Solve each system by graphing: y=-1/2x+2 y=-3/2x-2

What two numbers multiply to -1620 and add to -9

mars1129 [50]

The answer is -45 and 36 because -45+36=-9

5 0

4 years ago

The radius of a right circular cone is increasing at a rate of 1.9 in/s while its height is decreasing at a rate of 2.2 in/s. At

musickatia [10]

Answer:

Volume of the cone is increasing at the rate $9916\pi \frac{in^3}{s}$ .

Step-by-step explanation:

Given: The radius of a right circular cone is increasing at a rate of $1.9$ in/s while its height is decreasing at a rate of $2.2$ in/s.

To find: The rate at which volume of the cone changing when the radius is $134$ in. and the height is $136$ in.

Solution:

We have,

$\frac{dr}{dt} =1.9 \:\text{in/s}$ , $\frac{dh}{dt}=-2.2\:\text{in/s}$ , $r=134 \:\text{in}$ , $h=136\:\text{in}$

Now, let $V$ be the volume of the cone.

So, $V=\frac{1}{3}\pi r^{2}h$

Differentiate with respect to $t$ .

$\frac{dv}{dt} =\frac{1}{3}\pi \left [ r^2\frac{dh}{dt}+h\left ( 2r \right )\frac{dr}{dt} \right ]$

Now, on substituting the values, we get

$\frac{dv}{dt} =\frac{1}{3}\pi\left [ \left ( 134 \right )^2\left ( -2.2 \right )+\left ( 136\right )\left ( 2 \right )\left ( 134 \right )\left ( 1.9 \right ) \right ]$

$\frac{dv}{dt} =\frac{1}{3}\pi\left [ -39503.2+69251.2 \right ]$

$\frac{dv}{dt} =\frac{1}{3}\pi\left [ 29748 \right ]$

$\frac{dv}{dt} =9916\pi \frac{in^3}{s}$

Hence, the volume of the cone is increasing at the rate $9916\pi \frac{in^3}{s}$ .

6 0

3 years ago

Charlie bought a 2 1/2 pound bag of oranges for $3.75. What is the cost of one pound of oranges?

madam [21]

Charlie bought 2.5 lb/pounds of oranges for a total of $3.75

One pound of oranges equals to $1.50

8 0

3 years ago

Evaluate. 2³ ⁺ 4 · 2 ₋ 7 A. 1 B. 5 C. 9 D.36

jonny [76]

Answer:

2³ ⁺ 4 · 2 - 7 = 9

8 + 8 - 7 = 9

Step-by-step explanation:

4 0

4 years ago

A student worked out the following problem to find

polet [3.4K]

We have that

y=x²+3x-5
y=4x+1

using a graph tool
see the attached figure

the solution are the points
(-2,-7)
(3,13)

the solution obtained by the student
(-2,0)
(3,0)
is incorrect because the values of the coordinate y are incorrect
the values of x are correct
x1=-2
x2=3

with those values of x obtained, the student had to substitute it in any of the two equations to obtain the value of y
so
for x=3
y=4x+1------> 4*(3)+1-----> y=13

for x=-2
y=4x+1------> 4*(-2)+1-----> y=-7

7 0

4 years ago