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soldi70 [24.7K]
2 years ago
11

1. What is the slope of the line tangent to the curve defined by y2 + xy - x2 = 11x at the point (2, 3)?

Mathematics
1 answer:
andreyandreev [35.5K]2 years ago
7 0

Step-by-step explanation:

By using Implicit Differentiation,

d/dx (y² + xy - x²) = d/dx (11x)

d/dx (y²) + d/dx (xy) - d/dx (x²) = 11

2y * dy/dx + x * dy/dx + y - 2x = 11

dy/dx (2y + x) = 11 + 2x - y

dy/dx = (11 + 2x - y) / (2y + x).

At the point (2, 3), we have x = 2, y = 3.

=> dy/dx = (11 + 2(2) - (3)) / (2(3) + (2))

= 12 / 8 = 1.5.

P.S. Your question is weird because (2,3) is not on the graph, let me know what is the correct question thanks!

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15
Evgesh-ka [11]

Answer:

Height = 14.4

Step-by-step explanation:

The diagonals meet at right angles. Interesting property.

The hypotenuse is the side of the rhombus = 15 cm

One of the sides of the small triangles created by the intersection of the diagonals = 24/2 = 12

You can find the other side of the the triangle by using the Pythagorean Theorem

a^2 + b^2 = c^2

c = 15

a = 12

b = ?

12^2 + b^2 = 15^2

144 + b^2 = 225

b^2 = 225 - 144

b^2 = 81

b = 9

The area of this right angle = 9 * 12/2 = 54

There are 4 of them so 4 * 54 = 216

That's the area of the rhombus.

The h= Area / b

b = 15

h = 216/15

h = 14.4

8 0
2 years ago
Please anyone can give me it's urgent....​
Pavlova-9 [17]

Step-by-step explanation:

From the figure it is clear that:

x+110°=180

x=180-110

x=70

For y:

the left exterior angle of line q is also70.

By the definition of alternate exterior angle:

y=70

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2 years ago
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3 years ago
The Smith's are building a fence around their rectangular shaped yard. The posts are 2 yards apart. There are 7 posts along the
vovangra [49]

Answer:

Posts: 34

Area:  264 yard²

Step-by-step explanation:

Posts: (7 x 2) + (10 x 2) = 34

Area: 2 x (7 - 1) x 2 x (12 - 1) = 2 x 6 x 2 x 11 = 264 yard²

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3 years ago
Suppose we want to assess the effect of a one-day SAT prep class at a 5% level of significance. Scores on the SAT writing exam c
aalyn [17]

The conclusion is that since the value of 0.028 is less than 0.05 so we reject the null hypothesis at 5% level of significance and conclude that the mean of the difference in SAT writing scores for all students who take SAT prep class is equal to 0.

<h3>What is a null hypothesis?</h3>

A null hypothesis is a hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling error.

Here, the effect of a one-day SAT prep class at a 5% level of significance was assessed.  Since the value of 0.028 is less than 0.05 so we reject the null hypothesis at 5% level of significance and conclude that the mean of the difference in SAT writing scores for all students who take SAT prep class is equal to 0.

Learn more about hypothesis on:

brainly.com/question/11555274

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