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artcher [175]
3 years ago
14

a line passed through the point (8,9) and has a slope of -3/4. write an equation in slope intercept form.

Mathematics
1 answer:
bagirrra123 [75]3 years ago
8 0

Answer:

y = -3/4x + 3

Step-by-step explanation:

y - 9 = -3/4 (x-8)

y-9 = -3/4x -6

y = -3/4x - 6 + 9

y = -3/4x + 3

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Let V be the volume of the solid obtained by rotating about the y-axis the region bounded by y=√x and y=x^2. Find V either by sl
Ede4ka [16]

Answer:

The volume of the solid is 3\pi/10

Step-by-step explanation:

In this case, the washer method seems to be easier and thus, it is the one I will use.

Since the rotation is around the y-axis we need to change de dependency of our variables to have f(x)\rightarrow f(y). Thus, our functions with y as independent variable are:

x=\sqrt{y}\\ x=y^2

For the washer method, we need to find the area function, which is given by:

A=\pi\cdot [(\rm{outer\ radius)^2 -(\rm{inner\ radius)^2 ]

By taking a look at the plot I attached, one can easily see that for a rotation around the y-axis the outer radius is given by the function x=\sqrt{y} and the inner one by x=y^2. Thus, the area function is:

A(y)=\pi\cdot [(\sqrt{y} )^2-(y^2)^2]\\A(y)=\pi\cdot (y-y^4)

Now we just need to integrate. The integration limits are easy to find by just solving the equation \sqrt(y)=y^2, which has two solutions y=0 and y=1. These are then, our integration limits.

V=\pi\int_{0}^1 (y-y^4)dy\\ V=\pi (\int_{0}^1 ydy - \int_{0}^1 y^4dy)\\ V=\pi/2-\pi/5\\\boxed{V=3\pi/10}

3 0
3 years ago
PLS HELP WILL GIVE BRAINLY!!
LenaWriter [7]

Answer:

24.68 gram

Step-by-step explanation:

Given that :

Volume = 182.8 ml

Density of liquid = 0.135 gram/ml

Recall :

Density = mass (g/ml) / volume (ml)

Substitute the value into the equation :

0.135 = mass / 182.8

Mass = 0.135 * 182.8

Mass = 24.678 gram

Hence, weight = 24.678 grams

8 0
2 years ago
Solve. 7 x 3/12 plz answer. and tell me, is it 21/12 ?
finlep [7]
7 *  \frac{3}{12} = \frac{7*3}{12}= \frac{21}{12}
4 0
3 years ago
!!!!HELP PLS!!!! <br><br> WHAT IS:<br><br> 2.039 x 31.5
tatyana61 [14]

Answer:

2039/1000×315/10

642285/10000

=64.2285

7 0
2 years ago
For the graph of an exponential function suppose the y-intercept is negative in the common ratio or is greater than one for this
Mnenie [13.5K]

Answer:

Option (1) increase.

Step-by-step explanation:

Let an exponential function is having common ratio = 3 ( greater than 1) and y-intercept = -1

So the function is,  f(x)=3^{x}-2

Now we prepare a table for the values of x and f(x),

x          -1          0        1        2

f(x)      -1.67     -1        1        7

We find from the table that the values of the function are increasing with the increase in the values of x.

Therefore, Option (1) increase will be the answer.

5 0
3 years ago
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