(b) Find the coefficient of d in the expansion of $$ (\mathrm{d}-3)(\mathrm{d}+4) $$ (c) If $$ \mathrm{y}=2 \mathrm{x}-5 $$; find the values of y when $$ \mathrm{x}=-2,-1,0,1,2 $$ (a) Find the value of $$ 2 \pi \sqrt{\frac{l}{g}} $$, when $$ \pi=\frac{22}{7}, \mathrm{~L}=49 $$ and $$ g=16 $$

Question

UpStudy AI · Accepted Answer

**(b) Coefficient of $$ d $$ in the expansion of $$(d-3)(d+4)$$:**

1. First, expand the product:
   $$
   (d-3)(d+4) = d \cdot d + d \cdot 4 - 3 \cdot d - 3 \cdot 4
   $$
2. Simplify the expression:
   $$
   = d^2 + 4d - 3d - 12 = d^2 + d - 12
   $$
3. The coefficient of $$ d $$ is $$\boxed{1}$$.

---

**(c) Values of $$ y $$ when $$ y = 2x - 5 $$ for $$ x = -2, -1, 0, 1, 2 $$:**

1. For $$ x = -2 $$:
   $$
   y = 2(-2) - 5 = -4 - 5 = \boxed{-9}
   $$

2. For $$ x = -1 $$:
   $$
   y = 2(-1) - 5 = -2 - 5 = \boxed{-7}
   $$

3. For $$ x = 0 $$:
   $$
   y = 2(0) - 5 = 0 - 5 = \boxed{-5}
   $$

4. For $$ x = 1 $$:
   $$
   y = 2(1) - 5 = 2 - 5 = \boxed{-3}
   $$

5. For $$ x = 2 $$:
   $$
   y = 2(2) - 5 = 4 - 5 = \boxed{-1}
   $$

---

**(a) Value of $$ 2 \pi \sqrt{\frac{l}{g}} $$ for $$\pi = \frac{22}{7}$$, $$ l = 49 $$, and $$ g = 16 $$:**

1. Substitute the given values into the expression:
   $$
   2 \pi \sqrt{\frac{l}{g}} = 2 \times \frac{22}{7} \times \sqrt{\frac{49}{16}}
   $$
2. Evaluate the square root:
   $$
   \sqrt{\frac{49}{16}} = \frac{\sqrt{49}}{\sqrt{16}} = \frac{7}{4}
   $$
3. Now, the expression becomes:
   $$
   2 \times \frac{22}{7} \times \frac{7}{4}
   $$
4. Simplify by canceling the $$ 7 $$ in the numerator and denominator:
   $$
   = 2 \times \frac{22}{4} = 2 \times \frac{11}{2} = \boxed{11}
   $$
**(b) The coefficient of $$ d $$ is 1.** **(c) The values of $$ y $$ are:** - For $$ x = -2 $$: $$ y = -9 $$ - For $$ x = -1 $$: $$ y = -7 $$ - For $$ x = 0 $$: $$ y = -5 $$ - For $$ x = 1 $$: $$ y = -3 $$ - For $$ x = 2 $$: $$ y = -1 $$ **(a) The value of $$ 2 \pi \sqrt{\frac{l}{g}} $$ is 11.**

(b) Find the coefficient of d in the expansion of
© If ; find the values of y when
(a) Find the value of , when and

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Algebra Questions

(b) Find the coefficient of d in the expansion of © If ; find the values of y when (a) Find the value of , when and