$A$[/tex], of an investment of [tex]$P$[/tex] dollars at a yearly simple interest rate, [tex]$r$[/tex], for [tex]$t$[/tex] years. The equation to model the value, [tex]$A$[/tex], of an investment of [tex]$$54$[/tex] at [tex]$9.26 \%$[/tex] for [tex]$t$[/tex] years is given by [tex]$A=54+5 t$[/tex] The equation to model the value, [tex]$A$[/tex], of an investment of [tex]$$84$[/tex] at [tex]$2.38 \%$[/tex] for [tex]$t$[/tex] years is given by [tex]$A=84+2 t .$[/tex] Assuming [tex]$A$[/tex] has the same value, the given equations form a system of two linear equations. Solve this system using an algebraic approach and interpret your answer. a. [tex]$t =5$[/tex] The two investments will reach the same value in 5 years. b. [tex]$t=20$[/tex] The two investments will reach the same value in 20 years. c. [tex]$t =1000$[/tex] The two investments will reach the same value in 1000 years. d. [tex]$t =10$[/tex] The two investments will reach the same value in 10 years.

📝 Answered - Homework Progress 84% 61 / 95 Marks By rounding to 1 significant figure, estimate the answers to these questions: a) $\quad 426 \times 894$ b) $657 \times 889$ c) $287 \times 494$

📝 Answered - In the following expression collect like terms: [tex]$13 p^2+5-4 p+7-10 p^2+6 p-9$[/tex]

📝 Answered - Which expression is equivalent to $\sqrt[3]{\frac{75 a^7 b^4}{40 a^{13} c^9}}$ ? Assume $a \neq 0$ and $c \neq 0$. A. $\frac{a^3 b\left(\sqrt[3]{15 b^2}\right)}{2 c^3}$ B. $\frac{b(\sqrt[3]{15 b})}{2 a^2 c^3}$ C. $\frac{a^3 b\left(\sqrt[3]{15 b^2}\right)}{6 c^3}$

📝 Answered - Evaluate the definite integral: \[ \int_{\sqrt[3]{\log 3}}^{\sqrt[3]{\log 4}} \frac{x^2 \sin(x^3)}{\sin(x^3) + \sin(\log 12 - x^3)} \, dx \]

📝 Answered - The ratio of incomes of Ajith and Sunil last year was 4:5. The ratio of their own incomes of last year and this year are 6:7 and 2:3 respectively. If the total sum of their present incomes is 9636, find the last year income of Ajith. (a) 31680 (b) 33600 (c) 35000 (d) 30720

📝 Answered - Amir has $4,600,000 in his bank account. He decided to divide the amount between his three children, Mustafa, Khalil, and Faisal, in a ratio of 3 : 5 : 6, respectively. How much money is Khalil going to get from his father? A. Approximately $985,714 B. Approximately $1,550,050 C. Approximately $1,598,922 D. Approximately $1,642,857 E. Approximately $1,971,428