Ask question

Ask question

All categories

3 years ago

6

beth is putting liquid fertilizer on the plants in 4 flowerpots. Her measuring spoon holds 1/8 teaspoon. the directions say to p

ut 5/8 teaspoon of fertilizer in each pot. how many times will beth need to fill the measuring spoon to fertilize the plants in the 4 pots?

2 answers:

evablogger [386]3 years ago

8 0

Beth neads 4/8 more.hope I helped .good night

leonid [27]3 years ago

7 0

5 times for each pot since 1/8+1/8+1/8+1/8+1/8=5/8 then you do 5/8+5/8+5/8+5/8=2 4/8 or 2 1/2 teaspoon

You might be interested in

HELP MEeeeeeeeee g: R² → R a differentiable function at (0, 0), with g (x, y) = 0 only at the point (x, y) = (0, 0). Consider<im

GrogVix [38]

(a) This follows from the definition for the partial derivative, with the help of some limit properties and a well-known limit.

• Recall that for $f:\mathbb R^2\to\mathbb R$ , we have the partial derivative with respect to $x$ defined as

$\displaystyle \frac{\partial f}{\partial x} = \lim_{h\to0}\frac{f(x+h,y) - f(x,y)}h$

The derivative at (0, 0) is then

$\displaystyle \frac{\partial f}{\partial x}(0,0) = \lim_{h\to0}\frac{f(0+h,0) - f(0,0)}h$

• By definition of $f$ , $f(0,0)=0$ , so

$\displaystyle \frac{\partial f}{\partial x}(0,0) = \lim_{h\to0}\frac{f(h,0)}h = \lim_{h\to0}\frac{\tan^2(g(h,0))}{h\cdot g(h,0)}$

• Expanding the tangent in terms of sine and cosine gives

$\displaystyle \frac{\partial f}{\partial x}(0,0) = \lim_{h\to0}\frac{\sin^2(g(h,0))}{h\cdot g(h,0) \cdot \cos^2(g(h,0))}$

• Introduce a factor of $g(h,0)$ in the numerator, then distribute the limit over the resulting product as

$\displaystyle \frac{\partial f}{\partial x}(0,0) = \lim_{h\to0}\frac{\sin^2(g(h,0))}{g(h,0)^2} \cdot \lim_{h\to0}\frac1{\cos^2(g(h,0))} \cdot \lim_{h\to0}\frac{g(h,0)}h$

• The first limit is 1; recall that for $a\neq0$ , we have

$\displaystyle\lim_{x\to0}\frac{\sin(ax)}{ax}=1$

The second limit is also 1, which should be obvious.

• In the remaining limit, we end up with

$\displaystyle \frac{\partial f}{\partial x}(0,0) = \lim_{h\to0}\frac{g(h,0)}h = \lim_{h\to0}\frac{g(h,0)-g(0,0)}h$

and this is exactly the partial derivative of $g$ with respect to $x$ .

$\displaystyle \frac{\partial f}{\partial x}(0,0) = \lim_{h\to0}\frac{g(h,0)-g(0,0)}h = \frac{\partial g}{\partial x}(0,0)$

For the same reasons shown above,

$\displaystyle \frac{\partial f}{\partial y}(0,0) = \frac{\partial g}{\partial y}(0,0)$

(b) To show that $f$ is differentiable at (0, 0), we first need to show that $f$ is continuous.

• By definition of continuity, we need to show that

$\left|f(x,y)-f(0,0)\right|$

is very small, and that as we move the point $(x,y)$ closer to the origin, $f(x,y)$ converges to $f(0,0)$ .

We have

$\left|f(x,y)-f(0,0)\right| = \left|\dfrac{\tan^2(g(x,y))}{g(x,y)}\right| \\\\ = \left|\dfrac{\sin^2(g(x,y))}{g(x,y)^2}\cdot\dfrac{g(x,y)}{\cos^2(g(x,y))}\right| \\\\ = \left|\dfrac{\sin(g(x,y))}{g(x,y)}\right|^2 \cdot \dfrac{|g(x,y)|}{\cos^2(x,y)}$

The first expression in the product is bounded above by 1, since $|\sin(x)|\le|x|$ for all $x$ . Then as $(x,y)$ approaches the origin,

$\displaystyle\lim_{(x,y)\to(0,0)}\frac{|g(x,y)|}{\cos^2(x,y)} = 0$

So, $f$ is continuous at the origin.

• Now that we have continuity established, we need to show that the derivative exists at (0, 0), which amounts to showing that the rate at which $f(x,y)$ changes as we move the point $(x,y)$ closer to the origin, given by

$\left|\dfrac{f(x,y)-f(0,0)}{\sqrt{x^2+y^2}}\right|,$

approaches 0.

Just like before,

$\left|\dfrac{\tan^2(g(x,y))}{g(x,y)\sqrt{x^2+y^2}}\right| = \left|\dfrac{\sin^2(g(x,y))}{g(x,y)}\right|^2 \cdot \left|\dfrac{g(x,y)}{\cos^2(g(x,y))\sqrt{x^2+y^2}}\right| \\\\ \le \dfrac{|g(x,y)|}{\cos^2(g(x,y))\sqrt{x^2+y^2}}$

and this converges to $g(0,0)=0$ , since differentiability of $g$ means

$\displaystyle \lim_{(x,y)\to(0,0)}\frac{g(x,y)-g(0,0)}{\sqrt{x^2+y^2}}=0$

So, $f$ is differentiable at (0, 0).

3 0

3 years ago

A public library wants to place 4 magazines and 9 books on each display shelf. The expression 4s+9s represents the total number

Bezzdna [24]

Answer: the answer would be s(9+4)

Step-by-step explanation:

8 0

3 years ago

(-1/3) to the power of five?

Bumek [7]

$\bf \left( -\cfrac{1}{3} \right)^5\implies \left( -\cfrac{1}{3} \right)\left( -\cfrac{1}{3} \right)\left( -\cfrac{1}{3} \right)\left( -\cfrac{1}{3} \right)\left( -\cfrac{1}{3} \right)\implies -\cfrac{1^5}{3^5}\implies -\cfrac{1}{243}$

recall minus * minus * minus * minus * minus is minus.

8 0

3 years ago

A cylinder is full at 471 cubic centimeters and has a radius of 5 centimeters. it currently contains 314 centimeters of water.

solniwko [45]

A cylinder is full at 471 cubic centimeters and has a radius of 5 centimeters. it currently contains 314 centimeters of water.
what is the difference between the height of the water in the full cylinder and the height when 314 cubic centimeters of water remains in the cylinder?
use 3.14 for pi
310 cm

6 0

3 years ago

Read 2 more answers

John is six years older than his sister Ella. Three times Ella’s age less two times John’s age is 13?

Vladimir [108]

Answer:

John is 31

Ella is 25

Step-by-step explanation:

Let sister's age be x, then John's age is (x + 6). So from sentence 2,

(3x) - 2(x + 6) = 13

3x - 2x - 12 = 13

x = 13 + 12 = 25

and x + 6 = 31

7 0

2 years ago